Work-Kinetic Energy Lab
NAMES__________________________________________
The work-energy theorem says that the net work done by all the forces acting on an object is the
change in kinetic energy of the object. That is,
W = K = ½ m·vf2 – ½ m·vi2
(1)
For a constant force in the direction of motion (taken to be along the x-axis),
W = F·x, where x is the distance moved while the force is applied.
(2)
If F is not constant, then
W =  F dx.
(3)
This integral is mathematically equal to the area under the curve of F vs. x, as shown by
the shaded region in the graph below.
Preliminary Questions.
1. I have two carts, one of mass 0.5 kg, and a second loaded with weights so its mass is 1.5 kg. I
push each of them (one at a time) with the same constant force, for the same distance, starting
from rest. After I have pushed them through this distance, I remove the force. Which of the
following statements will be true after the force is removed?
a. The kinetic energy of the empty cart is less than the kinetic energy of the loaded cart.
b. The kinetic energy of the empty cart is equal to the kinetic energy of the loaded cart.
c. The kinetic energy of the empty cart is greater than the kinetic energy of the loaded cart.
2. In the same experiment as in the previous question, which of the following is true?
a. The speed of the empty cart is less than the speed of the loaded cart.
b. The speed of the empty cart is equal to the speed of the loaded cart.
c. The speed of the empty cart is greater than the speed of the loaded cart.
Experimental procedure
In this experiment you will push a roller cart a short distance with a force sensor and monitor the
velocity of the cart with a motion sensor. From your data, you will measure the work done during
the push and the change in kinetic energy of the cart, and you will check the validity of the workenergy theorem.
F (N)
W
x (m)
v (m/s)
x(m)
vf
Place the motion sensor on one end of the track with the roller cart on the other. Adjust the
leveling screw at the end of the track to level the track. Place two weights on the cart. Connect
the force sensor and the motion sensor to the Pasco interface and adjust the trigger rate of each to
100 Hz (to reset the trigger rates, open the "setup" window and double click on the sensor). Set
the force sensor to "fast force changes (collisions)." Set up Data Studio to display graphs of
velocity versus time and force versus position. To plot force versus position, first display a graph
of force versus time and then click and drag “position” under the Data window onto the time axis
of the force versus time graph.
Before taking a measurement, set the force sensor to zero by pressing the “tare” button. Hold the
force sensor in one hand, start the measurement, and gently push the cart toward the motion
sensor with the force sensor. You want to push the cart for 10-20 cm. Make sure that you stop
the cart by hand before it hits the motion sensor. Determine the work done on the cart by finding
the area under the force versus position curve. Determine the maximum value of the final velocity
of the cart (the velocity graph is upside down since the sensor records negative values of the
velocity when the cart moves toward the sensor). Weigh the cart and masses, and calculate the
change in the kinetic energy from the value of the velocity.
You only need one graph for a good run. Repeat several times your experiment until you are able
to reproduce the two graphs above, and then take the data.
What is the Work?
What is Kinetic Energy?
Is the work equal the change in the kinetic energy?
Repeat the procedure with only one weight in the cart, answering the same questions.
Analysis
1. Did you find, within reasonable errors, that the work done on the cart equaled its final kinetic
energy?
2. Refer to the preliminary questions. Do your results agree with your answers there? If not,
write down and explain the correct answers.