Ph191M – Practice Final
Section A: Complete all questions.
1. A truck moving uniformly at 18 m/s passes a patrolman. At this instant, the
patrolman starts his car with uniform acceleration of 6.0 m/s2 until his car catches up
and is abreast with the truck. Find (a) the time taken in the chase and (b) the total
displacement in the chase.
2. A child sets off a toy rocket, which accelerates at 5.3 m/s2 at 35° above the horizontal
to the east. The weight of the rocket is 2.5 N. Ignoring the effects of friction, what
force must the toy rocket’s engine exert on the rocket to get this acceleration?
3. The radius of the path of an object in uniform circular motion is doubled. The
centripetal force needed if its speed remains the same is
a. half as great as before
b. the same as before
c. twice as great as before
d. four times as great as before
4. A symmetrical sign in the shape of a rainbow is made from two semicircles, as shown
in the diagram. The radius of the outer semicircle is 35 cm, while the radius of the
inside semicircle is 25 cm. In order to hang the sign, it has a circular hole of
diameter 4.0 cm drilled into it, whose centre is 3.0 cm below the top of the sign, on
the axis of symmetry. If the sign is of uniform thickness, where is the centre of mass
of the sign?
(10 points)
5. A novice bowler “lofts” (throws) the ball down the alley. The ball leaves the
bowler’s hand at a height of 1.10 m above the alley with a speed 3.20 m/s at an angle
of 15° above the horizontal.
a. How high does the ball rise above the ground?
b. How far in front of the bowler’s hand does the ball hit the alley?
c. What is the velocity of the ball just before it hits the alley?
6. Two identical 2.5-kg masses are connected by a string running over an ideal,
massless, frictionless pulley as shown in the diagram. The incline is frictionless,
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while the horizontal surface has a coefficient of kinetic friction of 0.15. If the angle
that the incline makes with the horizontal is 35°, what is the acceleration of m1, and
what is the tension in the string?
m1
m2
7. A hoop and a disk of the same mass and radius roll down an inclined plane. What of
the following statements is true?
a. They have the same velocity at the bottom of the plane.
b. They have the same angular velocity at the bottom of the plane.
c. They reach the bottom of the plane at the same time.
d. They have the same gravitational potential energy at the bottom of the plane.
8. A 175-N uniform boom which is 4.0 m long is secured by a horizontal rope, as shown
in the diagram. The angle between the beam and the wall is 35°. If the tension in the
rope is 85 N, how far up the boom does the rope need to be attached? Give your
answer in SI units.
9. A stone is thrown directly upward from a roof with a vertical velocity of vo at the
same time as a stone with twice the mass is given a horizontal velocity of vo. Which
of the following statements are true (you may pick more than one):
a. The two stones have the same acceleration just before they reach the ground.
b. The two stones have the same kinetic energies just before they reach the
ground.
c. The two stones have the same speed just before they reach the ground.
d. The two stones reach the ground at the same time.
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10. A wooden block of mass 310 g is placed on a turntable, which is then rotated at a
constant speed of 57 rpm (revolutions per minute). If the coefficient of static friction
between the block and the turntable is µs = 0.72, determine how far from the centre of
the turntable the block can be placed without flying off.
11. A traffic light hangs from a cable, as shown in the diagram. Is it possible to increase
the tension in the cable so much that the cable is perfectly horizontal? Explain your
reasoning.
Section B: Complete three (3) out of the six (6) questions for 10 marks
each. Clearly indicate which questions you do not want marked by a
slash through any writing. If it is not clear, the first three questions
with writing will be marked.
12. A student lifts a 25-kg block of metal off the ground using a massless, frictionless
pulley as shown in the diagram to the lower left. If the student holds the block in
equilibrium for a minute which deciding what to do with it, what is the tension in the
hook supporting the pulley? What is the angle that the hook makes with the
horizontal?
θ
FA
80°
13. A circus performer is attempting to twirl a ring-shaped prop about an off-centre
handle that is 24 cm from the geometric centre of the ring, as shown in the diagram to
the upper right. The ring has an inner radius Ri = 12 cm, and an outer radius of Ro =
30 cm. If the moment of inertia of the ring about the handle is 0.626 kg m2, find the
mass of the ring.
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14. A motor boat is to go from point A on the south bank of a river to point B on the
north side in a direction of 30° west of north. The distance between A and B is 1.5
km. The water current is 9.0 m/s westward and the water speed of the boat is
14.0 m/s.
a. In what direction should the boat head from point A to reach point B?
b. How long will it take to get across the river?
15. A uniform solid sphere of mass 7.05 kg and radius 3.45 cm is spinning about an axis
through its centre of mass initially at 11.00 rads/s. The sphere is then accelerated
rotationally for 17.3 s, during which it completes 733 revolutions. Find:
a. the angular acceleration of the sphere,
b. the final rotational speed in radians/s, and
c. the torque required to do this.
16. A crate, traveling at an initial speed vI, starts to slide up a ramp which is 3.21 m high
and has a horizontal length of 11.3 m. The coefficient of sliding friction between the
crate and ramp is µk = 0.12. Determine the initial speed of the crate at the bottom of
the ramp if it is supposed to just reach the top of the ramp, and not go any farther.
(You must solve this problem using the concepts of work and energy to receive full
marks.)
17. A pulley system is shown in the diagram. When the free end of the string is pulled a
distance of 1.0 m, how much does the load rise? What, then, is the IMA of the
system? A force of 40.0 N is needed to support the 10.0-kg load. Calculate the AMA
and efficiency of this system. What is the mass of the lower pulley?
dout: ___________________
IMA: __________________
AMA: _________________
Eff: ___________________
40.0 N
M: ____________________
10.0 kg
An inclined plane has the same IMA as the pulley system described above. What is
the angle of the plane?
θ = ____________________