Texts: The next two questions pertain to the situation described below.
Box 1 has mass M and slides down a frictionless incline, starting from rest at a vertical height H above the bottom (see the top part of the figure). At the bottom of the incline, it slides onto a horizontal frictionless floor, where it collides with and sticks to Box 2, which has mass 2M and is initially at rest. The boxes slide together until they run into one end of a massless spring with spring constant k. The spring compresses a distance x as it stops the blocks (see the bottom part of the figure).
Before:
Box 1: M
Box 2: 2M
After:
Box 1: 2M
Box 2: 2M
12. (8 points) Which of the following is the correct expression for the compression of the spring in terms of the other variables?
a. x = 4k/(3MgH)
b. 4x = 4MgH/(3k)
c. x = √(3MgH)/(4x)
d. 4x = 2MgH/(3k)
e. x = MgH/(2k)
13. (4 points) The two boxes are pushed back to the right as the spring uncompresses, and they move together up the incline, reaching some new maximum height. During this motion, which of the following statements best describes the system:
a. Both total momentum and total mechanical energy are conserved.
b. Total mechanical energy is conserved, but total momentum is not.
c. Total momentum is conserved, but total mechanical energy is not.
