# Phy138 Practice Test 1

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```					                             Phy138 Practice Test 1

Question 1

A girl throws a ball at a vertical wall 4 m away (as shown in the diagram). The ball is 2 m
above the ground when it leaves the girl’s hand with an initial velocity of v0 = (10î + 10ĵ)
m/s. When the ball hits the wall, the horizontal component of its velocity is reversed,
while the vertical component remains unchanged. How far from the wall does the ball hit
the ground? (All answers are in m).
a) 19.3
b) 18.2
c) 17.0
d) 15.9
e) 13.5

Question 2

A boy (mass 70 kg) is standing on a sled (mass 30 kg) with a load of two boxes (mass 10
kg each) that is moving at 3 m/s along a horizontal frictionless surface. The boy wants to
go faster so he is going to throw the two boxes of 10 kg off the back of the sled one at a
time. He can throw each box off the sled with a speed of 30 m/s relative to the sled. What
is the maximum speed of the boy after he has thrown the two boxes off the sled? (All
answers are in m/s).
a) 4.53
b) 5.52
c) 7.54
d) 8.23
e) 9.05
Question 3

A solid sphere, spherical shell, solid cylinder, and cylindrical shell all have the same
mass, m and radius R. If they are all released from rest at the same elevation and roll
without slipping down an inclined plane, when they reach the bottom which one has the
largest angular velocity ω?
a) The solid cylinder        b) The cylindrical shell        c) The solid sphere
d) They are all equal      e) The spherical shell

Question 4

Three objects m1, m2, and m3 are suspended from three massless and frictionless pulleys
as shown in the diagram. m1 is 6 kg, m2 is 2 kg, and m3 is 3 kg. Find the tension of the
string when the system is set in motion (i.e. all masses are moving). (All answers are in
N).

a) 11.3
b) 12.1
c) 13.5
d) 14.2
e) 15.7
Question 5

A car travelling at 70 km/h has to brake suddenly. If the coefficient of static friction
between the tires and the road is µs = 0.5, and the coefficient of kinetic friction is µk =
0.3, what is the minimum distance needed to stop?
A. 3.2 m          B. 3.9 m          C. 6.4 m          D. 5.0 m           E. 8.33 m

Question 6

A small car pushes a stalled truck up a hill. The magnitude of the force on the truck from
the car is Fct. The magnitude of the force on the car from the truck is Ftc. What can you
say about the relationship between these two forces?
A. Fct = Ftc because the forces form an action-reaction pair.
B. Fct = Ftc only because the car is pushing the truck up hill.
C. Fct = Ftc only if the car and the truck do not accelerate.
D. Fct < Ftc otherwise they wouldn’t move.
E. Fct < Ftc because the truck is heavier.
Question 7

In the diagram below, the spring has been stretched to 10 cm. The cylinder of mass 10 kg
and radius 5 cm is free to rotate about an axis through the center. A massless string is
connected to one end of the spring of force constant 50 N/m and wraps around the
cylinder (partially) and is connected to a point on the cylinder as shown in the figure
below. The other end of the spring is fixed to the ground. When the system is released
from rest the cylinder rotates in a clockwise direction. Calculate the angular speed of the
cylinder when it has rotated through 60°. (All answers are in rad/sec).
a) 7.25
b) 6.15
c) 5.56
d) 4.32
e) 2.53

Question 8
You climb Grouse Mountain with a heavy backpack. Your combined mass is 100 kg.
The path is 2 km long and the altitude gain is 800 m. By the time you reach the top, how
much work have you done on the gravitational field?
A. 80 kJ          B. 200 kJ        C. 784 kg        D. 2 MJ          I. E. 784
MJ

A small hoop of mass m and radius r rolls without slipping along the loop-the-loop track
shown, having been released from rest somewhere on the straight section of track. Use R
= 10m, m = 2kg, r = 1 cm in parts a) and b).
a) From what minimum height, h, above the bottom of the track must the hoop be
released in order that it not leave the track at the top of the loop? (The radius of the
loop-the-loop is R: assume R>>r.)
b) If the hoop is released from height 6R above the bottom of the track, what is the
horizontal component of the force acting on it at point Q?

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