Group5_6_ch4

toc =** Gravity and Law of Inertia Lab **= Remzi Tonuzi, Molly Lambert, Lindsay Marella


 * Objectives:**
 * Find the value of acceleration due to gravity
 * Determine the relationship between acceleration and incline angle
 * Use a graph to extrapolate extreme cases that cannot be measured directly in the lab.
 * What is the relationship between the mass of the rolling ball and its acceleration?
 * Hypothesis:**
 * The acceleration due to gravity is 9.8 m/s^2 (from knowledge of free fall and projectiles).
 * The relationship between acceleration and incline is indirect because the downward acceleration due to gravity is always the same on Earth.
 * Mass doesn't affect the acceleration of the rolling ball.

Get all of the required materials. The needed materials are a stopwatch, ramp, a clamp for the ramp, a ring stand, and a ball. First, start by setting up your ramp. Attach the clamp to the ring stand and then to the ramp. Now measure the first height of 15cm from the surface you are doing your experiment on, to the bottom of the ramp. Now find 120cm, 90cm, and 60cm on the ramp and roll the ball down. Make sure you measure the height of the ramp at each distance and time how long it takes to go down. Once you do three trials, change the height of the ramp to 20cm. Now use the same distances and measure their heights. Again, time the ball rolling down to the bottom. Now set the height to 30cm. Again, measure the heights of the same distances on the ramp. Once you have all of your data, you can complete your calculations.
 * Methods and Materials:**

N stands for the normal force that the ramp is applying to the ball. W stands for the weight that the ball is exerting at all times.
 * Free-Body-Diagram:**

**Video:** media type="file" key="Movie on 2011-11-15 at 13.28.mov" width="300" height="300"
 * Results:**
 * Class Data:**
 * Graph:**

In the acceleration vs. sin(thea) graph, the x axis of our graph represents sin(theta) and it goes from 0-1 because that is where the sin function lies. The y axis represents acceleration and goes from 0-10 because 10 is the maximum acceleration due to gravity. Our equation is 4.7411x + 0.376, and the slope represents our acceleration due to gravity which is 4.7411 m/s 2. Our acceleration is clearly much lower than the expected value of 9.8 m/s 2. This was probably due to inaccurate measurements of time and distance during the various trials and the presence of friction.
 * Data Calculations:**
 * Analysis:**
 * Analysis Explanation**:

**Discussion Questions:** 1. Is the velocity for each ramp angle constant? How do you know? 2. Is the acceleration for each ramp angle constant? How do you know? 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 of freefall in the same manner?
 * The velocity for each ramp angle is not constant. This was discovered when we made the distances shorter for each ramp angle and saw that the velocity was lowered each time.
 * No, the acceleration for each ramp angle is not constant. When we made the distance shorter for each ramp angle, the ball's acceleration was lower.
 * We could have used two photogates to measure the change in time. The we could have used that time to determine the velocity of the ball at its starting point and ending point. After, we could have divided the change in velocity by the change in time to find the ball's acceleration.
 * Galileo was able to time the position or distance covered by the ball on an incline (vertical free fall would have been too fast), and therefore could translate his time ratios and distances into a kinematic equation. He is known to have used the time-squared law of uniformly accelerated objects to determine the acceleration of gravity. He could have also used the kinematics equation we employed above: [[image:honorsphysicsrocks/Screen_shot_2011-11-16_at_5.33.28_PM.png caption="Screen_shot_2011-11-16_at_5.33.28_PM.png"]], which would have yielded a relatively similaranswer. Understanding that the largest possible angle was ninety degrees, and that its sine value is 1, he was probably able to determine that the value of gravitational acceleration was around 9.8 m/s2.
 * Yes, the mass of an object increases the rate of acceleration down the ramp. The more mass the object has, the lower the acceleration, and the acceleration of an object with a lower mass would be higher. This wouldn't affect an object of freefall in the same manner because the object changes at the rate of 9.8m/s/s due to gravity every time (during freefall).

Our entire hypothesis was proved wrong after finding the results of the lab. In the first part of our hypothesis, we thought that the acceleration of the ball rolling down the ramp would be 9.8 m/s/s due to gravity, because of our previous knowledge of freely falling objects and projectiles. The acceleration of the ball on the incline was lower than 9.8 m/s/s. The average acceleration for each run is listed on our charts – Trial 1 was .96m/s/s, trial 2 was 1.15 m/s/s, and trial 3 was 1.55 m/s/s. The second part of our hypothesis was false. As the angle of the incline increased, so did the acceleration. Our results show that the average acceleration for trial one was lower than trials two and three, which proves the second part of our hypothesis false. The third part of our hypothesis was also false because mass does affect the rate of acceleration on the incline. The class data collected from everyone during class proved this. The groups that had balls with more mass than others had lower accelerations. The class used 15cm in height as a standard point to compare results. Our ball, with a mass of .282kg, had an acceleration of .94 m/s/s. Another group’s ball’s mass was .535kg with an acceleration of .746m/s/s. A group that had a ball with amass of .008047kg had an acceleration of .803m/s/s. The groups with the lowest mass had the higher accelerations and the groups with the larger masses had the lower accelerations.There were many causes of error in our lab that caused our results to be off. An example of error was that we let go of the ball and pressed the timer button to early or to late, as well as when the ball reached the end of the ramp. Also, we didn't correctly line up the ball to its exact measurement each trial. Not only did we do this, but we did not account for friction in our experiment. Friction was opposing movement of the ball rolling down the ramp.To change this lab to minimize error as much as possible, we could use more exact methods of measurement. We should have taped the tape measure to the ramp to make sure the same point was measured every time. Another way to reduce our error would be to have each group member time each run down the ramp to produce an average time. We could have recorded the lab on Photo Booth and then paused it to see if the ball started exactly on the decided starting point. An oil or another lubricant of some kind could have been used to reduce the friction, but these materials could alter the course, acceleration, and velocity of the ball. This leaves the only option of wiping the ramp down with a towel of some sort to get rid of anything that could be an obstacle, even a tiny one, in the way of the ball's path. A relevant concept in life would be biking. If there is a stop sign at the end of a downward incline, then you know you must slow down before reaching the stop sign because you are accelerating while riding down it. This is important to know and understand because if you don't stop at the stop sign and continue accelerating, you can get hit by a car, or some type of automobile moving the other way.
 * Conclusion:**

=Newton's Second Law Lab= Lindsay Marella, Molly Lambert, Rehemzee Tuhnoozee


 * Objective:** What is the relationship between system mass, acceleration, and net force?


 * Hypothesis:**
 * If a system has greater mass, it will have smaller acceleration. They are inversely proportional.
 * If a net force is bigger, the acceleration is bigger. They are directly proportional.
 * Acceleration is dependent on the net force. Acceleration occurs when net force is not zero, because an object will stay in a constant state of motion unless acted upon by a force.
 * This is what we predict our graphs to look like:


 * Materials:**
 * Dynamics Cart with Mass
 * Dynamics Cart, track
 * Photogate timer
 * Data studio
 * Super Pulley with Clamp
 * Base and Support rod
 * String
 * Mass hanger and mass set
 * Wooden or metal stopping block
 * Mass balance
 * Level

We clamped the Dynamics Cart track to the table and attached a Photogate time to the clamp. We then attached a Super Pulley to the Photogate timer. It looked like: Then we put a Dynamics Cart on the track at 65cm away from the clamp set-up with one 5g weight on it and two 10g weights on it. We attached one end of a piece of string to the cart and a 5g mass hanger was tied to the other. The 5g mass hanger end was hung over the edge of the table, touching the Super Pulley. Our first trial was done to calculate the acceleration the cart would undergo if a 5g mass hanger were dropped to the floor. On our second trial, we took the 5g weight off of the cart and put it on the mass hanger (now, 10g). For the third, we took one 10g weight off of the cart and placed it on the mass hanger (now, 20g). And finally, we took the last 10g weight off of the cart and placed it on the hanger (now, 30g). Using the DataStudio, we were able to find the time that the Photogate had recorded for how long each spoke was going through the laser.
 * Method/****Procedure:**

media type="file" key="Second law lab.mov" width="300" height="300"
 * Video:**
 * Calculations:**
 * Graphs:**


 * Sample Calculations:**

Net Force:



**Analysis:**
 * 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. Net Force graph came out to be a linear graph as acceleration and force are directly proportional. The slope of our trendline is 1.8475. The theoretical value, however, is 1.87. This was attained by doing 1/m, as the reciprocal mass of our mass of 0.535 kg is 1.87. This value is very close to our experimental. The slope of this linear equation is representative of the reciprocal of mass, found by the acceleration equation underneath. Our percent error is only 1.20 %, showing that our experimental value is very accurate. The y-intercept is related to friction. This value is friction divided by the system mass. Therefore we can multiply the y-intercept by the system mass to find the force of friction. The equation shows the y-intercept as negative, explaining why friction has a negative effect on the system.



>>> >>> The equation below shows why the coefficient is equal to the net force. In this equation, A is equal to the net force=mg >> without friction.
 * 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 for Mass vs. Acceleration was non-linear. The power on the x is -1.432, but the theoretical value should be equal to -1. The coefficient in our equation is 0.0361, which represents the net force which is the hanging mass times gravity. The theoretical value for the coefficient is 0.03626. This resulted from multiplying the hanging force (0.0037) by gravity (9.8). Because of the little percent error we calculated of 0.44%, we can conclude that our results were accurate.
 * Theoretical Coefficient
 * 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 cause a decrease in our acceleration. As a result of friction moving in the opposite direction, a larger force would be necessary to maintain the same acceleration.The original force plus the equivalent value of force of friction would have to be pushing the cart forward so that the friction pulling in the opposite direction would cancel out and not affect the acceleration. Friction is a source of error in our lab because it is not possible to eliminate it given our procedure and materials. Friction causes the cart to have a lower acceleration and can be found on the ramp, wheels, rope, and the wheel that the rope goes through. When our calculations our redone with the presence of friction, our acceleration is slower at .0579 m/s 2, compared to our calculated acceleration of .0595 m/s 2



After completing this experiment, we found that our hypothesis and conclusion were correct. We first hypothesized that mass and acceleration are inversely proportional. This was proven by our mass vs acceleration graph. The graph showed that when we increased the mass of the cart we also decreased its acceleration. Newton's second law also supports our hypothesis. When acceleration increases and force stays the same in ∑F=ma, mass must decrease. We then hypothesized that net force and acceleration of directly proportional. Our force vs acceleration graph supported these findings. Whenever the acceleration increased the net force was also increased and whenever the net force grew then the acceleration grew. Finally, we hypothesized that acceleration is dependent on net force, and occurs when net force is greater than zero. If the net force were zero, the object would have stayed at rest because no unbalanced forces were acting on it. When the cart moved, however, the net force was always above zero. The percent error we calculated for our force vs acceleration graph was only 1.2%, proving that our results were very close to the theoretical ones. The theoretical slope was 1.87 and our results lead us to a slope of 1.8475. Our percent error for our mass vs acceleration graph was also very low at .44%. We found the coefficient to be .0361 while the expected is actually .036262. We also were able to calculate very close R squared values to 1, which also supports that are results are accurate.In order to eliminate sources of error in future procedures, we would firstly make sure that Data Studio was fully functioning and cohesive with our equipment. By doing so we would have been able to do this lab and possibly result with lower percent errors. The sources of error could have occurred in many places, one of which being the friction of the straight track. This could have caused the cart to slow down and cause the acceleration to be lower than it actually is. Also, the track may not have been completely level, causing the cart to either slow down or speed up. Also, the photogate system may not have been lined up correctly, which may have altered the time, thus altering the acceleration. We would try to minimize the friction of the track by adding some sort of lubricant. The track not being leveled could be corrected by taking a level to check for an incline, and then either put something under the track to level it, or move it to a level area for superior results. To fix the photogate issue, simply line the system up properly, as well as the rest of the experiment for proper timing.This could have been done more accurately with the use of a bubble level as well. A real life application of this concept is in an elevator. The elevator must have a certain capacity because the net force (weight of people in the elevator) must not exceed the tension of the cable. The net force must not be too great, because the acceleration of the of the hanging mass (elevator) cannot increase too much or it will snap the cable. This is why there are a maximum capacity signs on elevators.
 * Conclusion:**

 (Level used to level track to minimize % error)

=Coefficient Of Friction Lab= Remzi Tonuzi, Molly Lambert, Lindsay Marella


 * 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.
 * Hypothesis:**
 * To measure the coefficient of both static and kinetic friction, we must isolate µ from the equation f=(µ)(N), thus the equation we will use will be µ= f/N. The coefficient of static friction will be greater than the coefficient of kinetic friction because this friction is keeping the object from sliding. The coefficient of static friction will be closer to 1 than the coefficient of kinetic friction.By dividing f/N, we can figure out µ.
 * Because µ is a constant, the friction force and the normal force are directly proportional. When the friction force increase so does the normal force and vice versa.

First, gather all of the materials. You will need a Force Meter, a USB link, a friction "cart", miscellaneous masses, string, aluminum foil, an aluminum track, a laptop, and a clamp. Next, you will need to find the mass of the friction "cart". Once this is completed, place the cart on the surface and put 500 g in it. Tie a short string to the block at one end, and to the force meter on the other. Make sure the string is horizontal or your results with be inconsistent. Then, using your laptop, plug in the force meter, choose the application Data Studio, and click on "Create Experiment". Then you will need to go into the setup and uncheck force-push positive and check off force-pull positive. Then change the y-axis to force-pull positive as well. Once done setting up data studio, you can then press zero on the sensor while leaving a little slack on the string. Then you can press start on data studio and pull the block with the force sensor horizontally at a very slow and constant speed. Your data will appear on the graph and you can then display the mean and maximum point of each trial. Repeat this process three times for five different masses and record your results.
 * Methods and Materials:**


 * Setup:**
 * Video:**


 * Data:**

Static = Blue Kinetic = Red
 * Chart: Static vs Normal:**

The acceleration is equal to zero because the object is moving at constant speed and as a result, that side of the equation is cancelled out, making the tension equal to friction. The tension is the average mean of each weight. Therefore the friction is 1.57 N for 1.250 kg because the tension is equal to 1.57. Again, the acceleration is equal to zero because it's not acceleration upwards, or, on the y-axis. This cancels out that side of the equations, making the Normal force (N) of the track equal to the weight (mass multiplied by gravity).
 * Calculations and Analysis:**


 * Class Data:**


 * Discussion Questions:**
 * 1) //Why does the slope of the line equal the coefficient of friction? Show this derivation.//
 * The equation of our kinetic friction line is y=(0.118)x, 0.1108 being the only constant value. Similarly, µ is the only constant value in the theoretical equation for friction (f=µ*N). Also, just as µ is calculated in the theoretical equation by dividing friction by normal force, 0.118 is calculated by dividing the rise of each point on the line (y) by the run (x).
 * [[image:honorsphysicsrocks/Screen_shot_2011-12-07_at_8.28.43_PM.png caption="Screen_shot_2011-12-07_at_8.28.43_PM.png"]]
 * 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 smooth 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 0.1636, which is kind of close to the low end of the theoretical value. The theoretical value for the coefficient of kinetic friction ranges from 0.1 to 0.3. Our coefficient of kinetic friction is 0.118, which falls within this range. ( [] )
 * 1) <span style="font-family: Tahoma,Geneva,sans-serif;">//What variables affected the magnitude of the force of friction? What variables affected the magnitude of the coefficient of friction?//
 * <span style="font-family: Tahoma,Geneva,sans-serif;">Because the object was traveling at constant speed the acceleration was 0. This caused the friction force to be equal to the tension force, thus the force of friction was directly affected by the magnitude of the tension force. The surface the object was rubbed against also affected the force of friction. If there was another type of surface, the magnitude of friction would have changed.
 * <span style="font-family: Tahoma,Geneva,sans-serif;">The weight of the friction cart (normal force) and the coefficient of friction affected the magnitude of the force of friction.
 * <span style="font-family: Tahoma,Geneva,sans-serif;">The force of friction and the weight of the cart (normal force) affected the magnitude of the coefficient of friction. Because the acceleration is 0, the normal force is equal to weight so as the weight of the object moving across the surface changes, as does the coefficient of friction because of the equation
 * [[image:honorsphysicsrocks/MU_sdlfkjds.gif width="75" height="26" caption="MU_sdlfkjds.gif"]] ||
 * 1) <span style="font-family: Tahoma,Geneva,sans-serif;">//How does the value of coefficient of kinetic friction compare to the value for the same material’s coefficient of static friction?//
 * <span style="font-family: Tahoma,Geneva,sans-serif;">The coefficient of static friction is greater than that of coefficient of kinetic friction by 0.0456. This is because when an object is not in motion, the force of friction is stronger than when the object is sliding. The static friction was the maximum tension to get the object to move so it will be larger than the coefficient of kinetic friction.

<span style="font-family: 'Times New Roman',Times,serif; font-size: 130%;">In this lab, we had to determine what the coefficient of friction between the track and the cart going across it, as well as the relationship between kinetic and static friction vs. normal force. Our hypothesis was true. We said the friction force and normal force are directly proportional. Our graphs of kinetic friction vs. normal force and static friction vs. normal force prove that these forces have a direct correlation. The graph showed that when the friction increased the normal force increased, and when the normal force increase, so did the friction. In our hypothesis we said that coefficient of static friction would be greater than one, and that the coefficient of kinetic friction would be less than one. The first part of this is incorrect because according to the slope of our graphs, the coefficient of static friction is .1636. The second part is true, because the slope is .118, so kinetic friction is less than one. (Kinetic friction is the mean value on the data chart and static friction is the maximum value on the data chart.)
 * Percent Difference:**
 * Conclusion:**

<span style="font-family: 'Times New Roman',Times,serif; font-size: 130%;">Our percent difference is very small as the percent difference for the coefficient of kinetic friction was .17%, but in contrast, our percent difference for the coefficient of static friction is higher at 27.75%.When comparing our results to the class we obtained small percent differences: 4.71% for the coefficient of static friction and 2.70% for the coefficient of kinetic friction. This provides evidence that our data was very accurate and by eliminating various sources of error we would have precise results in the future. This experiment could have been done more accurately if there was a better way to maintain __exactly__ a constant velocity. Though we chose the points that were the most consistent on the Data Studio graph, they were not exact, which is why our percent difference is so high. For example, we could have tied the friction cart to a CMV, which would have at least have made it closer to constant speed. Also, the weights were not exactly 500 grams. One of ours was 499.2, but we rounded up to make the math simpler. Another source of error could have occurred because on occasion the person who was pulling the cart accidentally jerked it forward. This forced us to re-do the run in order to get a more accurate collection of data. Finally, the aluminum track wasn't perfectly smooth which resulted in more friction at some positions. The concept of friction is especially important in real life. Car manufacturers needed to understand how friction on the car and a variety of surfaces effects the driver, as well as how weather affects it. For example, rain could reduce the amount of friction, therefore lowering the amount of traction the tires have on the road causing it to slide/hydroplane.