PHY 131
MIDTERM 2
Version
Put FULL NAME, ID#, and EXAM VERSION on the front cover of the BLUE BOOKLET!
Do all problems in order
, write legibly
, and show all work for partial credit
!
Note: make sketches where appropriate and show your axis conventions. Do not forget units, number of signifi
cant digits, and check your results for consistency. This exam will last 1.5 hr. Success!
v
0
⊥
disk!
A
1.
A dart of mass
m
= 0.100 kg (considered a pointlike particle) hits a uniform thin
cardboard target disk close to its lowest edge with horizontal velocity
v
0
= 9.00 m/s
perpendicular to the plane of the disk
. After hitting, the dart sticks to the card
board. The cardboard disk is suspended loosely at point A on its rim, so that is can
swing without friction on an axis tangential to the disk in the plane of the disk.
The disk has mass
M
= 0.400 kg, and radius
R
= 0.400 m.
(Solution)
a.
Show that the moment of inertia of the disk for this rotation axis is
I
= 5
MR
2
/4.
b.
Calculate the angular velocity of the disk plus dart just after collision.
c.
After collision, disk plus dart rotate around A; show that if the center of the
disk rises by a vertical distance
h
, the dart – stuck at the edge – must rise by 2
h
.
d.
Calculate the maximum vertical distance that the center of the disk rises after collision.
2.
A failing elevator car, with total weight
W
= 20 kN, drops down (from rest) on a safety spring 10 m below,
with spring constant
k
= 60 kN/m and assumed massless. All during the ride, the failing brakes exert a con
stant frictional force on the rails equal to 10 kN. (You may take
g
= 10 m/s
2
to ease calculations)
(Solution)
a.
Calculate the kinetic energy of the car when it hits the spring.
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 Fall '03
 Rijssenbeek
 Physics, Force, Work, North Pole, 3.0 kg, 1.5 hr

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