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Dynamics 2e 667
Chapter 4 Solutions
Problem 4.1
A rocket lifts off with an acceleration
a
. During liftoff, in terms of absolute values, is
the work done on an astronaut by gravity larger than, equal to, or smaller than the work
done by the normal reaction between the astronaut and her or his seat?
Photo credit: NASA.
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
668 Solutions Manual
Problem 4.2
A soft rubber ball bounces against a wall. Assuming that the wall’s deformation due
to the ball’s impact is negligible, does the contact force due to the wall do positive
work, no work, or negative work on the ball?
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
Dynamics 2e 669
Problem 4.3
Determine the kinetic energy of the bodies listed below, when modeled as particles. Express all answers
using both U.S. Customary units and SI units.
(a) A .30-06 bullet weighing 150 gr (1lb D7000 gr) and traveling at 3000 ft=s.
(b) A 25 kg child traveling in a car at 45 km=h.
(c) A 415;000 lb locomotive traveling at 75 mph.
(d) A 20 g metal fragment from a space vehicle traveling at 8000 km=s.
(e) A 3000 lb car traveling at 60 mph.
Solution
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
670 Solutions Manual
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
Dynamics 2e 671
Problem 4.4
A man whose mass is
mD80 kg
is in an elevator that accelerates at
aeD1:5 m=s2
over a distance of
dD2
m. Determine the work done by the weight force acting
on the man and the work done by the normal force the floor of the elevator exerts
on him. Explain why the magnitudes of the work of the forces are not the same.
Solution
672 Solutions Manual
Problem 4.5
Consider a 3000 lb car whose speed is increased by 30 mph.
Modeling the car as a particle and assuming that the car is traveling on a rectilinear and horizontal
stretch of road, determine the amount of work done on the car throughout the acceleration process if the
car starts from rest.
Solution
We model the car as a particle subject to its own weight
mg
, the propulsion force
F
and the reaction from the ground
N
. We will denote by
¿
the starting position
Dynamics 2e 673
Problem 4.6
Consider a 3000 lb car whose speed is increased by 30 mph.
Modeling the car as a particle and assuming that the car is traveling on a rectilinear and horizontal
stretch of road, determine the amount of work done on the car throughout the acceleration process if the
car has an initial speed of 45 mph.
Solution
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permission of McGraw-Hill, is prohibited.
674 Solutions Manual
Problem 4.7
A
75 kg
skydiver is falling at a speed of
250 km=h
when the parachute is
deployed, allowing the skydiver to land at a speed of
4m=s
. Modeling the
skydiver as a particle, determine the total work done on the skydiver from the
moment of parachute deployment until landing.
Solution
Dynamics 2e 675
Problem 4.8
The crate of mass
m
is pushed to the left until the linear elastic spring of constant
k
has compressed a distance
d
from its unstretched length
`0
. The crate is
released from rest, and friction between the crate and the horizontal surface is
negligible.
Using the work-energy principle, determine the speed of the crate at the
instant the spring becomes uncompressed.
Solution
Referring to the bottom part of the figure at the right, we denote by
¿
and
¡
the positions at which the crate is first released and at which
676 Solutions Manual
Problem 4.9
The crate of mass
m
is pushed to the left until the linear elastic spring of constant
k
has compressed a distance
d
from its unstretched length
`0
. The crate is
released from rest, and friction between the crate and the horizontal surface is
negligible.
Using the work-energy principle, determine the value of
k
so that the crate is
moving at
3m=s
the instant the spring becomes uncompressed. Use
mD20 kg
and dD0:75 m.
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permission of McGraw-Hill, is prohibited.
