Group2_6_ch6

=The Law of Conservation of Energy = toc

Julie, Rachel, and Andrea

**Objective**- Find the relationship between changes in kinetic energy and changes in gravitational potential energy.

Hypothesis: The initial energy of the object should equal the final energy of the object due to the law of conservation of energy which states that energy cannot be created or destroyed. Due to this the initial energy (possibly kinetic or gravitational) must equal the final energy (Kinetic and gravitational).

**Methods and Materials-**

**Station 1**: Drop a cart that holds a plastic piece with a picture of a picket fence down the metal ramp. The cart passes through photogate so we are able to collect the time to calculate the velocity. At this station we also measure the initial and final height of the cart on the ramp with a meter stick. We weighed the mass of the cart. media type="file" key="Movie on 2012-01-31 at 12.54.mov" width="300" height="300"

**Station 2:** Measure the height of the launcher with a meter stick Insert a ball into the horizontal launcher at short range and shoot. The ball will go through photogates so we are able to obtain the time it was in between the gates. We measured the distance between the photogates as well for our velocity. We weighed the mass of the ball. media type="file" key="Movie on 2012-01-31 at 13.00.mov" width="300" height="300"

**Station 3:** A wooden cylinder attached to a string swung through a photogates. We used a meter stick to measure the initial height of the object 20 centimeters above the photogate. We measured the diameter of the cylinder, using this information plus the time that it was in the photogate, to calculate the velocity. We weighed the mass of the cylinder. media type="file" key="Movie on 2012-01-31 at 13.06.mov" width="300" height="300"

**Station 4:** Using a meter stick, we measured the initial height of the ball from the counter to the top of the ramp. We then dropped the metal ball and recorded the height the ball went up to on the other side of the ramp, which we used as our final height. We weighed the mass of the ball. media type="file" key="Movie on 2012-01-31 at 12.53.mov" width="300" height="300"

**Station 5**: We inserted the ball into a vertical launcher on short range. We recorded the time it was in the gate using photogate. We also measured the diameter of the ball using a ruler and weighed the mass of the ball. media type="file" key="Movie on 2012-01-31 at 13.00

<span style="font-family: Tahoma,Geneva,sans-serif;">**Station 6:** We dropped a ball down a roller coaster ramp and measured the initial height using a meter stick. We recorded the time the ball was in the gate at the top of loop. We measured the diameter of the ball and weighed its mass. We also measured its height at the top of the loop. <span style="font-family: Tahoma,Geneva,sans-serif;">media type="file" key="Movie on 2012-01-31 at 13.04.mov" width="300" height="300"

<span style="font-family: Tahoma,Geneva,sans-serif;">**Data Table-** <span style="font-family: Tahoma,Geneva,sans-serif;">

<span style="font-family: Tahoma,Geneva,sans-serif;">**Sample Calculations-** <span style="font-family: Tahoma,Geneva,sans-serif;">

<span style="font-family: Tahoma,Geneva,sans-serif;">**Analysis-**

<span style="font-family: Tahoma,Geneva,sans-serif;">Station1

<span style="display: block; font-family: Tahoma,Geneva,sans-serif; text-align: center;">Station 2

<span style="display: block; font-family: Tahoma,Geneva,sans-serif; text-align: center;">Station3

<span style="display: block; font-family: Tahoma,Geneva,sans-serif; text-align: center;">Station 4 <span style="display: block; font-family: Tahoma,Geneva,sans-serif; text-align: center;">Station 5 <span style="display: block; font-family: Tahoma,Geneva,sans-serif; text-align: center;">Station 6

<span style="font-family: Tahoma,Geneva,sans-serif;">**Conclusion-** <span style="font-family: Tahoma,Geneva,sans-serif;">After calculating the initial and final energy for each station it is seen that our hypothesis was wrong. Even though the initial and final energy is supposed to equal one another our data shows that this is false. This may mean that some of the energy was transformed into something other than kinetic potential energy or gravitational kinetic energy, such as heat. Only the initial and final energy for station 2 equals one another. Our hypothesis energy not being able to be created or destroyed is true due to the laws of physics and thus we can conclude that although our calculations were off no energy was created or destroyed during the experiment. Our percent differences came out to be 12.9%, 39.42%, 49.1%, 13.9%, 5.6%, and 40.9%, for stations 1-6 respectively. Stations 1, 4, and 5 had percent differences less than 20% so the results during these experiments were more accurate. In experiment 6, there was the highest percent difference, which was probably because the ball was dropped down a rollercoaster ramp and the friction, which was not accounted for, affected the energy transfer. To erase this error we could have found a way to calculate friction into the equations and calculate the work at each station or perform the experiments in a frictionless environment. Doing so would decrease the percent difference between the initial and final energy. To decrease the error at stations 2 and 3, we would have to use a more precise meter stick to get more accurate results. This lab can be related to real life situations in various ways. Engineers must take into account all these calculations and how physics works to design roller coasters. Experiments like these must be done to ensure that the theoretical values will match up to those of the experimental.

=<span style="font-family: Tahoma,Geneva,sans-serif;">Law of Conservation of Energy for a Mass on the Spring = <span style="font-family: Tahoma,Geneva,sans-serif;">Molly, Julie, Andrea, and Rachel

<span style="font-family: Tahoma,Geneva,sans-serif;">**Objective:** <span style="font-family: Tahoma,Geneva,sans-serif;">vDetermine the spring constant k of several springs. <span style="font-family: Tahoma,Geneva,sans-serif;">vMeasure the elastic potential energy of the spring. <span style="font-family: Tahoma,Geneva,sans-serif;">vMeasure the gravitational potential and kinetic energy at 3 positions during the spring oscillation.

<span style="font-family: Tahoma,Geneva,sans-serif;">**Hypothesis:**
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Using the given information on the spring box, we can hypothesize that the red spring will have the smallest k value because it is the softest spring, and that the green spring will have the largest k value.

<span style="font-family: Tahoma,Geneva,sans-serif;">**Methods and Materials:** <span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;">Using a balance and rods, we attached four springs by clamps. We added various masses onto the springs and measured the resulting difference in heights with a meter stick. <span style="font-family: Tahoma,Geneva,sans-serif;">media type="file" key="Movie on 2012-02-07 at 13.29.mov" width="300" height="300" <span style="font-family: Tahoma,Geneva,sans-serif;">For the second part of the lab, we added a 0.5 kg mass on the spring, and taped cardboard to the bottom so that the surface was larger. Thus, it would be easier for the motion sensor underneath the spring to detect movement.

<span style="font-family: Tahoma,Geneva,sans-serif;">**Data Tables and Graphs:** <span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;">

<span style="font-family: Tahoma,Geneva,sans-serif;">**Class Data:** <span style="font-family: Tahoma,Geneva,sans-serif;">

<span style="font-family: Tahoma,Geneva,sans-serif;">**Percent Error:** <span style="display: block; font-family: Tahoma,Geneva,sans-serif; text-align: center;">Red

<span style="display: block; font-family: Tahoma,Geneva,sans-serif; text-align: center;">Blue

<span style="display: block; font-family: Tahoma,Geneva,sans-serif; text-align: center;">White

<span style="font-family: Tahoma,Geneva,sans-serif;">Green

<span style="font-family: Tahoma,Geneva,sans-serif;">**Percent Difference:** <span style="display: block; font-family: Tahoma,Geneva,sans-serif; text-align: center;">**Green**

<span style="display: block; font-family: Tahoma,Geneva,sans-serif; text-align: center;">**Red**

<span style="display: block; font-family: Tahoma,Geneva,sans-serif; text-align: center;">**White**

<span style="display: block; font-family: Tahoma,Geneva,sans-serif; text-align: center;">**Blue** <span style="font-family: Tahoma,Geneva,sans-serif;">

<span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;">**Percent Difference**

<span style="font-family: Tahoma,Geneva,sans-serif;">**Discussion Questions:** > 1. When the hanging mass starts at rest the only force acting upon it is GPE. Then when it is stretched there is only EPE. Then when it is released and moving then their is KE+EPE.
 * 1) <span style="font-family: Tahoma,Geneva,sans-serif;">Do the data for the displacement of the spring versus the applied force indicate that the data for the spring constant is indeed constant for this range of forces?
 * 2) Yes, because the data shows a linear form we can conclude the force of the spring and the displacement are directly proportional and that the spring constant remains constant no matter what the displacement it.
 * 3) <span style="font-family: Tahoma,Geneva,sans-serif;">How can you tell which spring is softer by merely looking at the graph?Describe the changes in energy of the hanging mass, beginning with it starting at rest, you pulling the mass down and then releasing it, and then the mass cycling through one complete period. Describe the changes in energy of the hanging mass, beginning with it starting at rest, you pulling the mass down and then releasing it, and then the mass cycling through one complete period.
 * 1) We know that the smaller the spring force constant the softer the spring is, so by looking at the slope of the graph(which represents k) we can see that the spring with the smallest slope would be the softest, which in this experiment was the red spring.

<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 16px; line-height: 24px;"> <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 16px; line-height: 24px;"> <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 16px; line-height: 24px;"> <span style="font-family: Tahoma,Geneva,sans-serif; font-size: 16px; line-height: 24px;">

<span style="font-family: Tahoma,Geneva,sans-serif;">**Analysis:** <span style="font-family: Tahoma,Geneva,sans-serif;">Conclusion <span style="font-family: Tahoma,Geneva,sans-serif;">After testing and calculating all the different spring force values of all the springs, we found our hypothesis to be true. The Red spring had the smallest k value and the green spring had the biggest k value. Our results were that k for the red spring was 25.769, for the blue we got 30.301, for the white we got 43.458, and for the green we got 50.905. Through our experiment and these results we see that our claim was true.We had to find percent error and percent difference for all of the springs. Our results seemed to be good because our results were very close with the class results and the actual results. The highest percent error we got was 8.64% for both the white and green spring. For the red spring we got a percent of 3.07% and then for the blue we got a percent error of 1.003%. With our percent difference with the class the highest percent difference we got was 7.26% for the white spring. Then for the green spring we got .686% difference, for the red spring we got .406% difference, and for the blue spring we got .876%. After looking at all the percentages, we can conclude that over all our results were good because our error was small. There may have been error when we were measuring the distance that the spring stretched. This is because our results may not have been precise and when we were measuring the spring we may have pulled on the spring by accident making the distance the spring stretched bigger than it actually was. We also found the total energy of the red spring at three different point, the maximum, minimum, and equilibrium. The total energy for when the spring was at a maximum 1.42J. When it was at equilibrium the total energy was 1.31J. Lastly, the total energy for the minimum was 1.35J. After finding all of these total energies we proceed by finding the percent difference of each of the places. The greatest percent difference was 6.5% at the minimum, the least was 0.4% was at equilibrium, and the last one was at the maximum with a percent error of 6.10%. We see through this that our percent error was not that high and so we can conclude that our total energies were very close to one another. These values may not be equal because when you have a spring it looses energy after it moves. Another source of error may be because the spring may not have been right above the motion detector. The lab could be fixed by using a more stable ruler to ensure that the measurements are correct. Also, we could have ensured that the red spring was right above the motion detector for better results. This can relate to many situations in real life. One Real life scenario may be bungee jumping. In order to ensure safety among all the people that jump off bridges the company would need to know the amount of weight that a spring can withstand. They would need to know the spring force constant to figure out the maximum weight that the spring can gold and the maximum amount that the spring can be stretched.To make sure that jumping is safe for the client the company would need to test these thing and find the answers.

<span style="color: #000000; font-family: Tahoma,Geneva,sans-serif;">Roller Coaster Project
<span style="color: #000000; font-family: Tahoma,Geneva,sans-serif;">Julie, Molly, Rachel, and Andrea

<span style="display: block; font-family: Tahoma,Geneva,sans-serif; text-align: center;">INTRODUCING THE NEWEST AND MOST THRILLING ROLLER COASTER SWEEPING THE NATION - <span style="display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 140%; text-align: center;">** LOVE //BURNS// ** <span style="font-family: Tahoma,Geneva,sans-serif;">**Discussion of Concepts:** <span style="font-family: Tahoma,Geneva,sans-serif;">Our knowledge of the Energy conservation Law states that, theoretically, the total amount of energy should remain constant throughout the length of the whole roller coaster. However, when doing our calculations for the total energy, we ignore friction and air resistance, which are both types of work acting against the coaster. Because we ignore these, instead of the total energy remaining constant throughout, as the law states, we see it gradually decreases from start to finish. In order for the total energy to remain constant throughout, we would have to create a frictionless track. Newtons laws of motion are applied to our roller coaster in various ways. The first law states that an object in motion will remain in motion unless acted upon by an opposing force. This is seen how the marble on our roller coaster will stay in motion until the end of the ride when the theoretical spring forces it to stop. Due to the fact that there was friction on the track, the velocity of the marble was not constant due this outside force. Not only does out coaster demonstrate Newtons first law, it also incorporates his second and third laws. Because of Second Newton's Laws, we know that that there is going to be a coefficient of friction between the track and the ball, no matter how low it is. Work is defined a force that cause a displacement, so in this case friction can be considered work, in this case negative work, because it is opposing the motion of the ball, causing a displacement. Throughout the course of the roller coaster, this work is gradually slowing the ball down, decreasing both the velocity and the acceleration. Newton's second law also explains how unbalance forces causes acceleration. In our roller coaster this is seen as the marble travels down the incline as friction, normal force and the force of gravity will act upon the marble creating a net force which accelerates the marble. Newton's third law states that every action has an equal and opposite reaction. This is seen in our roller coaster at every point. In order for the marble to stay in contact with the track there must be a force pushing down on the track from the marble and an equal opposite force of the track pushing up on the marble. This will hold true when the roller coaster is actually built, as the people will exert a force on the cart and the cart will exert a force on the people allowing them to stay in the cart and not fall out. Acceleration is the change in velocity over time and is needed to ensure that the ball will be able to make it over the hills, through the loops, and around the turns. In finding the acceleration at the different points we began by using kinematics and the equation V f 2 =V i 2 +2ad. We did this by choosing the point at which we were finding the acceleration, then we measure equidistant away from that point in both directions and found what the balls velocity was at those points. For example, minimum velocity at the top of a loop was able to be found by using Newton's second law and the properties of centripetal forces. Here both the normal force and weight were pointing toward the center of the circle, and normal was zero, so the equation become N+w=ma and then mg=ma. Because this is circular motion, acceleration is equal to V 2 /r. Here we plugged in the radius of the loop (.063m) and the masses cancel out to give us the minimum velocity (.7857m/s) which was needed to get around the loop. Power, is the rate at which work happens, so it measures how long it takes something to be displaced. In order for the cart to reach the top of the roller coaster, there must be a power source to supply the energy. We created a hypothetical time that was realistic for the cart to approach the incline, which was 30 seconds. Using the equation, P = w/t, in which work in this situation was gravitational potential energy, since there is a change in height, we were able to calculate the power necessary to start the coaster. We used the height of the starting point (.659 m), the mass of the ball (.028 kg), and the acceleration due to gravity (9.8 m/s/s), along with the theoretical 30 seconds to come up with .00603 watts of power. When the cart is on the roller coaster, there are two forces acting on it - the gravitational force from the Earth (weight) and the contact force of the track on the cart (normal force). At the top of a hill, the normal force is equal to zero, which is why people feel weightless because there is no apparent weight. While on the bottom of the hill, the free body diagram would show that the normal force points upwards towards the center of the circle, so in this situation the normal force is greater than weight, which points down on the FBD. Therefore, a person would feel heavier at the bottom of the hill because the apparent weight is larger than the gravitational force. Hooke's law is used when a spring is at equilibrium. The equation for this law is F= kx, so the force exerted by the spring is equal to the spring force constant times the distance of the spring. Since our spring is not at equilibrium we would not use Hooke's law, instead we used kinematics and the equation <span style="font-family: Tahoma,Geneva,sans-serif;">V f 2 =V i 2 +2ad. We knew the final velocity was zero and by using our calculations we found our initial velocity to be 3.45 m/s and then used -9.8 as the acceleration. With this we found the distance needed to stop to be .607m. Then after finding this value we used the law of conservation of energy the spring force constant. We used the equation KE=GPE by plugging 3.45m/s in for velocity and the distance found in the previous equation for x, which is .607m. After doing all of the calculations we found the spring force constant,k, to be equal to .905 N/m.

<span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;">media type="file" key="Movie on 2012-02-17 at 13.05.mov" width="300" height="300"

<span style="font-family: Tahoma,Geneva,sans-serif;">Loop and free body diagram <span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;">

<span style="color: #000000; font-family: Tahoma,Geneva,sans-serif;">**Safety:**
 * <span style="font-family: Tahoma,Geneva,sans-serif;">We are sure that this roller coaster is safe because we have calculated the physics needed to make this work and tested it multiple times. By starting at the minimum height required in order for the roller coaster to have the velocity to make it until the end without stopping, we have ensured that it will not get stuck making it up a hill or going around the vertical loop. Also, we have ensured that it will reach the minimum velocity necessary to make it around the vertical loop. Throughout the roller coaster, we have made sure that the maximum acceleration that will be experienced by its passenger will never be greater then 4 g's and that it is greater then 1 g while going around the vertical loop. By adding a spring at the end and other brakes, we will ensure that the roller coaster comes to a safe stop without jerking around the passengers. However, the roller coaster is unsafe after the first drop because the ball bounces off the track. In reality, the cart would not be on the track, thus this area would be dangerous.
 * <span style="font-family: Tahoma,Geneva,sans-serif;">There are various sources of error that would have affected our results. The measurements using a ruler were not exact and therefore our calculated GPE could be off. When using the photogate to capture the time the ball spent in the gate, the time varied each trial, showing the inaccuracy of these devices with this experiment and leading to not exact velocities at given areas. The paper used to construct the roller coaster is very flimsy and not sturdy, causing a great amount of energy loss when the ball travels down the track. This is why there is a great percent error because our theoretical and experimental results for the velocities. Friction was not accounted for in the calculations, however that is not realistic because the ball against the paper creates friction and makes the velocity lower. This is yet another reason the velocities were not correct. If designers find that in their calculations their velocity isn't large enough to make it around the vertical loop then they may either increase the height of the hill or decrease the radius of the loop to ensure the roller coaster would safely make it through. Just incase there is an emergency, a back up break would be built in the roller coaster and different sensors would ensure that the correct velocities are kept at all times so that nothing can go wrong. In a real roller coaster friction and air pressure would need to be accounted for to ensure safety.
 * <span style="font-family: Tahoma,Geneva,sans-serif;">To improve this roller coaster, a different material would need to be used that is both thick and pliable. By having another material, it would be better for the photogate devices and the time trials would be more consistent. More supports would have also helped to make the track more stable and the data analysis easier. We would have also constructed the vertical loop after the initial drop so that there would be a higher velocity to ensure better safety.
 * <span style="font-family: Tahoma,Geneva,sans-serif;">This roller coaster is just a model of what it would be in real life, due to this everything would be multiplied by a factor of 1000.

<span style="font-family: Tahoma,Geneva,sans-serif;">** Data Tables: **

<span style="color: #000000; font-family: Tahoma,Geneva,sans-serif;">**Theoretical** <span style="color: #000000; font-family: Tahoma,Geneva,sans-serif;"> <span style="color: #000000; font-family: Tahoma,Geneva,sans-serif;">**Actual** <span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;">**Percent Error** <span style="font-family: Tahoma,Geneva,sans-serif;">

<span style="font-family: Tahoma,Geneva,sans-serif;">Excel speadsheet <span style="font-family: Tahoma,Geneva,sans-serif;">

<span style="color: #000000; font-family: Tahoma,Geneva,sans-serif;">**Sample Calculations:**

<span style="display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">**//Actual Velocity//**

<span style="display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">**//Theoretical Velocity//** <span style="display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">**//Total Energy//**

<span style="display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">**//Kinetic Energy//**

<span style="display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">**//Gravitational Potential Energy//**

<span style="display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">**//Minimum Height at First Hill//**

<span style="display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">**//Minimum Velocity at Top of Vertical Loop//**

<span style="display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">**//Power Required For Roller Coaster To Get Rolling//** <span style="display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 130%; text-align: center;">//**Percent Error**//

<span style="display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">//** Energy Disipated **//

<span style="display: block; font-family: Tahoma,Geneva,sans-serif; font-size: 120%; text-align: center;">//** Elastic Potential Energy for Theoretical Spring **//

<span style="display: block; font-family: Tahoma,Geneva,sans-serif; text-align: center;">Lab: Elastic and Inelastic Collisions <span style="font-family: Tahoma,Geneva,sans-serif;">**Objectives:** <span style="font-family: Tahoma,Geneva,sans-serif;">**Hypothesis:**
 * <span style="font-family: Tahoma,Geneva,sans-serif;">What is the relationship between initial momentum and final momentum of a system?
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Which collisions are elastic collisions and which ones are inelastic collisions?
 * <span style="font-family: Tahoma,Geneva,sans-serif;">The total initial momentum will equal the final momentum of the system.
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Elastic collisions conserve kinetic energy, while inelastic collisions do not.

<span style="font-family: Tahoma,Geneva,sans-serif;">**Materials and Methods:**
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Two carts were placed on a dynamic track with a motion sensor on each end of the track. USB links were connected to the computers so we could use data studio to collect our velocities. Different collision scenarios were used and repeated multiple times with different masses.

<span style="font-family: Tahoma,Geneva,sans-serif;">Picture of setup: <span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;">We set up a ramp with motion detectors on both sides.

<span style="font-family: Tahoma,Geneva,sans-serif;">**Data Tables:** <span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;">

<span style="font-family: Tahoma,Geneva,sans-serif;">**Sample Calculations** <span style="font-family: Tahoma,Geneva,sans-serif;">

<span style="font-family: Tahoma,Geneva,sans-serif;">**Analysis:**
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Is momentum conserved in this experiment? Explain using actual data from the lab.
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Momentum is conserved in all of the different experiments with the carts because the initial momentum and the final momentum are very close. Because no momentum is lost form start to finish we can tell the it was conserved. In the head on collision the initial momentum was .148 and the final momentum was .147, with a .128% difference. Because this difference is so minute we can conclude that the momentum was conserved.
 * <span style="font-family: Tahoma,Geneva,sans-serif;">When carts of unequal masses push away from each other, which cart has a higher velocity? Explain why this is.
 * <span style="font-family: Tahoma,Geneva,sans-serif;">When the carts push away from each other, the one with the smaller mass has the higher velocity. This is because when the cart with more mass pushes against the cart with the smaller mass, the force exerted upon the smaller one is greater then that exerted on the larger one.
 * <span style="font-family: Tahoma,Geneva,sans-serif;">When carts of unequal masses push away from each other, which cart has more momentum?
 * <span style="font-family: Tahoma,Geneva,sans-serif;">The cart with the larger mass would have a greater velocity because momentum equals mass times velocity, so the greater the mass, the larger the momentum.
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Is the momentum dependent on which cart has its plunger cocked? Explain why or why not.
 * <span style="font-family: Tahoma,Geneva,sans-serif;">No the momentum is not dependent on which cart has the plunger cocked. We knew that newton's third law states that ever action has an equal and opposite reaction. Due to this the forces on both the carts are the same. The other reason is due to the equation for momentum P=mv. When you look at the chart and the results that we get we see the momentums for both carts are mostly equivalent. This is because as the mass of one of the carts increased it velocity decrease. The momentum of both carts are mostly the same, the only difference is that one is going in a positive direction and the other one is negative.

<span style="font-family: Tahoma,Geneva,sans-serif;">**Conclusion** <span style="font-family: Tahoma,Geneva,sans-serif;">After collecting all of our data and comparing it we found that our hypothesis was partly correct. By looking at all of the elastic collision experiments we saw that the initial momentum does in fact equal our final momentum. This is because the momentum's turned out to be similar if not the same initially as they were in the end. However for the inelastic collisions, the initial and the final momentum did not turn out to be equal.This is because when a explosion occurs the initial momentum is 0 while the final is not. Due to this the percent error would be very high, which we found to be true. Our hypothesis that elastic collisions would conserve energy while the inelastic would not proved to be correct. The initial and final KE in the elastic potential experiments only differed by less then 10%, while the inelastic differed by over 200%. Here we can see that energy was in fact conserved when the collisions were elastic because the difference was so minute. The large percent difference between the inelastic collision leads us to the conclusion that energy was not, in fact, conserved throughout the experiment. <span style="font-family: Tahoma,Geneva,sans-serif;">In this lab we had a very low percent difference meaning that there was not a lot of error that could have greatly altered the results. Not including the inelastic collision, our largest percent difference was 9.13% which leads us to conclude that are results are pretty accurate. This shows that our hypothesis is right that energy has been conserved. Even though we got 200% error for the explosion, this seems to be what we were supposed to get. Inelastic experiment are supposed to get high percent errors and as you can see we got a very large number. In an elastic collision the energy is conserved so the initial and final momentums should be relatively close. With having this low percent error we are able to conclude our experiment turned out successful and that the energy was conserved throughout the crash. In and inelastic collision the energy is not conserved and this is why the percent error is so high. The initial velocity is 0 and since it is so low, what ever final velocity that the cart would have would lead to a larger momentum. Though it may seem as though our result are off due to the high percent error, this actually shows that our experiment was good and had good results. We saw that our results are also good due to the low percent error seen in all of the elastic collisions trials. <span style="font-family: Tahoma,Geneva,sans-serif;">In order to make this lab more accurate we would have changed a few things to ensure that the momentum's would be the same. First of all, we would have made sure the track was as frictionless as possible to ensure that didn't have any effect on our results. Also, we would have used a leveling tool to make sure that the track was as balanced as possible so that too didn't change or alter our results in any way. We could have read the data on the computer wrong by choosing the wrong points. This would lead to false data and could be a reason why our momentum;s aren't exactly equal. So in order to fix this we would need to understand the graph being made on the computer from the collision and be able to choose the right points. Another source of error may have been if something got caught in front of the senors. At one point in the lab we by accidentally suck our hand in front of the senor so instead of it calculating the carts velocity, it was calculating the velocity of our hand. In order for this to not happen we would have to ensure that nothing in near or in the way of the sensors to make sure that it is collecting good and accurate data. In everyday life, elastic and inelastic collisions are seen everywhere. This can range from two trains having a head on collision to a car bumping to another car that is at rest. This may be used to make cars safe. Car companies may test car crashes to try to make the impact and the force less so that the people inside the car aren't injured. This is also seen when something explodes and the contents of that object shoots out in all different directions.

=<span style="font-family: Tahoma,Geneva,sans-serif;">Ballistic Pendulum Lab = Rachel, Julie, Molly, and Andrea

<span style="font-family: Tahoma,Geneva,sans-serif; font-size: 14px;">**Objective:** What is the initial speed of a ball fired into a ballistic pendulum?

<span style="font-family: Tahoma,Geneva,sans-serif;">** Hypothesis: ** We hypothesize that the initial speed of the ball will be relatively similar for the three different ways we used to find it. Of the three, the photo gate will be the most accurate and the technique using the law of conservation of momentum will be the least. This is because the most energy is lost in the collision.

<span style="font-family: Tahoma,Geneva,sans-serif;">** Methods and Materials :** <span style="font-family: Tahoma,Geneva,sans-serif;">We started by taking the horizontal launcher and clamping it to the table so that it would not move. After that we started off by trying to find the velocity by using kinematics. For this we used a ruler and measured the height to the launcher. Then we taped down carbon paper to the floor and shot the ball at low range. We did this 5 times and after we measured the distance from the dot on the paper to the horizontal launcher and took an average of our measurements. Once this was done we were able to find the velocity. The second way we found initial velocity was by using s a photo-gate timer. We placed it right after the end of the horizontal launcher and then hooked it up to the computer and found the time in gate. Once we did this we took a ruler to measure the diameter of the ball so we were able to find the initial velocity. We repeated this 5 times. Lastly, we found the initial velocity by using Energy conservation and the Law of conservation of momentum. We launched the ball into the Ballistic pendulum and then looked to see what angle it made at the highest point. We did this 5 times and then used the information found to find initial velocity.

<span style="font-family: Tahoma,Geneva,sans-serif;">**Videos:** <span style="font-family: Tahoma,Geneva,sans-serif;">Kinematics <span style="font-family: Tahoma,Geneva,sans-serif;">media type="file" key="Movie on 2012-03-13 at 12.53.mov" width="300" height="300" <span style="font-family: Tahoma,Geneva,sans-serif;">Photogate Timer <span style="font-family: Tahoma,Geneva,sans-serif;">media type="file" key="Movie on 2012-03-13 at 13.08.mov" width="300" height="300"

<span style="font-family: Tahoma,Geneva,sans-serif;">Law of Conservation of Momentum

<span style="font-family: Tahoma,Geneva,sans-serif;">**Data Tables-** <span style="font-family: Tahoma,Geneva,sans-serif;">Photo Gate Timer <span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;">Kinematics <span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;">Law of Conservation of Momentum <span style="font-family: Tahoma,Geneva,sans-serif;"> Percent Difference

<span style="font-family: Tahoma,Geneva,sans-serif;">**Sample Calculations-** <span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;"> <span style="font-family: Tahoma,Geneva,sans-serif;">

<span style="font-family: Tahoma,Geneva,sans-serif;">**Analysis-**
 * 1) <span style="font-family: Tahoma,Geneva,sans-serif;">In general, what kind of collision conserves kinetic energy? What kind doesn’t? What kind results in maximum loss of kinetic energy?
 * <span style="font-family: Tahoma,Geneva,sans-serif;">In general, an elastic collision conserves energy. Inelastic collisions do not. A perfectly inelastic collision results in the maximum loss of kinetic energy.
 * 1) <span style="font-family: Tahoma,Geneva,sans-serif;">Consider the collision between the ball and pendulum.


 * Is it elastic or inelastic?
 * It is inelastic
 * Is energy conserved?
 * Because the collision is inelastic, energy is not conserved.
 * Is momentum conserved?
 * Momentum is conserved as the law of the conservation of momentum was able to be used in the collision.
 * 1) <span style="font-family: Tahoma,Geneva,sans-serif;">Consider the swing and rise of the pendulum and embedded ball.
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Is energy conserved from the moment just before the ball strikes the pendulum to the moment the pendulum rises to its maximum height?
 * <span style="font-family: Tahoma,Geneva,sans-serif;">The energy is not conserved as this collision is inelastic and the ball sticks to the pendulum so some some kinetic energy is lost.
 * <span style="font-family: Tahoma,Geneva,sans-serif;">How about momentum?
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Momentum is always conserved because LCM applies to all collisions.
 * 1) <span style="font-family: Tahoma,Geneva,sans-serif;">It would greatly simplify the calculations if kinetic energy were conserved in the collision between ball and pendulum.
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Calculate the loss in kinetic energy as the difference between the kinetic energy before and immediately after the collision between ball and pendulum.
 * [[image:Screen_shot_2012-03-17_at_10.46.53_AM.png width="192" height="119"]]
 * [[image:Screen_shot_2012-03-17_at_10.49.11_AM.png]]
 * <span style="font-family: Tahoma,Geneva,sans-serif;">What is the percentage loss in kinetic energy? Find by dividing the loss by the original kinetic energy.
 * <span style="font-family: Tahoma,Geneva,sans-serif;">[[image:Screen_shot_2012-03-17_at_10.51.05_AM.png width="264" height="143"]]
 * 1) <span style="font-family: Tahoma,Geneva,sans-serif;">According to your calculations, would it be valid to assume that energy was conserved in that collision?
 * It would not be valid to assume energy was conserved because as we can see if we look above, energy was lost throughout the experiment.This is due to that fact that the collision was inelastic, which means the kinetic energy was not conserved.
 * <span style="color: #ff0000; font-family: Tahoma,Geneva,sans-serif;">Calculate the ratio M/(m+M). Compare this ratio with the ratio calculated in part (b). Theoretically, these two ratios should be the same. State the level of agreement for these two quantities for your data.?????
 * <span style="color: #ff0000; font-family: Tahoma,Geneva,sans-serif;">[[image:Screen_shot_2012-03-17_at_1.54.06_PM.png]]


 * 1) <span style="font-family: Tahoma,Geneva,sans-serif;">Go to [] Select “Ballistic Pendulum” from the column on the left. What is the effect of increasing the mass of the ball? What is the effect of increasing the pendulum mass? Try it. (NOTE: You have to read “Student Notes” first before you can run the simulation.)
 * Increasing the mass of the ball increases final height of the pendulum as well as theta between the original and final positions of the pendulum. Increasing the mass of the pendulum, however, decreases the final height of the pendulum as well as theta between the original and final positions of the pendulum. The larger the mass of the ball the higher the pendulum goes, but the larger the mass of the pendulum the lower the pendulum goes.


 * 1) <span style="font-family: Tahoma,Geneva,sans-serif;">Is there a significant difference between the three calculated values of velocity? What factors would increase the difference between these results? How would you build a ballistic pendulum so that momentum method gave better results?
 * 2) <span style="font-family: Tahoma,Geneva,sans-serif;">There is not a significance between the three calculated velocities as we can observe by looking at the percent differences. The largest percent difference was 7.4% which is not very high. Of these techniques, the photogate would be the most accurate because it precisely measures the velocity right after launching the projectile. Of the experiments, we found the kinematics one to be the most different from the actual velocity, which is strange considering that there should not be a tremendous loss in energy that we observed from our calculations. We can conclude that inaccurate measurements may have been the factor reasonable for slightly skewing our results. As we know, the spring for these launchers are not the most consistent, which could have also led to minute difference between these velocities. Being that air resistance does effect the results and it wasn't taken into account while doing the calculations, it could have been another factor that increased the difference between results. If we were to build a ballistic pendulum we would have tried to use a projectile with minimum air resistance so we could at least rule one factor out that could be effecting our results in any way.

<span style="font-family: Tahoma,Geneva,sans-serif;">**Conclusion-** <span style="font-family: Tahoma,Geneva,sans-serif;">Our hypothesis stated that we thought the initial speed on the ball for each different trial would be the same. This seemed to be true as our data wasn't that far off, but the were still different and not exactly the same. We found the initial velocity three different ways. First we used kinematics and launched the ball horizontally, then we used a photogate which told us the initial velocity, and lastly we found it using a ballistic pendulum. When using kinematics we found the initial velocity to be 2.06 m/s, but this should have been the part of the experiment with the greatest velocity. When using the photogate timer we got a initial velocity of 2.394m/s. When we used the ballistic pendulum we got a speed of 2.2m/s. In our hypothesis we said that when using law of conservation of energy that would be the least accurate compared to the photogate, but we found that when we used kinematics that had the least accurate results.Our hypothesis was somewhat right. We predicted that the data would be close, but the accuracy of our results may be off. The highest percent difference that we got was around 7%, which is pretty good because it means that our data was relatively close to one another. The part of the experiment where we had the most error was within our trials was when we usedd kinematics. When using the ballistic pendulum, we go the smallest percent difference of 1.79% and lastly when we used a photogate we got 5.6%. Since these percents are relatively small we can conclude that our data was good. In order for the data to be even more consistent and closer we could have done more than 5 trials for each part of the experiment. The launcher may not be consistent when it launched the ball each time so that may have caused all the difference in velocities. Error could have occurred in each different part of the experiment. When using kinematics, we may have measured the horizontal and vertical distances badly so that may be a factor to why our data is off for that one. When using the photogate it was hard to get it to stand up completely straight this may have lead to the time of the ball in the gate to be longer and we may have measured the diameter of the ball wrong. To fix this we should make sure that the photo-gate is completely straight and have more than one person measure each thing to ensure that our measurements are right. There isn't much error that could have occurred with the ballistic pendulum. When doing the trials it seemed pretty consistent, each time giving us the same angle. Overall, our results were pretty good and consistent with what they should have been. The only problem we had was with the part of the experiment when we used kinematics. This should have had the greatest initial velocity, but instead it had the smallest. This may have been due to our measurements and that we could have been off. We looked over our work to get the initial velocity and we did everything correctly so the most likely possibility to why our data is off is because we measured the distances wrong. Inelastic collisions are very common in real life, but the ballistic pendulum is not very commonly seen. The ball being launched can be compared to a cannon ball being launched. The pendulum part of the experiment can be compared to a clock or a swing. But in real life these two things are not seen occurring together. Because the ballistic pendulum is an inelastic collision, it can be seen in car crashes and physics can be used to determine who caused the accident and what circumstances must have been present for it to occur.

= Collisions with Hover Pucks =


 * 1) Determine the type of collision.

a.Calculate the loss in kinetic energy as the difference between the kinetic energy before and immediately after the collision.


 * Theoretical Velocities**

b.What is the percentage loss in kinetic energy? Find by dividing the loss by the original kinetic energy.

This collision turned out to be an inelastic collision. This is because when comparing the initial and final velocities they are different. Since the energy was not the same we were able to conclude the experiment was an inelastic collision.
 * 1) What type of collision is this? Explain.




 * 1) Error:

a.What assumptions did we make that may affect our results? We had to assume that before and after the collisions the pucks were moving at constant speed and that the ground was completely fricitonless because we didn't take it into account in our calculations.

b.How would you change this activity to address these issues? Many issues may have occurred that was due to human error. When using the stop watch it is hard to press the button the exact time the collision occurred and the exact time that it hit the wall, this may have caused for our velocities to be a little off. Another source of error may have been our measuring. We may have measured the distance that the pucks traveled wrong or may have even measured our angles wrong which would have lead to bad results. Other than human error there isn't much that could have gone wrong with the experiment.