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PROBLEM SET 4: Forces I
1. Uniform Circular Motion A tire 0.500 m in radius rotates at a constant rate of 200
rev/min. Find the speed and acceleration of a small stone lodged in the tread of the tire (on
its outer edge).
2. Uniform Circular Motion An athlete swings a ball, connected to the end of a chain, in a
horizontal circle. The athlete is able to rotate the ball at the rate of 8.00 rev/s when the
length of the chain is 0.600 m. When he increases the length to 0.900 m, he is able to rotate
the ball only 6.00 rev/s. (a) Which rate of rotation gives the greater speed for the ball? (b)
What is the centripetal acceleration of the ball at 8.00 rev/s? (c) What is the centripetal
acceleration at 6.00 rev/s?
3. Non-Uniform Circular Motion The figure represents the total
acceleration of a particle moving clockwise in a circle of radius 2.50
m at a certain instant of time. For that instant, find (a) the radial
acceleration of the particle, (b) the speed of the particle, and (c) its
tangential acceleration.
4. Non-Uniform Circular Motion A ball swings counterclockwise in
a vertical circle at the end of a rope 1.50 m long. When the ball is 36.9° past the lowest point
on its way up, it’s total acceleration is (−22.5 ̂ + 20.2 ̂) m/s2. For that instant, (a) sketch a
vector diagram showing the components of its acceleration, (b) determine the magnitude of
its radial acceleration, and (c) determine the speed and velocity of the ball.
5. Forces A hockey puck with mass 0.160 kg is at rest at the origin (x=0 m) on the
horizontal, frictionless surface of the rink. At time t = 0 a player applies a force of 0.250 N to
the puck, parallel to the x-axis; he continues to apply this force until t = 2.00 s.
(a) What are the position and speed of the puck at t = 2.00 s?
(b) If the same force is again applied at t = 5.00 s, what are the position and speed of the
puck at t = 7.00 s?
6. Forces You have just landed on Planet X. You take out a 100-g ball, release it from rest
from a height of 10.0 m, and measure that it takes 2.2 s to reach the ground. You can ignore
any force on the ball from the atmosphere of the planet. How much does the 100-g ball
weigh on the surface of Planet X?
7. Forces A 4.80-kg bucket of water is accelerated upward by a cord of negligible mass
whose breaking strength is 75.0 N. If the bucket starts from rest, what is the minimum time
required to raise the bucket a vertical distance of 12.0 m without breaking the cord?
8. Forces A ball is hanging from a long string that is tied to the ceiling of a train car traveling
eastward on horizontal tracks. An observer inside the train car sees the ball hang
motionless. Draw a clearly labeled free-body diagram for the ball if (a) the train has a
uniform velocity, and (b) the train is speeding up uniformly. Is the net force on the ball zero
in either case? Explain.
9. Forces Workmen are trying to free an SUV stuck in the mud. To extricate the vehicle, they
use three horizontal ropes, producing the force vectors shown in the figure.
(a) Find the x- and y-components of each of the three pulls.
(b) Use the components to find the magnitude and direction of the resultant of the three
pulls.
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