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PHYS 161:
Fall 2004
1. In a local bar, a customer slides an empty beer mug down the counter for a refill. The
bartender is momentarily distracted and does not see the mug, which slides off the counter and
strikes the floor at distance d from the base of the counter. The height of the counter is h.
a) (7 points) How much time elapsed between leaving the countertop and hitting the
floor?
b) (6 points) With what velocity did the mug leave the counter?
c) (5 points) What was the magnitude of the mug's velocity just before it hit the floor?
d) (7 points) What was the direction of the mug's velocity just before it hit the floor?
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PHYS 161:
Fall 2004
2.
Three objects are connected on the table as
shown.
The table is rough and has a coefficient of
kinetic friction of 0.350.
The objects have masses 4.00 kg, 1.00 kg and
2.00 kg, as shown, and the pulleys are
frictionless.
(i)
(8 points) Draw free-body diagrams of each of the objects.
(ii)
(10 points) Determine the magnitude and direction of the acceleration of each object.
(iii)
(7 points) Determine the tensions in the two cords.
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PHYS 161:
Fall 2004
3.
An amusement park ride consists of a rotating
circular platform 8.00 m in diameter from
which 10.0-kg seats are suspended at the end
of 2.50-m massless chains.
When the system rotates, the chains make an
angle θ = 28.0° with the vertical.
a) (4 points) Draw a free-body diagram of a 40.0-kg child riding in a seat.
b) (8 points) What is the speed of each seat?
c) (5 points) Find the tension in the chain.
d) (8 points) What is the angular momentum of a 20 kg child with respect to the center of
rotation?
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PHYS 161:
Fall 2004
4. Two constant forces act on a 5.00-kg object
moving in the xy plane, as shown.
Force F1 is 25.0 N at 35.0°, while F2 is 42.0 N
at 150°.
At time t = 0, the object is at the origin and
(
)
has velocity 4.00ˆi + 2.50ˆj m / s .)
(a) (6 points) Express the two forces in unit-vector notation.
(b) (6 points) Find the object’s acceleration in unit-vector notation
(c) (6 points) Find the object’s velocity at t = 2 s in unit-vector notation.
(d) (7 points) Find the net work done on the object by the two forces.
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PHYS 161:
Fall 2004
5.
a) (12 points) A 2.00-kg block situated on a
rough incline is connected to a spring of
negligible mass having a spring constant of
100 N/m
The pulley is frictionless. The block is
released from rest when the spring is unstretched.
The block moves 20.0 cm down the incline
before coming to rest. (i.e. Parallel to the
surface of the incline)
Find the coefficient of kinetic friction between
block and incline.
b) (6 points) A falling meteoroid of mass m is at a distance above the Earth’s surface of 3.00
times the Earth’s radius, what is its acceleration due to the Earth’s gravitation? Your answer
should be given in terms of G, ME, and RE.
c) (7 points) Find an expression for the period (time for one orbit) of a satellite at height h above
the surface of the Earth. Your answer should be given in terms of G, h, ME, and RE.
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PHYS 161:
Fall 2004
6. a) A wooden block of mass M resting on a frictionless
horizontal surface is attached to a rigid rod of length l and
of negligible mass . The rod is pivoted at the other end.
A bullet of mass m traveling parallel to the horizontal
surface and normal to the rod with speed v hits the block
and becomes embedded in it.
(i) (5 points) What is the angular momentum of the bullet-block system?
(ii) (8 points) What fraction of the original kinetic energy is lost in the collision?
b) (12 points) A student sits on a freely rotating stool holding
two weights, each of mass 3.00 kg. When his arms are extended
horizontally, the weights are 1.00 m from the axis of rotation and
he rotates with an angular speed of 0.750 rad/s.
The moment of inertia of the student plus stool is 3.00 kg·m2 and
is assumed to be constant.
The student pulls the weights inward horizontally to a position
0.300 m from the rotation axis.
Find the kinetic energy of the rotating system before and after he pulls the weights inward.
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