Chapter 5 Solutions
Problem 5.1
An airplane performs a turn at constant speed and elevation so as to
change its course by
180ı
. Let
A
and
B
designate the beginning and
endpoints of the turn. Assuming that the change in mass of the plane
due to fuel consumption is negligible, is the airplane’s momentum at
A
different from the airplane’s momentum at
B
? In addition, again
neglecting the change in mass between
A
and
B
, is the total work done
on the plane between Aand Bpositive, negative, or equal to zero?
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Dynamics 2e 851
Problem 5.2
In a simple force-controlled experiment, two curling stones
A
and
B
are
made to slide over a sheet of ice. Initially,
A
and
B
are at rest on the start
line. Then they are acted upon by identical and constant forces
E
F
, which
continually push
A
and
B
all the way to the finish line. Let
EpAFL
and
EpBFL
denote the momentum of
A
and
B
at the finish line, respectively. Assume
that the forces
E
F
are the only nonnegligible forces acting in the plane of
motion. If mA<m
B, which of the following statements is true?
(a) jEpAFL j<jEpBFL j.
(b) jEpAFL jDjEpBFL j.
(c) jEpAFL j>jEpBFL j.
(d)
There is not enough information given to make a comparison between
jEpAFL jand jEpBFL j.
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Problem 5.3
A train is moving at a constant speed
vt
relative to the ground, when a person who is initially at rest
(relative to the train) starts running and gains a speed
v0
(relative to the train) after a time interval
t
. Had
the person started from rest on the ground (as opposed to on the moving train), would the magnitude of the
total impulse exerted on the person during
t
be smaller than, equal to, or larger than the impulse needed
to cause the same change in relative velocity in the same amount of time on the moving train? Assume that
the person always moves in the direction of motion of the train.
Solution
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Dynamics 2e 853
Problem 5.4
A train is decelerating at a constant rate, when a person who is initially at rest (relative to the train) starts
running and gains a speed
v0
(again relative to the train) after a time interval
t
. Had the person started
from rest on the ground (as opposed to on the moving train), would the magnitude of the total impulse
exerted on the person during
t
be smaller than, equal to, or larger than the impulse needed to cause the
same change in velocity in the same amount of time on the moving train? Assume that the person always
moves in the direction of motion of the train and that the train does not reverse its motion during the time
interval t.
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Problem 5.5
A car of mass
m
collides head-on with a truck of mass
50m
. What is the ratio between the magnitude of
the impulse provided by the car to the truck and the magnitude of the impulse provided by the truck to the
car during the collision?
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Dynamics 2e 855
Problem 5.6
The spacecraft shown is out in space and is far enough from any other mass (e.g., planets, etc.) so as not to
be affected by any gravitational influence (i.e., the net external force on the rocket is approximately zero).
The system (i.e., the spacecraft and all its fuel) is at rest when it starts at
A
, and it thrusts all the way to
B
along the straight line shown using internal chemical rockets (which work by ejecting the fuel mass at very
high speeds out the tail of the rocket). We are given that the mass of the system at
A
is
m
and that it has
ejected half of its mass in thrusting from
A
to
B
. What will be the location of the system’s mass center
when the spacecraft reaches B?
Solution
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Problem 5.7
Use the definition of impulse given in Eq. (5.5) to compute the
impulse of the forces shown during the interval 0t2s.
Solution
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Dynamics 2e 857
Problem 5.8
The mass of the Earth is
meD5:9736⇥1024 kg
. Modeling the Earth (with everything in and on it) as an
isolated system and assuming that the center of the Earth is also the center of mass of the Earth, determine
the displacement of the center of the Earth due to
(a) a 2m jump off the surface by an 85 kg person;
(b) the Space Shuttle, with a mass of 124;000 kg, reaching an orbit of 200 km;
(c) 170;000 km3
of water being elevated
50
m (these numbers are estimates based on publicly available
information about the Aswan Dam at the border between Egypt and Sudan). Use
1g=cm3
for the
density of water.
Solution
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Problem 5.9
A
200 lb
skydiver deploys the parachute after
10
s of free fall and concludes
the jump by touching down with a speed of
15 ft=s
. Model the motion of the
skydiver as being a vertical drop from rest.
Neglecting the change in acceleration due to gravity with elevation, deter–
mine the impulse provided by gravity to the skydiver during free fall.
Solution
We model the skydiver as a particle subject only to the weight
W
and the aerodynamic force
Fp
due to the parachute (taken to be equal to zero during free fall). Using the component
Dynamics 2e 859
Problem 5.10
A
200 lb
skydiver deploys the parachute after
10
s of free fall and concludes
the jump by touching down with a speed of
15 ft=s
. Model the motion of the
skydiver as being a vertical drop from rest.
Determine the impulse provided by all the forces acting on the skydiver
from the beginning of the jump to touchdown.
Solution
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