Group4_6_ch6

Chapter 6, Group 4: Lindsay Marella, Sarah Gordon, Katie Dooman toc

=3/13 Ballistic Pendulum Lab=

What is the initial speed of a ball fired into a ballistic pendulum? The initial speed of a ball fired into the ballistic pendulum is going to be about 4 m/s. We got this from our "ball in the cup" lab when we found the initial velocity in the past.
 * Objectives:**
 * Hypothesis:**

First off, we found the initial velocity of a metal ball using kinematics. We shot the ball, at medium speed, from a launcher, clamped to the table to keep it steady, so it hit carbon paper we put on the ground. We measured the distance from the launcher to each dot and used that data to make our calculations. Next, we found the velocity by using a ballistic pendulum. We attached the ballistic pendulum to the launcher. We launched the ball, again at medium speed, into the ballistic pendulum and recorded the maximum angle achieved by the pendulum. We repeated this step and collected multiple angle measures. Lastly, we found the initial velocity of the ball using a photogate timer and Data Studio. We launched the ball at medium speed through the photogate timer and Data Studio recorded its velocity, which was easy for us to understand.
 * Methods and Materials:**


 * Pictures:**

loljk
 * Video:**


 * Data:**


 * Sample Calculations:**

1) In general, what kind of collision conserves kinetic energy? What kind doesn’t? What kind results in maximum loss of kinetic energy?
 * Discussion/Analysis Questions:**

2) Consider the collision between the ball and pendulum. a. Is it elastic or inelastic? b. Is energy conserved? c. Is momentum conserved?

3) Consider the swing and rise of the pendulum and embedded ball. a.Is energy conserved from the moment just before the ball strikes the pendulum to the moment the pendulum rises to its maximum height? b.How about momentum?

4) It would greatly simplify the calculations if kinetic energy were conserved in the collision between ball and pendulum. a.Calculate the loss in kinetic energy as the difference between the kinetic energy before and immediately after the collision between ball and pendulum. b.What is the percentage loss in kinetic energy? Find by dividing the loss by the original kinetic energy.

5) According to your calculations, would it be valid to assume that energy was conserved in that collision? a.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.


 * 1) 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.)

<span style="font-family: Arial,Helvetica,sans-serif;">6) 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?

<span style="font-family: Arial,Helvetica,sans-serif;">**Conclusion:**

=3/6 Elastic and Inelastic Collisions Lab=

-What is the relationship between the initial momentum and final momentum of a system? -Which collisions are elastic collisions and which ones are inelastic collisions?
 * Objectives:**

-The final momentum will be less than the initial momentum. -Elastic collisions have initial and/or final velocity. Inelastic collision does not concern kinetic energy.
 * Hypothesis:**

We set up two motion detectors on each end of a ramp and used two carts to perform whichever collision we were experimenting with.
 * Methods and Materials:**


 * Pictures:**

Cart A
 * Data:**

Cart B:

Data Table:


 * Analysis Questions:**
 * 1) Is momentum conserved in this experiment? Explain, using actual data from the lab. Momentum is conserved in the elastic collisions, which are the collisions where the momentums are very similar and yield a very low percent error. For example, for the first cart the initial momentum was .235 kgm/s and final momentum was .215 which is fairly close.
 * 2) When carts of unequal masses push away from each other, which cart has a higher velocity? Explain why this is.The lighter one because mv=mv. if the mass of the fist cart is 100kg and the other is 50 and we set the velocity of the first car to 1 m/s, the velocity of the smaller cart would have to be 2 m/s, thus it will be going faster.
 * 3) When carts of unequal masses push away from each other, which cart has more momentum? As seen in the explosion collision, their momentum is equal because the mass times the change in velocity will be equal.
 * 4) Is the momentum dependent on which cart has its plunger cocked? Explain why or why. No the plunger has no effect. The mass and velocity has an effect on the momentum but not the plunger.

-__Actual__ Initial Velocity Cart 1, Initial Velocity Cart 2, Final Velocity Cart 1, Final Velocity Cart 2:
 * Sample Calculations:**

-__Theoretical__ Velocity:

-Percent Difference:

=2/27 Roller coaster Project=

<span style="color: #f200ff; font-family: 'Comic Sans MS',cursive; font-size: 130%;">Introducing the //**Paper Cut**//- the newest, fastest, wildest roller coaster ever made! Get your heart racing and feel that rush of adrenaline next time you visit Ms. Burn's classroom! This ride is available Monday through Friday from 8:00 AM - 3:00 PM. So what are you waiting for? Come experience the thrill!
 * [[image:honorsphysicsrocks/swords-2.jpg width="190" height="190"]] The Paper Cut [[image:honorsphysicsrocks/papercut_small.gif width="157" height="165"]] **

//**Hey parents and contractors! Want to see how fantastic our roller coaster is?! Read below to find out EVERYTHING you would want to know about our roller coaster! Includes safety information, pictures, and conceptual descriptions!**//

28g --> .028 kg
 * Diameter of the Ball:**
 * Mass of Ball:**

<span style="color: #0021ff; font-family: Georgia,serif;">**Acceleration:** <span style="color: #0021ff; font-family: Georgia,serif;">Acceleration is the rate of change of velocity with time. For our roller coaster, the ball both positively and negatively accelerates at different points during the ride. When the ball has to go up an incline, it the acceleration is negative, while when the ball is going down a hill, the acceleration is positive. When looking at the equation for average acceleration, (vf-vi)/t, this seems logical because the velocity of the ball is greater at the bottom of the hill than at the hills highest point. Therefore, vf-vi yields a negative number. That number over time (which must be positive) will create a negative acceleration. Looking at our data, it becomes clear that the acceleration at the bottom of the second hill was positive 4.345 m/s/s, while the acceleration at the top of the second hill was negative .702 m/s/s. This also is supported by Newton’s second law of motion, which states that the acceleration of an object is directly proportional to the forces acting on it. In many cases, the only forces acting on the ball are its weight, normal force, and friction. For example, on a vertical loop, the force of the weight and normal force are both pointing in the same direction. However, at the bottom of the loop, the normal force and the weight are pointing in opposite directions. Therefore, it makes more sense that the acceleration going from the bottom of the loop to the top of the loop is less than the acceleration going from the top of the loop to the bottom. Also, Newton’s first law is clearly incorporated into the physics of our roller coaster. Because the force of friction on the ball is not enough to bring it to a complete stop, the ball continues to roll down our roller coaster. As expected according to Newton's first law, object in motion (the ball) stays in motion unless acted upon by an unbalanced force (which in this scenario would be friction).

<span style="color: #0021ff; font-family: Georgia,serif;">**Newton's Laws of Motion:** <span style="color: #0021ff; font-family: Georgia,serif;">Newtons three laws of motion are essential and are present in everyone's everyday lives. Our roller coaster shows all three of them. For example, Newtons first law of motions says that an object in motion will stay in motion or that an object at rest will stay at rest unless acted upon by an unbalanced force. Our roller coaster demonstrates this law at the start of the ride. Initially the ball is at rest at the top of the coaster, the force of gravity pulls on the ball which sends it rolling down the track. Also, because the force of friction (another unbalanced force) is not great enough to stop the ball from rolling, the ball continues to move through the entire ride. Newtons second law of motion states that acceleration is produced when a force acts on a mass. The greater the mass (of the object being accelerated) the greater the amount of force needed (to accelerate the object). Our roller coaster shows this because when the ball goes down a steep hill gravity causes the ball to speed up and when it goes up a hill the ball slows down. Newtons third law of motion states every action has an equal and opposite reaction. Our coaster demonstrates this at the end. When the ball nears the end of the tracks it hits into the wall of the horizontal loop which absorbs a large amount of the energy the ball had causing the ball to come to a complete stop thus ending the ride.

<span style="color: #0021ff; font-family: Georgia,serif;">**Gravity and Apparent Weight:** <span style="color: #0021ff; font-family: Georgia,serif;">Gravity, -9.8m/s, is a force that pulls every object back to the ground. For our roller coaster, gravity was the force that was pulling the ball down. This is what sent it rolling down the track. Apparent weight is a change in the direction of weight. An example on our roller coaster would be at our vertical loop. At the top of the loop, one experiences a feeling of weightlessness. This feeling of weightlessness occurs because there is no normal force there to support your body, or roller coaster cart, so its like you are in freefall. This is why roller coasters that go upside-down have a better system of strapping in because if you just have a bar across your lap, you would fall out and die. Or get severely injured, in which case you could sue and pay for your entire college tuition. Thank you, Six Flags.

<span style="color: #0021ff; font-family: Georgia,serif;">**Energy Conservation:** <span style="color: #0021ff; font-family: Georgia,serif;">The Law of Conservation of Energy states that "energy can not be created nor destroyed". However, our roller coaster experiences a negative work force of friction. This meant that the total energy was going to get smaller as the ball moved throughout the coaster. For example, we can compare the energy at the beginning of the ride to the energy at the very end of the ride. At the beginning there was only GPE because the ball was above the ground (the reference point where h=0). There was obviously no KE or EPE because there was no spring involved and the ball had a velocity equal to 0m/s/s. Therefore, the energy at the beginning of the roller coaster was .236 J. At the end of the roller coaster (at the bottom of the third hill to be more exact) there was KE and GPE because there was a height and a velocity. The final energy was .208J. This means that some energy was not conserved, which can be attributed to the negative work of friction.

<span style="background-color: #ffffff; color: #0021ff; font-family: Georgia,serif;">**Pow****er:** <span style="color: #0021ff; font-family: Georgia,serif;">Power is equal to work/time. This can be used to find the type of motor that could push the metal ball up our 1st hill and start the roller coaster. In reality, this would be used to find the type of motor that would be necessary to take the carts up the first incline that leads into the initial drop. The GPE at the beginning of the roller coaster was .236J. We decided we would make the time it took to get up to the top of the initial drop to be 10 seconds, to make the ride more suspenseful. Therefore, the power needed to get the cart up the incline would be .236/10=.0236 W.

<span style="color: #0021ff; font-family: Georgia,serif;">**Hooke's Law-Breaking System:** <span style="color: #0021ff; font-family: Georgia,serif;">For any roller coaster, it is essential to know when to stop the car in order to prevent a crash. To do this, a spring would need to be used. We used Hooke’s Law to calculate the spring constant and the distance of compression that the spring would undergo once the ball hit it. This information was then used to design our safety spring braking system. <span style="color: #0021ff; font-family: Georgia,serif;">Hooke’s Law is demonstrated in the equation: F=-kx, where K is the spring constant and x is compression of the spring. However, we did not use this equation because the spring is not at equilibrium. So we used the equation GPE + KE = EPE, where EPE ended up equaling .208 J. Then, we needed to find x, which is the distance needed to stop. For this we used the equation vf^2=vi^2 + 2ad, where the initial velocity is 2.48 m/s and the final velocity is zero. This yields a distance of .31 meters which is equal to x. By using the equation EPE=kx^2 and plugging in the values mentioned previously, k= 2.2 N/m.

<span style="background-color: #ffffff; color: #0021ff; font-family: Georgia,serif;">**Circular Motion:** <span style="background-color: transparent; color: #0021ff; font-family: Georgia,serif; font-size: 13px; text-decoration: none; vertical-align: baseline;">Lastly, circular motion was a topic covered in our roller coaster. Circular motion occurs when an object is being accelerated by a centripetal force. This particular centripetal force, in our vertical and horizontal loops, is weight, which is positive because it points to the center of the circle. This motion can be found when looking at both the vertical and horizontal loops of the track. The ball wants to continue in a straight line, or it's tangential speed. However, we want to keep coaster fans from dying, which would be very unfortunate, so paper rails were added onto the sides of the track in order to keep the ball on track. Circular motion can be used to find the minimum velocity of the ball at the top of the loop. For centripetal motion a=v^2/r, where r is the radius of the loop (.03 m) and a= 9.8 m/s/s. Therefore min velocity at this point is .54 m/s.

<span style="color: #0021ff; font-family: Georgia,serif;">**Energy Dissipated:** <span style="color: #0021ff; font-family: Georgia,serif;">Our roller coaster started off with a total energy of .236 J and ended with a total energy of .208 J, which was a loss of .028 J. This was due to friction and when the ball rammed into the paper walls on the side of the roller coaster sometimes.

-Side View
 * Look at some of these //<span style="color: #e81111; font-family: Arial,Helvetica,sans-serif;">RAD // photos of our coaster! Don't they make you want to take a ride?**

-Top View Side View Drawing: -This is a side view of our roller coaster. It starts with an initial drop (A) which leads to the first hill (b) then proceeds to a horizontal loop at C and then glides down to a vertical loop at D and ends with the second hill at E. The two loops were put before an incline because there needs to be a lot of energy to go through these loops and a high velocity. -Top View Drawing This is a top view of our roller coaster. It starts with an initial drop (A) which leads to a hill (b) then proceeds to a horizontal loop at C and then glides down to a vertical loop at D and ends with a hill at E. The two loops were put before an incline because there needs to be a lot of energy to go through these loops and a high velocity. media type="file" key="Sarah Gordon, Katie Dooman, Lindsay Marella per6 rollercoaster 2012.mov" width="300" height="300"
 * Video of our coaster working 3 times:**


 * Data Table:**


 * Sample Calculations:**

This is the velocity at the bottom or the first hill. The ball starts at rest but is higher than the bottom of the hill, so there is only gravitational potential energy at the beginning. At the bottom of the hill there is still GPE because it is still of the ground (the ground is the reference point) and the ball is also moving so it has kinetic energy.
 * Gravitational Potential Energy-**
 * Kinetic Energy-**
 * Total Energy-**
 * Theoretical Speed-**


 * Acceleration**-
 * Minimum Speed at the top of Vertical Loop:**

-Sketch: -Free Body Diagram:


 * Spring system:**

Theoretical Spring Force Constant:

Diagram: Spring Acceleration: So, with a little over 4gs, our spring system will safely stop our dangerous, faulty, and potentially fatal roller coaster cart.


 * Minimum height for the first hill base on ^^:**

One type of **motor** that we could use is the linear induction motor. This type of motor uses electromagnets to build two magnetic fields, one on the bottom of the cart and one on the track. The magnetic field on the track is moved by the motor which pulls the train cart along behind it at a very high velocity. This motor is both durable and efficient. Also, a linear synchronous motor (LSM) could be used. This type has low acceleration, high speed, and high power. This uses alternate pole magnets and its magnetic field is controlled. However, LSM's are very expensive, so we probably would use the linear induction motor instead to keep the cost down.
 * Power**

Diagram: Ground


 * Energy Dissipated:**


 * Percent Error:**



If we had the opportunity to start over again, we would take spend more time planning out how to build our coaster, definitely using more physics to find out where to start placing the beams. We would also add more supports between the beams to prevent shakiness when the ball is moving through the track. In addition, we had a lot of trouble with the creation our vertical loop, and getting the ball to go through successfully. If we had paid more attention to the Law of Conservation of Energy we probably could have made the loop in a shorter time, had better results, and just made a more consistent loop in general. It took us a while to figure out where to put each hill based on how fast the ball was moving. If we had figured that out with kinetic energy we would have known which hills it could make and which ones it would roll back on, instead of relying on trial and error to figure this out.
 * Error in the Coaster:**

Our roller coaster is **safe** for many reasons. Most importantly, the cart will always go through the entire roller coaster without falling off the sides. In addition, it never exceeds 4g's which means that the humans on this roller coaster will not contribute to anyone passing out. In fact, the g's are so low that even more sensitive riders should be fine to go on this ride.* (More information please see Terms and Conditions)
 * How safe, or unsafe, our roller coaster is:**

Terms and Conditions: __Warning__: This roller coaster is not safe at all for its passengers. This is true for many reasons. First, our roller coaster does not have a proper ending so the 'cart' (ball) does slow down while still on the tracks. Instead, it just ends before reaching the ground, which causes the 'cart' to go flying off the end without being stopped. This could have been corrected had the track continued on longer and a breaking system been used, like a spring. In addition, the roller coaster wobbles while the ball is passing through, which would be very dangerous if this roller coaster actually had passengers riding on it. Although additional supports were added, it still shakes when the ball goes through. There was some variability in the speed of the ball at each significant point which, although this does not pass 4g's, could still lead to an increased chance in the roller coaster not working properly. __The makers of this roller coaster are not responsible for any deaths, injuries, or destruction that occurs due to going on this ride or being near this ride. Ride at your own risk.__

=2/7 Mass on a Spring Lab=

Objectives: -Directly determine the spring constant 'k' of several springs by measuring the elongation of the spring for specific applied forces -Measure the elastic potential energy of the spring -Use a graph to find the work done in stretching the spring -Measure the gravitational potential and kinetic energy at 3 position during the red spring oscillation

Hypothesis: -The spring with the smallest spring constant will have the smallest elastic potential energy and be softer and stretch more whereas the spring with the largest spring constant will stretch the least.

Methods and Materials: We first attached two clamps to a ring stand and then attached 3 springs, red, yellow, and green, to the hook on the clamps. Then we hooked a variety of masses onto the bottom of the springs:

Then for the second part, we put .5kg on the red spring, taped some cardboard to the bottom for a bigger surface, and placed a motion sensor underneath it:

Data Collection:

Sample Calculation of Finding Force of the Spring: We said that the spring was at equilibrium when it had .2 kg hanging from it. So, whenever we added a mass, such as 1kg, we would subtract .2 from it, giving us .8 kg. Then we would multiply .8kg times gravity, 9.8 to get the force, 7.84N.

Graphs: K value: 25.2

K value: 36.7

K Value: 49.1

Percent Error: Theoretical Red: 25 N/m +/- 10% Actual Red: 25.2

Theoretical Yellow: 35 N/m +/- 10% Actual Yellow: 36.7



Theoretical Green: 50 N/m +/- 10% Actual Green: 49.1



Percent Difference: Class Data-





Red:



Yellow:



Green:



Part B Stuff:



Kinetic Energy of Red Spring: Discussion Questions:
 * 1) ** 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? ** Yes. The data shows a linear form so we can conclude that the displacement and the spring are directly proportional, while the spring constant remains constant despite the displacement.
 * 2) ** How can you tell which spring is softer by merely looking at the graph? ** The smaller the spring force constant is the softer the spring is, so, by looking at the graph where the spring force constant is the slope, one would have to look at the graph with the smallest slope to find the softest spring.
 * 3) ** 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. **When the hanging mass starts at rest it has GPE then when you pull down on it it has GPE, EPE, KE and when the mass is at the lowest point it has EPE.



Conclusions/Sources of Error: <span style="font-family: Tahoma,Geneva,sans-serif;">After testing and calculating all the different spring force values, we were able to find that our hypothesis was true. The Red spring was the softest and stretchiest, and therefore had the smallest k value. The green spring had the biggest k value, therefore it barely stretched. Our results were that k for the red spring was 25.2, for the yellow we got 36.7, for the white we got 43.458, and for the green we got 49.1. These values that we obtained through our experimentation were very close to the theoretical values on the package that the springs came in.

<span style="font-family: Tahoma,Geneva,sans-serif;">To analyze our results, we calculated percent error for each of our actual values. Our highest percent error, 4.86%, was for the yellow spring. The green spring had a percent error of 1.80%, while the red had a percent error of 0.8% which is incredible. These results show that our experimental values were extremely accurate.

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

<span style="font-family: Tahoma,Geneva,sans-serif;">In real life, this can be related to bungee jumping. You would need to know the k constant of the cord to find out what the maximum weight that cord can hold and the maximum amount that it can be stretched or else...



toc =1/31 Law of Conservation of Energy Lab=

Objective: To 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. Because of this, the initial energy (kinetic or gravitational) will equal the final energy.

Total Data Table:

Procedure, Picture, Calculations (Law of Conservation of Energy and Percent Difference), and Our Data Collected for each station:

We released a .519 kg cart down an incline after measuring it's initial and final heights. We put a piece of plastic on top so it would trigger the photo-gate sensor.
 * Station 1-**

-Mass of cart: .519 kg -Distance of fence: .025 m

Our Data Collected:

Calculations:

This was a horizontal launch with a .01 kg ball. We called it's height zero and said that it stayed at approximately the same height from the first timer to the second. Then used to two times we collected to find the initial and final speeds.
 * Station 2-**

Diameter of yellow ball: .02 m Mass of ball: .01 kg

Our Data Collected:

Calculations:

-Because this experiment has two photo-gate timers, it will produce two times plus a time in between gates. You ignore the time in between gates and use the first time to find the initial velocity and the second to find final velocity.

A .07 kg mass was hung on a string as a pendulum. We moved it sideways so that it was raised it 20 cm above it's original height and then used to the time from the photo-gate timer and the width of the mass to calculate speed.
 * Station 3-**

Diameter of cork: .015 m

Our Data Collected:

Calculations:

After measuring the initial height, we released a silver ball, with a mass of .225 kg, down the shorter incline. We found it's max height after it rolled back, measured the spot, and found the final height.
 * Station 4-**

Mass of silver ball: .225 kg

Our Data Collected:

Calculations:

This was a vertical launch with a .01 kg ball. We used the width of the ball and the time we recorded to find initial speed, which we used to find final, or max, height.
 * Station 5-**

Diameter of yellow ball: .02 m Mass of yellow ball: .01 kg

Our Data Collected: -Find speed by measuring the width of the ball (this now equals the distance) and then divide it by the time, in seconds, that the photo-gate timer gave when the ball passed through

Calculations:

Sample Problem of finding the speed of the ball: Ball width = .02 m Time = .008 s

We released a .01 kg ball down the incline of the "roller coaster" after measuring it's initial height. Again, we used the time recorded and width of the ball to find final speed.
 * Station 6-**

Diameter of yellow ball: .02 m Mass of yellow ball: .01 kg

Our Data Collected: -Find speed by measuring the width of the ball (this now equals the distance) and then divide it by the time, in seconds, that the photo-gate timer gave when the ball passed through

Calculations:

Conclusion: The Law of Conservation of Energy (LoCoE) states that energy can not be created or destroyed, so the initial energy and the final energy must be equal. Obviously, our calculations did not result in equality and as shown by our extremely high percent differences, there was a lot of experimental error. This is because some energy "escaped" (-W in the equation for the LoCoE) due to things such as friction. For the roller coaster experiment, station 6, there was a ton of friction acting upon the ball, but we didn't take it into account and ended up with much less energy than we had started with. Another possible source is that, when the ball/cart/pendulum mass passed through the photo-gate timer, it didn't go through exactly in the middle, which would change the diameter (distance) which effects the speed and eventually the answer of the entire problem.