Page 47 - 2023-bfw-physics-stewart-3e-new.indd

Chapter 7 Review Problems 329

(b) What is the speed when the object is 5.00 cm from does the kinetic energy of the baseball change in the colli-
equilibrium? sion with the wall? Where does the energy go?
(c) What is the speed when the object is at the equilib- 19. Gravel-filled runaway truck lanes are designed to
rium position? stop trucks that have lost their brakes on mountain
11. Wei drags a piece of driftwood for 910 m along an grades. Such a lane is horizontal or uphill and about
irregular path. If Wei ends 750 m from where he 35.0 m long. We can think of the ground as exerting a
started and exerted a force of constant magnitude friction force on the truck. If a truck enters the gravel
625 N, at all times directed parallel to his path on lane with a speed of 55.0 mph (24.6 m/s), use the
the piece of driftwood, how much work did he do work-energy theorem to find the minimum coefficient
on the driftwood? of kinetic friction between the truck and the lane to be
8
12. Earth orbits the Sun at a radius of about 1.5 × 10 km. able to stop the truck if the lane is horizontal.
2
At this distance the force of gravity on Earth due to 20. Three clowns try to move a 3.00 × 10 -kg crate 12.0 m
the Sun is 3.6 × 10 22 N. Assuming Earth’s orbit to to the right across a smooth, low- friction floor. Moe
2
be perfectly circular, how much work does the Sun’s pushes to the right with a force of 5.00 × 10 N,
2
gravity do on Earth in one year? Larry pushes to the left with 3.00 × 10N, and Curly
2
13. An ideal spring of constant 8.0 N/m is fixed at one pushes straight down with 6.00 × 10N. Calculate the
end to the wall, and at the other end to a low-friction work done by each of the clowns.
cart of mass 750 g that is initially at rest on a hori- 21. The 2010 Americans with Disabilities Act established
zontal table. A student moves the cart a distance of a standard for wheelchair ramp inclinations. Assuming
0.50 m, stretching the spring and holds it at rest at the ramp is a right triangle with the inclined surface as
that position. its hypotenuse, the horizontal base of the ramp must
(a) Sketch a graph of the force exerted on the cart by have a length 12 times greater than the vertical height
the spring as a function of the distance the cart is of the ramp. Justify the selection of data that guided
moved, from 0 to 0.50 m. engineers in the creation of this standard by describing
(b) Use your graph to calculate the work done on the the data they must have sought and the forces exerted
cart by the spring, and the potential energy stored on the wheelchair.
in the spring when it is stretched 0.50 m. 22. A child slides down a slide that is 4 m in length and
°
(c) The cart is released from rest at 0.50 m and the has an inclination, relative to the horizontal, of 28.
spring pulls it back to the equilibrium position. Describe in words how you will determine the change
Calculate the speed of the cart as it passes through in potential energy of the child–Earth system as she
the equilibrium position. descends the slide. In your description include your
14. Draw and describe a physical situation to which the choice of the origin for the definition of initial and
final positions, the algebraic expression for potential
following equation could apply:
energy, and any assumptions about friction forces
1  20 N  (0.10m) 2 − 1  20 N  (0) 2 = 1 (5 kg)( ) 2 − 1 (5 kg)(0) 2 exerted on the child.
v
2   m   2   m   2 f 2 23. A boy ties a string to a horizontal pipe and attaches a
ball with a weight of 6 N to the other end of the string
15. A 40.0-kg boy steps on a skateboard and pushes off so that the ball is 1 m from the horizontal pipe. He
from the top of a hill. What is the change in the poten- holds the ball so that the string is taut and level with
tial energy of the Earth–boy system as the boy glides the pipe. He then releases the ball. The complete path
down to the bottom of the hill, 4.35 m below the of the ball is a nearly semicircular arc followed by a
starting level?
return swing that nearly reaches the boy, who then
16. How much additional potential energy is stored in a grabs the ball. Use the ball as your system in answer-
spring that has a spring constant of 15.5 N/m if the ing the following questions.
spring is stretched so that the displacement of the end (a) What is the work done on the ball by the gravi-
of the spring moves from 10.0 cm to 15.0 cm, measured tational force and the tension force in the string
from its relaxed equilibrium position? during the complete path of the ball?
2
17. An ideal spring with spring constant k = 2.00 × 10 N/m (A) 31.4 J (B) 10 J (C) 6 J (D) 0 J
is oriented vertically with one end on the ground. (b) If the ball is allowed to continue to swing until it
(a) What distance must the spring compress for a comes to rest, what is the work done by the gravi-
2.00-kg object placed on its upper end to reach tational force?
equilibrium? (A) 31.4 J (B) 10 J (C) 6 J (D) 0 J
(b) By how much does the potential energy stored in (c) If the ball is allowed to continue to swing until
the spring increase during the compression? (Later it comes to rest, what is the work done by the
in this book, we will see why this answer makes tension force?
sense.) (A) 31.4 J (B) 10 J (C) 6 J (D) 0 J
18. A 0.145-kg baseball rebounds off of a wall. The rebound 24. A common classroom demonstration involves holding
speed is one-third of the original speed. By what percent a bowling ball attached by a rope to the ceiling close

Uncorrected proofs have been used in this sample. Copyright © Bedford, Freeman & Worth Publishers.
Distributed by Bedford, Freeman & Worth Publishers. For review purposes only. Not for redistribution.

08_stewart3e_33228_ch07_284_333_8pp.indd 329 20/08/22 8:46 AM