Download Set #8 - McMaster Physics and Astronomy

Practice Problems 8
1. A 13.6 kg block is dragged over a rough, horizontal surface by a 73.2 N force acting at
16.6 degrees above the horizontal. The block is displaced 4.66 m, and the coefficient of
kinetic friction is 0.272. Find the work done by the 73.2 N force.
Answer: 3.27e+02 J
2. Find the work done by the normal force.
Answer: 0 J
3. What work does the gravitational force do on the block?
Answer: 0 J
4. How much energy is lost due to friction?
Answer: 1.43e+02 J
5. [1 point, 10 tries]
Find the total change in the block's kinetic energy.
Answer: 1.84e+02 J
6. Calculate the scalar product of the vectors in the figure below.
Assume θ1 = 109°, θ2 = 130°, F = 37.2 N and v = 18.1 cm/s.
Answer: 5.77E+00 W
7. A force F = (4.41xi + 2.85yj) N acts on an object as it moves in the x direction from
the origin to x = 4.53 m. Calculate the work done on the object by the force.
Answer: 4.52E+01 J
8. When a 4.43 kg mass is hung vertically on a certain light spring that obeys Hooke's
law, the spring stretches 2.91 cm. If the 4.43 kg mass is removed how far will the spring
stretch if a 1.53 kg is hung on it instead?
Answer: 1.01e-02 m
9. How much work must an external agent do to stretch the spring 4.19 cm from its
unstretched position?
Answer: 1.31e+00 J
10. If it takes 4.01 J of work to stretch a Hooke's law spring 13.0 cm from its unstressed
length, determine the extra work required to stretch it an additional 10.0 cm.
Answer: 8.54E+00 J
11. A cyclist and her bicycle have a combined mass of 72.2 kg. She coasts down a road
inclined at 2.10° with the horizontal at 3.90 m/s and down a road inclined at 4.20° at
7.80 m/s. She then holds on to a moving vehicle and coasts on a level road. What power
must the vehicle expend to maintain her speed at 3.10 m/s? Assume that the force of air
resistance is proportional to her speed and that other frictional forces remain constant.
(Warning: You must not attempt this dangerous maneuver.)
Answer: 6.40E+01 W
12. A constant torque of 26.4 N·m is applied to a grindstone whose moment of inertia is
0.143 kg·m2. Using energy principles, calculate the angular speed (in revolutions per
second) after the grindstone has made 16.0 revolutions. (Neglect friction.) Do not enter
units.
Answer: 3.07E+01
13. The top shown in the figure below has a moment of inertia of 3.95×10-4 kg·m2 and is
initially at rest. It is free to rotate about the stationary axis AA'.
A string, wrapped around a peg along the axis of the top is pulled in such a manner that a
constant tension of 5.32 N is maintained. If the string does not slip while it is unwound
from the peg, what is the angular speed of the top after 81.0 cm of string has been pulled
off the peg?
Answer: 1.48E+02 rad/s
14. A 2.46 kg particle moving along the x-axis experiences the force shown, where
Fmax=6.40 N, Fmin=-6.40 N, d1=1.61 m, d2=3.22 m, d3=4.83 m, and d4=6.44 m. At
x=0.00 m the particle's velocity is 3.20 m/s. What is its velocity at x=3.22 m?
Answer: 1.36e+00 m/s
15. What is its velocity at x=6.44 m?
Answer: 3.20e+00 m/s
16. How much work does an elevator motor do to lift a 1013.0 kg elevator a height of
81.5 m?
Answer: 8.10e+05 J
17. How much power must the motor supply to do this in 41.2 s at constant speed?
Answer: 1.97e+04 W
18. A 2.01 hp electric motor on a water well pumps water from 11.0 m below the surface.
Take one unit of horsepower to be equivalent to 746 watts. The density of water is
1.00 kg per liter. How many liters of water does the motor pump in 1.19 hr?
Answer: 5.95e+04 L
19. A car is designed to get its energy from a rotating flywheel with a radius of 2.20 m
and a mass of 483 kg. Before a trip, the flywheel is attached to an electric motor, which
brings the flywheel's rotational speed up to 4900 revolutions per minute. Find the kinetic
energy stored in the flywheel.
Answer: 1.54e+08 J
20. If the flywheel is to supply energy to the car as would a 14.9 hp motor, how long
could the car run before the flywheel would have to be brought back up to speed?
Answer: 3.84e+00 hr