Lab 11 Work-Kinetic energy theorom

Purpose: The purpose of this laboratory is to learn how to calculate work using a force vs. distance graph. Also we will see how the work don on the cart by the spring compares to its change in kinetic energy. Finally, Using the kinetic energy theorem the work will be determine from a graph and the kinetic energy will also be calculated and both with will be compared with each other to see the relationship.

The apparatus that we used measures the force of the spring as the cart is being pulled and plots the data into logger pro.
Procedure:
1. Calibrate the force probe with a force of 4.9N applied.
2. Set up the ramp, cart , motion detector, force probe, and spring as shown in the diagram. you may wish to use cart "stops" or something else to support the spring so that it can be horizontal and unstretched.
3. Be sure that the motion detector sees he cart over the whole distance of interest- from the position where the spring is just unstretched to the position where it is stretched about .5 m .
4. Open the experiment file called L11E2-2(stretched spring) to display the force vs. position axes .
5. Zero the force probe and the motion detector with the spring supported loosely and unstretched. Verify that the motion detector is set to "Reverse Direction", so that toward the detector is the positive direction. Then begin graphing force vs. position as the cart is moved slowly towards the motion detector until the spring is stretched about .5 m . (keep your hand out of the way of the motion detector).
6. Sketch your graph.
a. determine the spring constant of your spring explain how you did that.
b. use the integration routine in the software to find the work done in stretching the spring.

here is a sketch of our graph of force vs. time.

Using the integration routine in logger pro we were able to find that the work is .6561 J.

Expt 2. Kinetic Energy and the Work Kinetic Energy Principle.

We use the same apparatus for this part of the experiment.

Procedure:
1. Measure the mass of the cart. The mass of our cart was .573 kg.
2. Under Data- new calculated column, enter a formula that would allow you to calculate the kinetic energy of the cart at any point.
3. Be sure that the motion detector sees the cart over the whole distance of interest- form the position where the spring is stretched about .5 m to the position where it is just about unstretched.
4. Make sure that the x-axis of your graph is "position". Zero the force probe with the with the spring hanging loosely. Then pull the cart along the track so that the spring is stretched about .5m from the unstretched position.
5. Begin graphing, and release the cart, allowing the spring to pull it back at least to the unstretched position. when you get a good set of graphs, save them.

Note that the top graph displays the force applied by the spring on the cart vs. position. It is possible to find the work done by finding the area under the curve using the integration routine in the software. The kinetic energy of the cart can be found directly form the bottom graph for any position of the cart.

6. Find the change in kinetic energy of the cart after it is released form the initial postion (where the kinetic energy is zero) to several different final positions. Use the analysis feature in logger pro. Also find the work done by the spring up to that position. Record these values of work and change in kinetic energy in a table determine from your graph the position of the cart where it is released and record it in the table.

 Work and kinetic energy was found for many positions in the graph and it indicates that the work and kinetic energy is the same value only the work is negative because the cart is initially moving and at the end it is at rest.

The work - energy principle states that W = 1/2mvf^2 - 1/2mvi^2

Expt. 3 Work- KE theorem

Procedure:
On the laptop is a movie file entitled Work KE theorem cart and machine for Phys 1 .mp4. In the video, the professor uses a machine to pull back on a large rubber band. The force being exerted on the rubber band is recorded by an analog force transducer onto a graph.
The stretched rubber band is then attached to a cart of known mass. The cart, once released, passes through two photogates a given distance apart. By knowing the distance and the time interval between the front of the cart passing through the first photogate and then the second photogate, you can calculate the final speed and thus the final kinetic energy of the cart.

At a convenient place in the movie, stop the movie, make a careful sketch the force vs. position graph, and determine the work done by the machine in stretching the rubber band in it.

Use the data in the last few frames of the video to get mcart , change in distance of photogate and change in time of photogate and to determine the final KE of the cart attached the machine. Compare the results to what you would expect from your Fore vs. Postion graph. Comment on uncertainties in your results.

The Force distance graph that we drew from the video is .

We calculated the work to be 25.675J.

And the calculated Kinetic energy turned out to be 23.9 J.

The calculations are close, but there could have been error from the graph because we technically approximated some of the values on the graph because they could not be 100 exact and some points landed between two points on the y axis and not exactly on a value. But the method gives a good approximation to correct amount of work done.