Physics 218 Honors; Secs. 201,202,203; Exam 3, FaIl-il
Name:
Section. No:________________________
NOTE: Each problem is worth 20 points
I. Jack and Jill are standing on a crate at rest on a frictionless horizontal
surface of a frozen pond. Jack
has a mass of 75.0 kg, Jill has a mas of 45.0 kg, and the crate has a mass
of 15.0 kg. They remember
that they must fetch a pail of water so each jumps horizontally from the
top of the crate. Just after each
jumps, that person is moving away from the crate with a speed of 4.00 m/s
relative to the crate.
a) What is the final speed of the crate if both Jack and Jill jump simultaneous
ly and in the same
direction? (Hint: use an inertial coordinate system attached to the ground
)
b) What is the fmal speed of the crate if Jack jumps first and a few seconds
later Jill jumps in the same
direction?
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2. An object with mass m, initially at rest, explodes into two fragme
nts, one with mass ma and the other
with mass mb, where ma+mb = m.
a) If energy Q is released in the explosion, how much kinetic
energy does each fragment have
immediately after the explosion?
b) What percentage of the total energy released does each fragme
nt get when one fragment has four
times the mass of the other?
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3. A thin, light wire is wrapped around the rim of a wheel, as
shown in the figure below. The wheel rotates
about a stationary horizontal axle that passes through the cente
r of the wheel. The wheel has a radius of
0.180 m and moment of inertia for rotation about the axle
of I 0.480 kg-rn
. A small block with mass
2
0.340 kg is suspended from the free end of the wire. Whe
n the system is released from rest, the block descends
with constant acceleration. The bearings in the wheel at the
axle are rusty, so friction there does -6.0 J of work
as the block descends 3.00 m. What is the magnitude of the
angular velocity of the wheel after the block has
descended 3.00 m?
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4. A 5.0 kg ball is dropped from a height of 12.0 m above one end of a uniform
bar that pivots at its center. The
bar has mass 8.00 kg and is 4.00 m in length. At the other end of the
bar sits another 5.00 kg ball, unattached to
the bar. The dropped ball sticks to the bar after the collision. How high will
the other ball go after the
collision? NOTE: Moment of inertia of rod of mass M and length L about
center is
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5. A 1.05-rn-long rod of negligible weight is supported at its ends
by wires A and B of equal length. The
cross sectional area of A is 2.00 mm
2 and that of B is 4.00 mm
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2
Young
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1.80 x 1011 Pa; that for B is 1.20 x 1011 Pa. At what point x along
the rod should a weight w be
suspended to produce
a) equal stresses in A and B?
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b)equalstrainsinAandB?
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