Lab 14: Impulse Momentum

The goal of this experiment is to try and find the relationship between impulse and momentum.

Equations useful to this experiment are p = m*v and J = F * t.

In the top image the blue kart collides into the red kart and we use it to determine the momentum of the system

In the middle image there should be a weight on top of the blue kart, however unfortunately I must have forgotten to take a picture of it at the time. 

In the last and bottom picture, there is an inelastic collision. Meaning that the system gets suck together and that energy is lost, as the system then gets connected to each other. 

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Results of Experiment 1

 Results of Experiment 2 (block)

Results of Experiment 3 (clay)

In experiment one, our impulse was -.2723 N*s

In experiment two, our impulse was -.6706 N*s

In the final experiment, our impulse was -.2351 N*s

This was the experimental calculations that we did by hand.

Our third and first experiment was really close for our actual and expected results.

Unfortunately that success was nonexistent in the second experiment. Where our impulse was -.6706 compared to our calculated implies of -.764 which is quite a bit off. We were mostly successful as two of the three results were within expected range. 

Lab 15:Magnetic Potential Energy

The purpose of this lab is to find an equation for the magnetic potential energy.

Above is an air track with an air glider. A magnet is attached to the air glider an we tilt the system at an angle by adding more books to the bottom. There is also a magnet at the end of the air track, which repels the cart some distance. In an "ideal" situation the track is completely frictionless by letting air go through the miniature holes in the track.

This is the result of of trials. Where we tested eight different angles and received eight different equilibrium points for the distance between the two magnets. 

Using the angles and the distances between the two magnets, we were able to graph a force vs distance graph. By integrating the graph we were able to get the kinetic, potential, and total energy of the graph.

Our data set used to obtain the force vs distance graph.

What our force vs distance graph looked like

Integrating our force vs distance graph to get the energies in the system. 

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The picture above shows the kinetic energy in purple, the potential in green, and the goal energy in orange. 

In the picture below, a straight line should be made for the total energy as no energy should be lost. So if it started with 750 joules the system should end with 750 joules. 

Our total energy is not a straight line, which was unexpected. This could be due to human error such as incorrectly determining the equilibrium point and also due to friction. While our graph was not horrible, there was quite a bit of error in the experiment. 

Lab 20: Conservation of Linear and Angular Momentum

This lab was a class lab, where Professor Wolf did the experiment once. We are trying to show that linear and angular momentum is conserved. 

A ball is put on top of the ramp and flies off and hits a spot on the floor.

Using kinematics, we solve for the velocity at which the ball leaves the ramp.

We found that the velocity at which it exited the ramp was 1.4 m/s.

Above is the calculations for the moment of inertia of the ball. 

Using logger pro, we find the angular velocity of the system

Our answer for angular momentum was 1.74 rad/s

Our answer was close to all other groups. The real angular momentum is most likely smaller though, as we did not account for human error, friction, air resistance, and any other anomalies. All in all, the experiment was successful.

Lab 18: Moment of Inertia of a Triangle

The purpose of this lab is to try to find the moment of inertia of a triangle.

Initially we will solve for the moment of inertia of a triangle symbolically. We will then find the angular acceleration so that the moment of the inertia of the system can be solved thereafter. 

When the triangle is placed horizontally, this is the result.

The result of placing the triangle vertically.

Above is the calculations where we used the parallel axis theorem to derive the moment of inertia of the two positions of the triangles.

Our experiment was fairly close with our results. Differences can be due to not taking into account of friction, air resistance, mathematical errors, or rounding.

Lab 17: Angular Acceleration

In this lab we are trying to find if there is a relationship between the factors that will affect the angular acceleration of a system, 

This is what the lab set up looked like.

We attached a string around the pulley and on the other side of the string was a mass.

The results of the experiment from the first run. We plotted the velocity against time, and by taking the slope, we would get the acceleration. 

This is the v(t) graph for the first trial run.

This is v(t) graph when we doubled the weight

This is the v(t) graph with triple the starting amount of weight.

This is what happens when the size of the torque of the pulley is changed.

These are the actual values we received from doing the experiment. 

From the above graphs, clearly there is a correlation between the acceleration of the system and the weight of the mass. As seen above, when the mass is doubled, the acceleration roughy doubled. Same for when it tripled. All in all, I believe this was a successful lab.

Lab 16: Moment of Inertia

In this lab, we tied a string to a cart and a pulley. We were supposed to determine the time it would take for the kart to descend the track,

We first calculated the moment of inertia of the two cylinders holding the disk in place. Then we calculated the moment of inertia of the system by adding those moment of inertia of the disk.

This is the graph we got from our data table and it shows the velocities of the x and y direction. 

By square rooting the squares of the velocities in the x and y direction and then adding them, we get the graph below which shows the tangential velocity.  

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These are our calculations. As can be seen in the image on top, the moment of inertia is 1.92x10^-2kgm^2/s^2. 

The image below shows our calculations for which the time it should take for it to drop one meter. 

Our experiment was unsuccessful. We were expecting  a time of around nine seconds yet it was always around thirteen seconds. After looking at it, the professor said our moment of inertia might be too small even though our calculations are right.

Lab 19: Conservation of Angular Moment

In this lab, we try to see if linear and angular momentum is conserved. A meter stick is going to hit a ball of clay and we have to find the amount of degrees that the system goes up.

We used logger pro and a video camera to capture how much it moved. 

We have to subtract .2 m from the graph as the clay was elevated .2 m from the floor.

Above is our calculations.

Our experiment was quite a bit off. As from our calculations it should have been .238 meters and the computer gave us .280 m. This could be due to friction, air resistance, and how well the hole was drilled in the meter stick. There is also a chance of human error as the release point of the meter stick might not have been parallel to the floor.