* noecho
66 b
Work = **F·s**. The Work-Energy Theorem says that the work done by a force is minus the change in PE.
In this case the force of gravity **F** is down whereas the displacement **s** is
partially up. Thus the dot product of these two vectors is negative; only **B** is negative!
Additionally gravitational PE is:

PE = *mgh*

thus the increase in PE of *mgh* means a negative work of -*mgh*.
67 a
Use conservation of energy!
The initial PE of *mgh* will be converted to KE of ½ *mv*^{2}. Thus:

*mgh* = ½ *mv*^{2}

2*gh* = *v*^{2}

so the answer is **A**
68 d
Use conservation of momentum!
Initially all the momentum is in the red sphere: *mv*_{before}.
Finally a total mass of *m*+5*m*=6*m* is moving at some speed
*v*_{after}. Thus:

*mv*_{before} = 6*mv*_{after}

(1/6) *v*_{before} = *v*_{after}

so the answer is **D**.
69 c
Use your experience or simultaneous conservation of energy and momentum or the fact that the relative velocity is reversed.
In the inelastic collision mechanical energy is converted to heat. Thus with an elastic collision there will
finally be more total kinetic energy than in an inelastic collision. So something must be
moving faster with an elastic collision! In an equal mass elastic collision, the target ends up moving with
the initial speed of the projectile and the projectile ends at rest. Thus the target moves faster
than in an inelastic case and the projectile moves slower. In an elastic collision where the projectile
is much lighter than the target, the projectile rebounds with an almost undiminished speed. The target
must then end up with about twice the initial momentum of the projectile, so that total momentum
is conserved. Thus both the target and the projectile end up moving faster than in an inelastic
collision. Hence see that B and C are the only options, and that since our 5-to-1 mass ratio
is most similar to the latter case, suspect **C** is correct. Here are the simultaneous
equations solved:

2

4

(1/3)

-(2/3)

Both of these are faster than the inelastic case. 70 c Galileo commented on this almost 400 years ago! Pendulum period depends mostly on

½

Thus with (1/6) the speed, we get (1/36) the height. 73 d Combine conservation of momentum and conservation of energy! Conservation of energy on the down swing says:

½ (

Conservation of momentum at the collision says:

(2

SO:

(1+

AND doubling

Of the * write n_quest i3 questions you attempted and marked "not sure", * write nint(n_right/n_quest*100) i3 percent were in fact correct. Your answers to questions not marked "not sure" were correct * write nint((nright-n_right)/(ntry-n_quest)*100) i3 percent of the time. * endif * endif

On the real exam, you should be sure to guess an answer
for each question. However, on this web exam I give you the
expected ¼ of a correct answer per blank answer.
Thus *if you have no idea* what the correct answer is
leaving the web answer form blank does no harm on average.
Your expected score (including blanks) is:
* let score=nright+nblank*.25
* write score f5.1
* log score '6Hscore=,f5.1'

*show