Work and Energy
Introduction
The purpose of this lab is to test the law of conservation of energy. The law of conservation of energy can be written as the following:
[1] ΣU1 + ΣK1 + ΣWnc = ΣU2 + ΣK2
U = potential energy
K = kinetic energy
Wnc = non-conservative work
If the speeds of all objects are the same at the beginning and end, then the above equation can be simplified and solved for the non-conservative work:
[2] ΣK1 = ΣK2
[3] ΣU1 + ΣWnc = ΣU2 (subtraction of [2] from [1])
[4] ΣWnc = ΣU2 – ΣU1 (rearrangement of [3])
You will use a hanging mass to move a carriage up and down a ramp. The following forces will act on the two objects during this experiment: weight, normal, friction, and tension.
- The weight force will be taken into account with the potential energy functions for the carriage and the hanging mass, U = mgy.
- The normal force has no effect on the energy because it acts perpendicular to the motion of the carriage.
- The friction force does negative work on the carriage.
- The tension force will do positive work on one object and an equal and opposite work on the other object, so the tension force does no net work on the system.
Using the above information, the following equations for work can be derived:
[5] Wnc = (mcsinθ – mu)gd (equation [4] when the carriage goes up)
[6] Wnc = (md – mcsinθ)gd (equation [4] when the carriage goes down)
mc = mass of the carriage
mu = hanging mass necessary to move the carriage up at constant speed
md = hanging mass necessary to move the carriage down at constant speed
Experimental Procedures
1)Measure the mass of the carriage, mc.
2)Use string to connect the carriage to a hangingmass. Place the carriage on the inclined plane, drape the string over the pulley, and allow the hooked mass to hang. Set the angle of the inclined plane to 40˚. Adjust the pulley so that the string is parallel to the surface of the plane. It is essential that the string be parallel to the surface. Adjust the length of the string so that the carriage can move a significant distance up and down the ramp.
3)Position the carriage near the top of the incline and use a pencil to mark a reference line on the surface of the incline. Do the same for the carriage near the bottom of the incline. Measure the distance between the marks, d.
4)With the carriage at the bottom reference line, add just enough mass to the hanger so that the carriage will roll up the incline at a constant speed when started with a slight nudge. Measure the value of this mass, mu.Be very careful in how you estimate the error associated with this value. It is not limited to the error in the scale. Consider your subjective assessment of constant velocity and the range of possible masses that will produce indistinguishable behavior when assessing this error. If you estimate the error as the error in the scale, you may have your report returned for resubmission.
5)With the carriage at the top reference line, remove just enough mass from the hanger so that the carriage will roll down the incline at a constant speed when started with a slight nudge. Measure the value of this mass, md.Be very careful in how you estimate the error associated with this value. It is not limited to the error in the scale. Consider your subjective assessment of constant velocity and the range of possible masses that will produce indistinguishable behavior when assessing this error. If you estimate the error as the error in the scale, you may have your report returned for resubmission.
6)Calculate the non-conservative work done by friction using equations [5] and [6] and compare them to each other. The law of conservation of energy predicts that these quantities will be equal.
7)Repeat steps 2 through 6 using an angle of 30˚.
8)Repeat steps 1 through 7 with additional mass in the carriage. You will have a total of four tests.
Notes
There will be friction on the carriage in this lab. This is the force that does non-conservative work. Since the force of friction opposes the motion of the carriage, the work and changes in potential energy should be negative. If your experiment does not support the theory, DO NOT blame friction.
Your conclusion should state definitively if your experiment supports the law of conservation of energy (no hedging allowed).