24 Apr, 2017: Collisions in two dimensions

Lab 15: Collisions in Two dimensions
Kevin Nguyen
Lab Partners: Kevin Tran, Jose Rodriguez
Date of lab performed: 24-Apr-2017

Purpose of the lab: The purpose of the lab is to observe two different collisions (one with two marbles and one with a metal ball and marble) and determine if momentum and energy is conserved


Theory: The idea behind is lab is to see if the conservation of momentum and conservation of energy can be verified from the two different collisions. Conservation of momentum is defined as "m1v1o* + m2v2o = m1v1f* + m2v2f" (* o stands for initial and f stands for final). The conservation of energy is defined as "1/2 m1 vo^2 + 1/2 m2 v0^2 = 1/2 m1 vf^2 + 1/2 m2 vf^2".  To verify conservation of energy and conservation of momentum, we measured the masses of the marble and metal ball and the initial velocity of the balls before and after they collide.

Summary of the apparatus:

We used this apparatus to do the collisions between two marbles and between marble and metal ball. We first measured and recorded the mass of the marbles and metal ball. We put the slo-mo camera on top in order to record the change in position of the balls as they collide. After recording both collisions, we put the videos in logger pro to plot the change in positions of the balls. We put the points on a position (y-axis) vs time (x-axis) graph

position vs time for collision between one metal ball and one marble

Position vs time for collision between two marbles

We found the initial velocity of the balls by taking the slope of the lines of the balls in the y - direction before the collision began. The way we determined when the collision began is when the x and y position lines of the second ball goes from a straight horizontal line to a sloped line. We took the final velocities of the balls by taking the slopes of the x and y position lines after the collision.

 Measured data

Calculated results

position vs time Graphs shown above

Verified if conservation of energy applied to the same ball collision in the x -direction

Verified if conservation of momentum applied  to both collisions in x and y directions

Explanation of Graphs

The reason why we made a position vs time graphs for both collisions was because we were able to find the velocities of the ball by taking the slope of the position lines. We were able to find initial and final velocities in x and y directions (method mentioned above) using this method. 

Conclusion

 

Although conservation of momentum applied for the x-direction and y-direction of the same ball collision as well as the x-direction of the different ball collision, momentum was not conserved for the different ball collision in the y-direction. This error may have occurred because the plots may have not been plotted correctly, which may lead to different values for velocities. Since the surface the collisions took place was not frictionless, the balls may have lost velocity as it travelled on the surface, which lowered the value of velocity and affected our calculations for both momentum and kinetic energy of the balls. The surface may have not been as leveled as we thought, so the velocities we have recorded may not have been the true velocities of the balls. 

Although the conservation of energy was verified for the same ball collisions in the x and y directions  as well as the different ball collisions in the x-direction, energy for the different ball collisions in the y-direction was not conserved. Again, this error may have occurred because of friction, uneven surface, or error in plotting points. 

19-Apr-2017: Impulse - Momentum Activity

Lab 14: Impulse - Momentum Activity
Kevin Nguyen
Lab Partners: Kevin Tran, Jose Rodriguez
Date lab was performed: April 12, 2017

Purpose of the lab: The purpose of this lab is to observe and verify the impulse - momentum theory (J = delta p) in two different collisions: elastic and inelastic.

Theory:
Experiment 1:

For this experiment, we attempt to verify the impulse-momentum theory in an elastic collision. We measured impulse by using the data the force sensor collects over that short period of time. We measured the initial and final momentum by measuring the mass of the cart with the force sensor and the velocity before and after the collision. Since impulse equals final momentum minus initial momentum, we verified the impulse momentum theory by using the equation "Force * Time = Final momentum - initial momentum."

Experiment 2:

We repeated experiment one except we added additional mass onto the cart.

Experiment 3: 

In this experiment, we verified the impulse-momentum theory of an inelastic collision. We did so by recording the force acted on the cart over time to find impulse. We recorded the mass and just the initial velocity of the cart in order to get its momentum. We didn't need to record the final velocity since the cart stays stuck there after colliding with the clay. We compared the value for impulse and momentum and see if they are the same (or similar) to verify the impulse-momentum theory.

Summary:

To set up the first experiment, we set it up like the picture below.

At the top of the picture, although it is not clear, the student is calibrating the force sensor so it can take accurate measurements. The track is laid and positioned so that it is parallel and under the cart with the springy bit towards the other end of the track. 

The springy bit was positioned so that it hit the rubber extension of the force sensor in order to create an elastic collision. We put a motion detector at the opposite end of the track so that it can record the initial and final velocity of the cart. We set the positive direction towards the motion sensor so that the initial velocity is recorded as negative. We did this so that subtracting the initial and final momentums doesn't give us a negative value. We made the track leveled to prevent the velocity from being affected by outside sources other than our gentle push. After recording our data, we made a force vs time graph (to measure impulse) and a velocity graph (to measure initial and final velocities). These graphs are shown below. 

For experiment 2, we added 500g to the cart with the force sensor and repeated the procedure. 

For experiment 3, we set up the lab like the pictures below. 

For experiment 3, we kept the 500g mass on the cart. We set the wooden block with clay at one end of the track and a motion sensor on the opposite end of the track (not shown in the third picture). We attached a nail to the force sensor (with the pointy end sticking out) so that the cart can "stick" to the clay to create an inelastic collision. We then gave the cart a gentle push and recorded the data after the collision is finished. We made a Force vs time graph and a velocity graph. They are shown below. 

Measured/ calculated data:

Experiment 1:

Experiment 2:

Experiment 3:

Explanation of graphs:

Since we used force vs time and velocity graphs for all three experiments, I will explain what they all do as a whole. The reason why we used a force vs time graph was because integrating the force vs time line from the point the force starts to increase to the point where the force returns to zero gave impulse. We used the velocity graph to find initial and final velocities of the cart by placing the velocity graph directly above the force vs time graph. We then recorded the initial velocity and final velocities by aligning the point the force begins to increase with the initial velocity and the point the force returns to zero with the final velocity. 

Conclusion: 

Overall, all three experiments were very successful. The values for impulse was very similar to the values of delta momentum. Although the values of impulse were very similar to the values of delta momentum, they were not exactly the same. This uncertainty may stem form multiple factors. One of the factors is friction of the track since the friction of the track decreases the cart's velocity, which will lower the initial and final velocity and therefore slightly affecting the value for momentum.  Air resistance may also affect the cart's velocity since air resistance slows down the cart. 

21-Apr-2017: Magnetic Potential Energy Lab

Lab 13: Magnetic Potential Energy Lab
Kevin Nguyen
Lab Partners: Jose Rodriguez, Kevin Tran
Date of lab performed: 21-Apr-2017

Purpose: This lab was designed to verify that conservation of energy applied to the apparatus (pictured below).

"r" represents the distance between the magnet at the end of the trash and the magnet on the glider. "h" represents the height of air track from the ground.

Before we verified that the conservation of energy applied to this apparatus, we needed to find an equation for magnetic potential energy.

Summary of experimental procedure

First, we set up our apparatus like the picture shown above. We made sure to make the air track as level as possible (0.0 degrees). We then tilted the air track at different angles to find the relationship between magnetic force (F)  and separation distance (r) (explanation in "List of Calculated Data" section). We then plotted a graph of magnetic force (y-axis) vs separation distance (x-axis). Since we assume that the relationship between magnetic force and separation distance takes form of the power law F = Ar^n, we made a power line fit of the graph.

This is a magnetic force vs separation distance graph, not force vs radius graph.
The uncertainty of the "A" parameter is plus or minus 4.619*10^-06
The uncertainty of the "B" parameter is plus or minus 0.08493

After finding the equation from the box, we integrated the magnetic force equation to find the magnetic potential energy equation. The magnetic potential energy equation we got was

"U(r) = (8.76756*10^-6)r^-1.566." 

Since we solved the problem of finding the equation for magnetic potential energy, we could now verify the conservation of energy.  we attached an aluminum reflector on top of the air track cart in order for the motion detector to accurately record the speed of the cart. After weighing the cart, we put it back on the track. We put the cart as close to the magnet as possible (without the magnets touching) and ran the motion detector in order to determine the relationship between the distance the motion sensor reads and the separation distance between the magnets.

After setting the motion detector to 30 samples per second, we created a new calculated column that allowed us to get the separation between the magnets from the position measured by the motion sensor. We also created other calculated columns that allowed us to find kinetic energy, magnetic potential energy, and total energy (graph below). We started with the cart at the far end of the track and, after starting the detector, gave it a small push. We made a single graph that showed kinetic energy, magnetic potential energy, and total energy in respect to time.

List of Measured Data

Angle between track and table/ separation between magnets/ magnetic force

List of Calculated Data

Solving for Magnetic Force

Graph of Kinetic energy (purple), potential magnetic energy (red), and total energy (blue)

Finding the separation distance

Equation for kinetic energy

Calculating magnetic potential energy

                                   
Explanation of Graphs/ Analysis:

First we made a graph of magnetic force vs separation distance. We made this graph because integrating the magnetic force in respect to separation distance gave us the magnetic potential energy. Finding the magnetic potential energy helped us in verifying if conservation of energy applied to this apparatus.

We also made a graph for kinetic energy, magnetic potential energy, and total energy. We made this graph to help us verify the conservation of energy by checking if the total energy is a straight line. The total energy line needs to be a straight line since the conservation of energy suggests that the energy lost from kinetic energy was transferred to magnetic potential energy. If the total energy line is a straight line, then that means that conservation of energy does apply to this apparatus.

Conclusion:

Using the graph containing the kinetic, magnetic potential, and total energy, we found that the total energy line is not a straight line. Since the total energy line was not a straight line, it meant that the conservation of energy does not apply to the apparatus. But this was not the case. When we adjusted the separation distance from .257 meters to .254 meters, the total energy line became more straight. The uncertainty in the separation distance greatly affects our results since a small change in the separation distance will change the shape of the total energy line completely, which affects our answer of verification of the conservation of energy of the apparatus.

Another source of uncertainty was that the track was not completely frictionless. This fact affects the velocity of the air track cart since friction decreases the cart's velocity. A decreased velocity leads to a decreased kinetic energy (since velocity is directly proportional to kinetic energy). The decreased kinetic energy affects our answer of verification of conservation of energy of the apparatus.

10 Apr 2017: Work-Kinetic Energy Theorem Activity

Lab 11: Work-Kinetic Energy Theorem Activity

Kevin Nguyen

Lab Partners: 

Date of Lab Performed: 10 April 2017

Theory/ Introduction: The theory behind this lab was that we attempted to establish a relationship between work and kinetic energy. We did this by testing two ideas of physics: Work equals the change in kinetic energy and the integral of force equals to Work. In this lab, there were three experiments that tests these ideas (technically, there were four experiments, but the last experiment involved watching a video and collecting data from it). 

In the first experiment, we used the force of tension force, a constant force, to measure the work done on a cart. We measured and graphed the tension force that was used to move the cart using Logger Pro. Then, we adjusted the force graph so that the graph would be a force (N) vs. position (m) graph, where force is on the y-axis and position is on the x-axis. We had done this because the area under the force vs position curve will give the work done on the cart. To find the change in kinetic energy of the cart, we made a new calculated column .5 * "mass" * "Velocity"^2 since this is the equation for finding kinetic energy. We then made a kinetic energy (J) vs time (s), where kinetic energy is on the y-axis and time is on the x-axis. This graph gave the kinetic energy of the cart at a given time. Ideally,   the area under the force curve (from starting position) equals to the kinetic energy at that moment.

In the second experiment, we measured the work done by the non constant spring force. To do this, we had set up an apparatus that allowed us to test the force applied by the stretched spring vs distance the spring was stretched. We made a graph of Force vs Distance, where force is on the y-axis and distance is on the x-axis. After slowly and manually stretching out the spring, the graph formed on Logger Pro. Integrating that graph gave the work done by spring force. To find the spring constant of the spring, we used the idea that spring force equals to spring constant times displacement. The slope of the force line gave us the spring constant.

In the third experiment, we measured the work done by the non constant spring force and the kinetic energy of the cart in order to see if they are equal to each other at a certain point. We had set up an apparatus that allowed us to test the force of the spring and the kinetic energy of the cart. After collecting the data, we made two graphs, a force (y-axis) vs position (x-axis) graph and a kinetic energy (y-axis) vs position (x-axis) graph. Then we integrated the force vs position graph (from its starting position to whatever position we selected) in order to find the work done by the spring. We compared the work done by spring to the kinetic energy at the same final position and found that value of Work done by the spring was similar to the kinetic energy of the cart.

In the final "experiment", we copied the force vs position graph from the video and found the total area under the curve in order to find the total work done stretching the rubber band. Then we got the mass of the cart, change in position, and change in time in order to find the final kinetic energy of the cart attached to the machine. We then compared the kinetic energy to the work done on the rubber band.

Summary of experimental procedure

In the first experiment, we had up our apparatus like this.

The track is set up on the table. The motion sensor was at least 50 centimeters away from the starting position of the cart. A hanging mass of 500 grams was placed at the end of the string and a mass of 500 grams was placed on the cart. Before using the force sensor, we made sure to zero the force sensor and verified that it read 4.9 N when the hanging mass was at 500g and the cart was against the track stopper. The force sensor was then attached to the top of the cart. A track stopper was placed near the end of the track and a pulley was attached at the end of the track. To perform this experiment, a person held the cart at the starting position. Once the motion detector started clicking very fast, the person let go of the cart, allowing the cart to travel until it hit the stopper.

In the second experiment, we had set up our apparatus like this. 

Again, the track was set up on the table with the motion sensor at least 50 centimeters away from the cart. The motion detector was set to "Reverse Direction" so that any direction towards the motion sensor was considered positive. The force sensor was attached to a metal rod at the end of the table. The force sensor was zeroed and calibrated with a force of 4.9N applied. A spring was attached to the force sensor and the cart. The cart was placed on the track.  To perform this experiment, the person holding the cart would slowly bring the cart towards the motion detector once the motion detector began collecting the data. 

In the third experiment, the same exact apparatus was used from the second experiment. The force sensor was zeroed. A kinetic energy vs position graph was set up along with a force vs position graph. The spring was stretched from its initial unstretched position to 0.6 meters. When the motion detector began collecting data, the person holding on to the cart let go of it. 

In the fourth experiment, we watched a video titled "Work KE theorem cart and machine for Physics 1.mp4" We copied the graph shown in the video along with the data (mass of the cart, change in position, change in time) and solved for total work and kinetic energy. Then we compared the two results.

Table of Measured/ Calculated Data:

Experiment 1

Ignore the position vs time graph and the velocity vs time graph (top two graphs)

Experiment 2

Ignore the bottom two graphs.

Experiment 3

Ignore the bottom graph

Experiment 4

This picture shows how work and kinetic energy are calculated.

Conclusion

Experiment 1

Judging from the results from the graph, it seems that the value of work is almost equal to the change in kinetic energy.

Experiment 3

The work done on the cart is equal to the change in kinetic energy.

Potential energy of spring equals to Kinetic energy of the cart.

Experiment 4

The true kinetic energy of the cart is between 23.227 J and 24.373 J.

05-April-2017: Work and Power

Lab 10: Activity - Work and Power
Kevin Nguyen
Lab Partners: Jose Rodriguez, Kevin Tran
Date of Lab Performed: 05 April, 2017

Statement of what the experiment is trying to accomplish: The purpose of the lab was to learn the relationship between work done and power used.

Theory/ Introduction: The idea behind this lab was that we needed to calculate the power that we used from performing several activities, including lifting masses from the ground using a rope and pulley, walking and running up the stairs.

To calculate the power required to lift masses vertically, we needed the distance between the ground and a point where we stopped lifting the mass (think of this as the finish line). The values of the masses were required to calculate work done to lift the mass up. The work done to lift the mass up is defined by "mgh". "M" stands for mass, "g" stands for the gravity constant, and "h" represents the distance from the ground to the finish line. We also recorded the time it took to get the mass form the ground to the finish line since power is defined by "W/t", or work divide by time. Work divided by time will give J/s, or Watts, a measurement of power.

To calculate the power required to walk and run the stairs, we recorded the masses of the person walking and running the stairs. Identical to the previous paragraph, we also used "mgh" to calculate the work done to walk/ run the stairs. The time was recorded for both running and walking the stairs in order to divide work by time. Dividing work by time will give the power done to walk/ run the stairs.

Summary:

The backpacks were set up like the picture below.

The backpack containing the masses was attached to the end of rope, which was set up over the pulley. A person would step on the end of the wooden stick so that the backpack won't pull the stick down. The person at the ground then wore gloves and prepared to pull the rope. Once the timer began, the person pulled the rope until the bottom of the mass passed the bottom of the gate. The same procedure was repeated for the two other masses. Only one person pulled the ropes since having different people pulling the ropes will result in inconsistent data.

For the stairs experiment (both walking and running), the distance from the bottom of the stairs to the top was recorded. The walker/ runner began at rest at the bottom of the stairs. Once the timer began, the person walked/ ran the stairs until they get to the top. The timer stoped once the person got to the top.

A list/table of measured data:

Calculated Results

Conclusion

a) 

The error in the results were not as large as expected. 

b) Assuming that we were running the flight of stairs, which takes 547.5 Watts to climb 4.39 meters, we would have to climb nearly double the height (4.39m times 2 = 8.78 m) in the same amount of time in order to match the amount of power the microwave uses.

c) 1100 Watts * 360 seconds = 396000 Watts

We would have to climb around 3175 meters of stairs per 5.8 second, or 547.4 steps a second, in order to match the power it took to run the microwave.

d) 1) The power is 20833.33 Watts

2) Around 209 people

3) 208.33 seconds

03-Apr-2017: Centripetal force with a motor

Lab 9: Centripetal Force with a Motor

Kevin Nguyen

Lab Partners: Jose Rodriguez, Kevin Tran

Date performed: 03 April 2017

Purpose of this lab: The purpose of this lab wass to teach us that if the motor spins at a faster angular speed, the radius between the mass and the central shaft along with the angle will increase. Using that fact, we must establish a relationship between angular speed and angle. 

Theory/ Introduction: We established the relationship between the angular speed and the angle below.

From the triangle on the upper right side, we were able to find the angle by finding the length of the string and the height of the apparatus minus the height of the mass above the ground.

We identified the forces going in the horizontal (x) direction and vertical (y) direction. Since the ball's centripetal acceleration was geared towards the central shaft, it was safe to say that the sine of tension force is equal to the centripetal force. Since gravitational force and tension force were the only forces acting on the masses in the vertical direction, the relationship of cosine of tension and gravitational force can be established. The forces in x and y direction was divided and the angular velocity was solved for, establishing the relationship between the angle and the angular velocity. After recording data for the five trials, we compared the calculated angular velocity to the recorded angular velocity to see if the relationship is accurate. We had done this by graphing the recorded angular velocity on the y-axis and the calculated angular velocity on the x-axis, made a linear fit model, and analyzed the slope of the line. The slope of the line told us how closely related the two data points are. The closer the slope of the line is to 1, the stronger the relationship is between the recorded angular velocity and the calculated angular velocity. If the correlation given from Logger Pro linear fit is also close to 1, it also implied a strong relationship between the calculated angular velocity and the recorded angular velocity. A strong relationship between the recorded angular velocity and the calculated angular velocity supported the relationship that we established between the angle and the angular velocity. 

Summary

In the lab, we collected data from this apparatus to support our relationship that we have established above. We were told to observe the apparatus below.

In the picture, the motor was on top of the tripod. A mass hung at the end of the string. We measured the height of the rod that holds the string from the ground, the height above the ground the mass is at when it is spinning, and the length of the string the mass is attached to. In order to get several data points, we recorded the height the mass was above the ground at different angular velocities. After we finished taking data, we calculated the angular velocity using the data of the heights of the mass above the ground and the apparatus, the distance between the mass and the central shaft, and the length of the string attached to the mass. After calculating the angular velocity, we graphed our recorded angular velocity on the y-axis and the calculated angular velocity on the x-axis, made a linear fit for the data plots, and analyzed the slope of the line.

Measured Data:

Calculated data:

Calculated angular velocity is in the bottom right. The calculated angle is on the bottom left.

Calculated angular velocity (x) vs Recorded Angular velocity (y)

Conclusion:

The graph above showed that the slope was 1.053 and that the correlation between the calculated and recorded angular velocity was 0.9981, or 99.81% correlation. With a slope value and correlation value very close to 1, those values imply that the relationship between calculated and recorded angular velocity is very strong. A strong relationship between the two also imply that the relationship we established between the angle and the angular velocity is valid. 

03-29-2017: Demonstration - Centripetal Acceleration vs. Angular frequency

Lab 8: Demonstration - Centripetal Acceleration vs Angular Frequency
Kevin Nguyen
Lab Partners: Kevin Tran, Jose Rodriguez
Date performed: 03-29-2017

Statement/ purpose: The purpose of this lab is to find the relationship between centripetal force and angular speed.

Theory/ introduction: This lab attempts to find the relationship between centripetal force and angular speed, or if "Centripetal Force=mr(omega)^2" is true. Centripetal force, or "centripetal force = mass x centripetal acceleration" is found from the force sensor in the middle of the disk while the angular velocity of the disk, or (omega), is found through the photo gate reading the tape attached to the end of the disk.

Three graphs will be made: a Force vs Mass graph, whose slope will give radius times omega squared, Force vs radius graph, whose slope will give mass times omega squared, and Force vs omega graph, whose slope will give mass times radius. Force will always be on the y-axis while the independent variables (mass, radius, or omega) will be on the x-axis.

We calculated our omega using the change in time from the first revolution to the 10th revolution (or 5th revolution for one of the trials). We used the constant radius and constant mass given to find and compare those values to the value of the slope.

Summary: First, the lab was set up like this.

The photo gate captures the angular velocity (the speed at which the disk rotates) by attaching a piece of tape at the end of the disk in order to find the angular velocity. The force sensor is set up in the middle with string attached between the sensor and the mass to find the centripetal force. Three situations were tested, such as collecting period and force data for different masses and fixed speed, same mass at fixed velocity, but different radii, and same mass at constant radius, but different rotational speeds. 

This is the graph used to find force. 

This graph is used to find time from the 1st revolution to the 5th revolution.

After gathering the data, we inputted it in three types of graphs: Force vs mass graph, Force vs radius graph, and Force vs omega graph.

Data Tables:

First Situation - Only radius is Varied
Trial 1
Mass = 200g
radius = 22.86cm
power = 3
Force Towards Center = 1.20N
Time at first revolution = 1.428 seconds
Time at 10th revolution = 14.769 seconds

Trial 2
Mass = 200g
radius = 29.24 cm
power = 3
Force Towards Center = 1.47N
Time at first revolution = 1.728 seconds
Time at 10th revolution = 14.88 seconds

Trial 3
Mass = 200g
radius = 34.29 cm
power = 3
Force Towards Center = 1.69 N
Time at first revolution = 13.36 seconds
Time at 5th revolution = 20.1 seconds

Trial 4
Mass = 200g
radius = 46.99 cm
power = 3
Force Towards Center = 1.98 N
Time at first revolution = 1.569 seconds
Time at 10th revolution = 15.6 seconds

Trial 5
Mass = 200g
radius = 58.42 cm
power = 3
Force Towards Center = 2.198N
Time at first revolution = 2.2 seconds
Time at 10th revolution = 17.4 seconds

Second Situation - Only mass is varied

Trial 1
Mass = 100g
radius = 46.99 cm
power = 3
Force Towards Center = 1.052N
Time at first revolution = 2.68 seconds
Time at 10th revolution = 17.02 seconds

Trial 2
Mass = 50g
radius = 46.99cm
power = 3
Force Towards Center = 0.57N
Time at first revolution = 1.54 seconds
Time at 10th revolution = 14.97 seconds

Trial 3
Mass = 300g
radius = 46.99cm
power = 3
Force Towards Center = 2.8N
Time at first revolution = 2.35 seconds
Time at 10th revolution = 16.46 seconds

Third Situation - Only Power (omega) is varied

Trial 1
Mass = 300g
radius = 46.99cm
power = 3.5
Force Towards Center = 5.39N
Time at first revolution = 1.245 seconds
Time at 10th revolution = 11.48 seconds

Trial 2
Mass = 300g
radius = 46.99cm
power = 3.8
Force Towards Center = 5.94 N
Time at first revolution = 1.12 seconds
Time at 10th revolution = 10.747 seconds

Trial 3
Mass = 300g
radius = 46.99cm
power = 4.1
Force Towards Center = 6.43 N
Time at first revolution = 1.46 seconds
Time at 10th revolution = 10.6 seconds

Calculated results:

Force vs. Radius Graph

Force vs. Mass Graph 

Force vs Power (omega) graph

Conclusion:

For the Force vs Radius graph, the slope was 2.729, which means the constant mass multiplied by omega squared. This value was less than the calculated value, which was 3.417.

For the Force vs Mass graph, the slope was 8.869, which means the radius multiplied by omega squared. This value was lower compared to our calculated value, which was 10.285.

For the Force vs Power graph, the slope was 1.733, which means the mass multiplied by the radius. This value was close to our calculated value, which was 1.4097.

A significant experimental error that may have affected the experimental data for the Force vs Radius graph and the Force vs Mass graph was the fact that the omega was varied due to the nature of the apparatus. Since the omega was varied, the slope values from the Force vs Radius graph and the Force vs Mass graph do not accurately reflect the actual omega value from the apparatus.