Download Investigating the Validity of the Work-Energy Theorem: A Laboratory Experiment and more Study notes Acting in PDF only on Docsity!
Name: Partner(s): Date:
Work-Energy Theorem
Purpose:
Everyone says, “Energy is conserved.” We decided early on that our decisions about the validity of every hypothesis must, ultimately, appeal to experiment. Here, then, is your chance to take on “the big one”: to investigate the validity of the work-energy theorem.
Theory:
If an amount of work, changes. The change in the kinetic ener W , is done on a system, then the kinetic energy,gy is equal to the amount of work done. Stated K , of the system quantitatively:
!
W = " K = mv 2^22 - mv 2^12 (1) Equation 1 is a statement of the work our science. As such, questions of its validity are certainly worth your c-energy theorem and is the foundation of much ofonsideration.
Procedure:
The experimental setup is depicted in Figure 1. The inclined plane is an air track and the mass M is meant to represent the levitated cart. The mass m is a hanging mass, which will provide the force that does work on the levitat (and if it is accidentally dropped, ask your instructor to inspect it carefully). Also,e cart. As before, don’t drop the cart adjust the pulley so that the string passing over the air track is parallel to its surface.
Figure 1: Experimental Setup with force-body diagram As a preliminary step, we need to calculate the work done on simplest if we ensure that the net force acting on the cart is parallel to the displacement M. The calculation is (that’s why we just asked you to adjust the pulley). Applyin right of the figure to beg Newton's second law to each of the two masses and defining the motion to the positive yields the following equations: for M : !
T - Mg sin " = Ma (2) for m : !
mg - T = ma (3) From this, we find (and hopefully you do, too) the acceleration of the levitated cart to be:
!
a = (m^ M-^ M +^ sin m^ " )g (4) Since the net force acting on the cart’s mass is displacing the mass a distance s is W = Mas. Using the expression we F = Ma , the work this force does in found above for the acceleration, we find the work done on the levitated cart.
!
W = M(m M^ - +M m^ sin^ "^ )gs (5) This is the work that the net, unbalanced force will perform, if the unbalanced force causes a displacement s of the cart up the inclined air track. Note that the work, W , can be calculated from easily measured quantities.
As always, you will want to take multiple measurements to increase the validity of your conclusions. As such, you will want to measure the change in kinetic energy for a number of distances, s. What factors influenced your choices of s?
Your data can be recorded below. Trial 1 s ( ) !x ( ) !t ( ) v ( ) v^2 (^23) (^45) 6 In the table below, calculate the work done on the cart and the change in the cart’s kinetic energy. Trial 1 W ( ) !K ( ) % Difference (^23) (^45) 6
!
W = M(m M^ - +M m^ sin^ "^ )gs !
" K = 12 Mv^2 Is the work-energy theorem valid?
Over the last few labs perform multiple independent experiments when testing a “new” idea. In this case, you, we have made a point of emphasizing how it is important to can use the kinematic equations as a sort of “check.” How is velocity related to the displacement?
P this data should allow you to extract a value for the acceleration of the cart. Describelot your velocity and displacement on the appropriate set of axes. An appropriate fit of what you plotted and why. Attach a copy of your plot and fit.
From you what is predicted in Equation 4?r fit, what is the acceleration of the cart? How does this value compare with
Initiative:
Conclusions:
