Group1_6_ch4

Lab Group 1 toc Joe, Katie, and Sarah

Gravity and the Laws of Motion Laboratory 11/15/11
Date Completed: 11/15/11 Date Due: 11/16/11
 * Part A:** Katie
 * Part B & D:** Joe
 * Part C:** Sarah
 * Period 6 Lab**

1) Find the value of acceleration due to gravity 2) Determine the Relationship between acceleration and incline angle 3) Use a graph to extrapolate extreme cases that cannot be measured directly in the lab 4) What is the relationship between the mass of the rolling and its acceleration
 * Objectives:**


 * Hypothesis with Rationale :**
 * We believe that the acceleration due to gravity is 9.8 m/s 2 based on the free fall objects and projectiles.
 * The standard acceleration for a projectile is 9.8 m/s 2 so it is safe to assume that because this is a projectile the same will be true
 * As the angle begins to increase or become steeper the acceleration of the projectile will also increase. Also as the angle becomes smaller or less steep the projectile will not travel as fast.
 * This is a simple concept. The idea can be explained using the example of a roller coaster. When the car drops off a steep incline the car accelerates and goes faster which makes all the people happy. This is also true because when the car goes off a small incline it doesn't accelerate as much and causes the car to move slower, which is not as much fun. :)
 * The mass of the projectile is inversely proportional due to the formula F=m*a; so in other words when acceleration increases mass decreases and vice versa.
 * If an object has a large mass it has a harder time accelerating because it weights more. The same is true with light objects, the object is light so it has a much easier time accelerating.

a) Materials and equipment used The equipment that we could have used during this lab are metallic balls of varying masses, an electronic scale, a metal ramp with a pre-installed measuring device, stop watch, ruler, clamp, a stand to hold the ramp, computer, calculator, notebook, protractor.
 * Method and Materials:**

b) Methods and Procedure used to carry out the experiment The procedure we used when doing this lab was as follows. First we set up the ramp at a very small angle. We than started the ball at the very top which is equivalent to 1.2m. We allowed the metallic ball to roll the distance and we recorded the time to the bottom of the ramp. We than redid this for several trials at distances of 1.2m, 1.1m, and 1.0m. We than adjusted the height of the ramp which in turn changed the angle, theta. We then repeated the steps stated before. We did this for three different heights until we were able to gather the needed data.

The ramp that the ball rolled down look like this:


 * Data:**
 * Newton's Law Lab Graph:**
 * A Link to our Document: [[file:newton's laws lab-1.xlsx]]**


 * Sample Calculations:**

Acceleration:

Average Acceleration:

Final Velocity:

Sine Theta:

As per the graph, our experimental value of the acceleration of gravity is 8.9116 m/s/s. The theoretical value of the acceleration of gravity is 9.8 m/s2 .
 * Analysis:**

Percent Error:  Percent difference: Class average:

Calculations:

Class Data: Some of our classmates did not post their data at the point when we made this chart


 * Free Body Diagrams:**

Explanation: Answer: The X-Component of the gravitational force is the force that is causing the ball to roll down the ramp
 * What force is causing the ball to roll down the ramp? Is the whole force or just a part of it? If just a part then which part?**


 * Use Newton’s second law to calculate acceleration of the ball down one of your ramps. How does it compare to your experimental (average) acceleration for that incline?**

The acceleration of our ball down that ramp at .15m in height is 1.025 m/s^2. The average for this incline is 1.017. This is because the other trials occurred from a lower point on the ramp which ultimately means they would have lower acceleration. The trial from the highest point will have a higher acceleration that the average acceleration for the ramp.

Calculations:



Using Newtons second law of motion we calculated the acceleration. We got 1.225m/s 2 which is pretty close to the results we got. Because of this we can assume that out results we pretty good.


 * Discussion Questions:**

The velocity for the each of the ramp angles is not constant. We know this because the ball accelerates as it travels down the ramp. By the very definition of acceleration, this shows that there is no possible way for the velocity to remain constant going down the ramp.
 * 1. Is the velocity for each ramp angle constant? How do you know?**

No the acceleration for each ramp is not constant and we know this because the acceleration value changes as the angle changes.
 * 2. Is the acceleration for each ramp angle constant? How do you know?**

Another option for finding the acceleration is graphing the velocity and making a tangent line. You than could find the slope of a tangent line to a point on the graph to find the acceleration. Another thing to consider is the possibility of using the formula: a=(Vf-Vi)/t and using this formula we probably could have determined the same value for acceleration. We could have used the ticker tape method and used that to calculate the final velocity. This value, along with the distance and time could be used to calculate the acceleration. In addition, a motion detector could have been used. He was able to do this by finding patterns in the distances covered. He noticed many patterns including that planes on different angles always produce the same progression of distances in equal time intervals. These distances were proportional to the sequence of odd numbers 1,3,5,7,etc. He also noticed that the total distances per each time interval (1 second, 2 seconds etc) always equaled a perfect square. This lead him to realize that the distance covered is directly proportional to the square of the time. With this crucial information he was able to see that the acceleration of a uniformly accelerating object (like one in free fall) followed this pattern. The mass of the object does not affect its rate of acceleration. This is because the acceleration is only affected by its initial velocity, final velocity, distance, or time. A free fall object is the perfect example of why the mass does not affect the acceleration. As we previously learned, two objects of different mass would fall at the same rate (ignoring air resistance). This means that the mass never affected its acceleration,which is why the only force acting on a free falling object is gravity, which is -9.8 m/s 2. The only time that the mass could affect the motion of the object is when it is first starting to move. It takes a larger force for an object with a greater mass to start moving from rest. However, this would NOT affect the rate at which the objects speed increases.
 * 3. What is another way that we could have found the acceleration of the ball down the ramp?**
 * 4. How was it possible for Galileo to determine g, the rate of acceleration due to gravity for a freely falling object by rolling balls down an inclined plane?**
 * 5. Does the mass of an object affect its rate of acceleration down the ramp? Should it affect the motion of an object in free fall in the same manner?**

The data that our experiment produced indicated that the acceleration due to gravity was 8.9116 m/s/s and our r 2 was .95727 when our y intercept was set to zero. We got this result by examining our acceleration vs. sin (theta) graph. Our first hypothesis indicated that we expected to get an acceleration of 9.8 m/s/s. However as the results show we did not get that in fact we were not that close, which is kind of disappointing. We also found that when we increased the angles the resulting acceleration also increased. So in other words when we raised the height of the incline there was a greater resulting acceleration. This is evident with the data of .15m height to an acceleration of 1.017 m/s 2 ; a height of .156m to an acceleration 1.144m/s 2 ; and a height of .235m to an acceleration of 1.828 m/s 2. This proves our second hypothesis. When we compared our results to that of the other groups from both our class and the other class we found that there is not a very significant difference (there is a difference but overall the values from both classes were decently close) in acceleration between a massive ball and a smaller ball when rolling down a ramp. I believe we can than say that mass has no bearing on acceleration of a ball down an incline. The one thing that I noticed with the results from the class was that several groups (especially ours) did not produce results with great accuracy. When we compared the results we got to the theoretical result we found that we had a 9.07% error. This is a better percent error than our first go at it but still not great. This lab does have quite a few sources of error so it is easy to see how a group may have struggled slightly. One of the biggest sources of error is a persons reaction time. The trials happen extremely quick and it is difficult for a person to start and stop the clock with the precision required to get good results. The slower the reaction time the worse the results. This source of error threw off our acceleration and thus affected the results displayed by our graph. The next thing to consider is the measurements. When measuring the heights it is hard to measure exactly and this could have led to slightly off results in the sin (theta) area of the graph. It would however not have played as significant a role as that of the time. Another thing that we really can control when doing a laboratory like this one is the friction that occurs between the ball and the surface of the ramp. This also like measurements would not effect the results greatly, especially due to the fact the ball was rolling but it is still a valid source of error. I would change this lab in a few ways in order to minimize error as much as possible. The first way that error could be cut down is by using more exact methods of measurement. A good idea would be to have a clip on maybe tape measure that could slide along the ramp as to make sure we measured to the same point on it each time. Another possibility to cut error would be to have multiple people time the lab. Also I considered the possibility that we could use technology like our computers and maybe a pressure sensor when the ball rides over 1 it starts the clock and when it rides over 2 it stops it. We could also have tried to record the process of the ball going down the ramp on imovie or photobooth and tried to slow it down to get a more precise method of time capture. As for the friction portion of error it is hard to remove friction because if we were to add oil or another lubricant it could alter the way the ball accelerates and that would have defeated the purpose. I think the best option would be to take a rag or towel and wipe the surface of the ball and that of the ramp with a cleaning solution that is non-greasy to help remove dirt and other particles that may slow the ball. Labs like this are related to many things that we do and see in our everyday lives. One example would be a rollercoaster when the cart gets to steep inclines and goes down the cart goes very fast and when it goes over a smaller incline it is far slower. Another example would be that of a driver. If the driver of a vehicle is not paying attention and goes down a steep hill without applying the breaks he or she will accelerate far above the speed they were previously going. If that same unaware driver were to go down a less steep hill he or she would not accelerate as much.
 * Conclusion:**

Newton's Second Law Lab
Date Completed: 11/29/11 Date Due: 11/30/11
 * Sarah was absent on the day of the lab***
 * Part A:** Joe
 * Part B & D:** Joe & Katie
 * Part C:** Katie
 * Period 6 Lab**




 * Purpose:**

Find the relationship between acceleration and net force Find the relationship between acceleration and mass
 * Objectives**:

**Hypothesis**: - We believe that the graph of acceleration vs net force will be linear. We think this because acceleration is caused by a difference in the net force of an object. They are proportional to each other. So as one increases so will the other. - We believe that the graph of acceleration vs mass will be inversely proportional based on Newtons second law. (∑F=ma) From this we can determine that as one increases the other decreases.

**Methods and Materials** The first thing we did was retrieve all of materials from the front table. We than took the metal track and laid it flat on the lab table. We than placed the cart onto the track and adjusted it until we were satisfied that the track was sufficiently level, which could be determined when the cart stayed still when let go. We then mounted the photogate pulley to that table right next to the track. We placed the track so that the bumper was in front of the photogate pulley as to stop the cart from running into it and potentially damaging it. We than tied a string to the cart and placed it back onto the track. The string than continued through the pulley and went down where it attached to the hanging mass and any additional weights we may have placed. Once the initial set up was complete we began to run through our trials. We placed the 5g and the 10g weights in the cart and added a 10g weight to the (5g) hanging mass. The next run we removed the 5g weight from the cart and placed it onto the hanging mass. We continued to redistribute weight amongst the cart and the hanging mass. Now we are in a bit of a grey area because we never truly completed the lab. We should have recorded all of our results in data studio and than transferred them. However, due to a bit of a problem with data studio, we had to take results from a previous year. It is assumed that the previous year would have followed a very similar path so the results should work with our collected data. The results from the previous year also focused on the distribution of 5g weights and was done repeatedly.


 * This is a picture of what the lab set up looks like:**

media type="file" key="Movie on 2011-11-29 at 13.06.mov" width="300" height="300"
 * A Video that shows the lab:**

The data table above shows the collected values for three trials along with several measurements and calculations needed to complete the lab.
 * Data Table:**

A Link to our excel file:


 * Our Graphs:**



Average acceleration is found using this equation:
 * Some Sample Calculations:**



**Analysis Questions:** //**Explain your graphs:**// //**If linear: What is the slope of the trendline? To what actual observed value does the slope correspond? How does it compare to this actual observed value (find the percent error between the two)? Show why the slope should be equal to this quantity. What is the meaning of the y-intercept value?**//


 * The acceleration vs force graph was a linear graph because acceleration and force are directly proportional. The y intercept deals with friction. The y-intercept represents friction divided by the system mass so, then, if you multiplied the y-intercept by the mass of the system, the result will be friction. It is due to this that we are able to find the force of friction. However, it is equally important to understand that the y intercept is negative, which shows that friction affects the system negativity.The slope of our graph came out as 1.8475, while the observed value is 1.87, which is found by taking the reciprocal mass of the mass. Our mass was .535kg which gives us 1.87. Our data proved to be extremely close and only produced a percent error of 1.21%. The equation below shows why the y intercept is negative. Negative friction over mass (-f/m):

//**If non-linear: What is the power on the x? What should it be? What is the coefficient in front of the x? To what actual observed value does the coefficient correspond? Find the percent error between the two. Show why this value should be equal to this quantity.**//


 * The graph of acceleration vs mass was non linear. The power of x for this graph turned out to be -1.441. The theoretical value for the power on the x is -1. This means that we were only 0.441 off, which is not terrible at all. The coefficient in front of the x represents the net force (hanging mass times gravity (m*9.8)). On our graph we got our coefficient to be .0363. The theoretical value for the coefficient is found by multiplying the hanging mass by gravity (.0037*9.8). By doing this we determined that the theoretical value is 0.03626. We found that our percent error was an incredible 0.11%. This value should be equal to this quantity because of this equation



What would friction do to your acceleration? Would you need a bigger or smaller force to create the same acceleration? Was your slope too big or too small? Can friction be a source of error in this experiment? Redo the calculation of acceleration WITH friction to show its effect. >
 * Friction would definitely slow down the acceleration. This is due to the fact that friction opposes motion. If friction were present, then it would act against the forward movement of the cart, which means that there is an additional variable that effects the acceleration of the cart. With friction present, we would need a bigger force to create the same acceleration, since the friction would be going in the opposing direction of the force, thus opposing the motion. To negate friction, you would need to have the original force //in addition to// the equivalent force of friction pushing forward so that the friction pulling the other way would cancel out with some of the force therefore making it able for the object to move at the same acceleration as it would in a system without friction present.
 * An example of this is if you had a cart pushed along a surface frictionlessly with a force of 20N and an acceleration of 5 m/s 2 . However, if that cart was now being pushed along a surface where friction was present with a force of 2N, you would need to change the force applied to the cart in order to keep the acceleration of 5 m/s 2 . This means that the force would now need to be 22N forward, as opposed to the 20N for a frictionless surface. Friction can be a source of error. Friction is a possible source of error however small because the carts were nearly frictionless as they slid along the ramp. Friction occurs all over the wheels, the ramp, the string, and the pulleys wheel. The slope of our line was was small and it was probably because of friction. This is evident in our percent error. If we were to incoperate the equation a=(hanging weight)(1/total mass)-(friction/total mass) and used friction we get. a=(9.8)(0.010)(1/0.53)-0.1253=0.0596 m/s2 . This is slightly higher than our acceleration which show that friction plays only a small role on the cart.

Both of our hypothesis were correct. We were successful in predicting that the acceleration vs. force graph would be linear. Our acceleration vs. net force graph served to prove that as the net force increases so does the acceleration. Additionally, we successfully hypothesized that the acceleration vs. mass graph would be inversely proportional, which was demonstrated by the graph (when we added mass the acceleration went down and when we subtracted mass the acceleration went up). Our graphs were both fairly accurate. The percent error for our acceleration vs. net force graph was only 1.21% which is great. This shows that our data was very close to what it should be. The percent error for our acceleration vs mass graph was only 0.11% which is astonishing. This means that our results were nearly perfect for this portion of the lab. The lab has several potential sources of error. One potential source of error would be if the tension rope/string was not completely taut. This would have thrown the acceleration value off slightly. To avoid this, groups should make sure before each test that the string is taut and in a good position. Another source of error could be that the track itself was not completely level or even the lab table that we worked on might not have been level. If either of these were not level, it would throw off the motion and ultimately skew the acceleration value. We also used the knob at the end of the track to determine if the track track was parallel with the table. This is based just on eyesight so its not going to be completely accurate.One of the major things we could have done to lessen the chance of error and produce more accurate results is to use a level to make sure that the table and track are level. Another way we could have lessened the chance of error is by checking that the string is taut each time. This concept is relevant to many things in our society. This concept is especially important to workers who are designing an elevator. They need to understand the relationship between the mass of the system, the acceleration, and the net force. They need to take into account the net force of the elevator when filled with people as well as its impact on acceleration of the mass. When we look around us we find that physics and in this case the drop and pull can be applied to various parts of everyday life.
 * Conclusion: **

=Lab 12/6/11=


 * Objectives:**
 * To measure the coefficient of static friction between surfaces
 * To measure the coefficient of kinetic friction between surfaces
 * To determine the relationship between the friction force and the normal force.

Our hypothesis is that in order to determine the coefficient of friction, one needs to divide the force of friction by the normal force. The static friction will be higher (closer to one) than kinetic friction.
 * Hypothesis**

We placed the cart on the aluminum track and pulled it as steadily as possible by a rope about 15 cm long. Then we hooked up the force meter which measures the friction between the cart and surface. We then added more weights to see how the coefficient of friction would change as a result.
 * Methods and Materials:**
 * Sample Graph From DataStudio**


 * Lab Data:**


 * Graph:** Mass v. Avg. Maximum Tension, Mass v. Avg. Tension




 * Analysis:**


 * Discussion Questions:**
 * 1) Why does the slope of the line equal the coefficient of friction? Show this derivation.
 * T (tension)
 * N (normal force)
 * w (weight), which is N in this problem.
 * 1) Look up the coefficient of friction between your material and the aluminum track. Discuss if your measured results fall within the range of theoretical values. Be sure to cite your source! Our material was plastic. //The theoretical value for the coefficient of static friction between plastic and metal ranges from 0.25 to 0.4. Our coefficient of static friction is 0.199, which is not in the appropriate range The theoretical value for the coefficient of kinetic friction ranges from 0.1 to 0.3. Our coefficient of kinetic friction is 0.145, which falls within this range. (// //[] ) //
 * 2) What variables affected the magnitude of the force of friction? What variables affected the magnitude of the coefficient of friction? //The force of friction was affected by the magnitude of the tension force. The surface the object was rubbed against also affected the force of friction. The weight of the friction cart or normal force affected the magnitude of the force of friction. The force of friction and the normal force affected the magnitude of the coefficient of friction.//
 * 3) How does the value of coefficient of kinetic friction compare to the value for the same material’s coefficient of static friction? the coefficient of kinetic friction is lower than the coefficient of friction of static friction. //As we can see from the graphs, the static friction graph (blue) has a slope of 1.96 (represents coefficient of friction) while the coefficient of kinetic friction is only .740. This is probably because it takes more force to start moving something, then to keep it moving.//


 * Conclusion **

The purpose of this lab was to determine the coefficient of friction between the object and the metal ramp by using normal and friction forces. Out hypothesis was correct because we guessed that the static friction would be higher than the kinetic friction. This did happen in our lab results because the coefficient of friction on the kinetic graph is .145 and the one on the static graph is .199. This makes sense because it requires more force to move a still object than to move an object that is already in motion. We were also correct in hypothesizing that f/N= the coefficient of friction. This is true because in our lab the coefficient of friction was the slope, where f= y values and N= the x values.

There are many possible sources of error. One source of error could have been that we were pulling the cart at an inconsistent rate. This could be changed by possibly attached the string to a motorized car that could pull it along at a steady rate. In addition, there are always imperfections in the aluminum. This could be changed by putting a form of protective covering on the ramp to make it smoother.

This concept is important for many things in life. For example, when the NBA started using syntheitc balls they forgot to take into account that the coefficient of friction changes as the players' hands sweat. Another example is tires. In the rain the coefficient of friction changes than when it is dry out which car and tire companies need to take into account when selling a car to a customer.