Cons. of Energy Exercise 4

4.1

a) Move the cart as near to the force sensor as the barriers allow, so that the spring is at its natural length. Click the Record button, wait several seconds, and then release the cart. Monitor its motion on Capstone through several oscillations. In particular, write down how far the weight falls on the first descent.

b) Is mechanical energy strictly conserved during the oscillation? What evidence supports your answer?

c) Use the Capstone calculator to create functions which describe

i)  the kinetic energy (K)

ii)  the gravitational potential energy (Ug)

iii)  the spring potential energy (Us)

iv)  the total mechanical energy of the system. (E)

Apply the functions to your data set.

d) On a single graph in your lab book, carefully sketch and label the measured energy functions over one complete cycle of an oscillation that begins with the spring unstretched.

e) On your graphs, identify where the cart is when each of the energies is at its maximum and minimum values. (Rather than a wordy description, a quick sketch of the apparatus with cart positions labeled A, B, C… might be more effective.) Make sure that your identification is consistent with all three plots.

4.2 The plot of the total mechanical energy as a function of time shows that energy is being lost from the system. We may still be able to approximate the mechanical energy as constant to predict the motion of the cart-spring-weight system during the first oscillation since only a small fraction of the energy is dissipated over that time.

a)  What is the initial mechanical energy of the system?

b)  Write an expression, as a function of the variables x and v, which describes the mechanical energy at any subsequent time.

c)  Use the fact that mechanical energy is approximately constant to predict how far you would have expected the hanging weight to fall when the system was released. How does it compare to your measured value?