Physics Solutions Manual

Chapter 4 continued
Solve equation 2 for T:
T F Earth’s mass on 3.0-kg block
m 3.0-kg block a
m 3.0-kg block g m 3.0-kg block a
m 3.0-kg block (g a)
(3.0 kg)(9.80 m/s 2 2.4 m/s 2 )
37 N
Thinking Critically
pages 115–116
93. Formulate Models A 2.0-kg mass, m A ,
and a 3.0-kg mass, m B , are connected to a
lightweight cord that passes over a frictionless
pulley. The pulley only changes the
direction of the force exerted by the rope.
The hanging masses are free to move.
Choose coordinate systems for the two
masses with the positive direction being
up for m A and down for m B .
a. Create a pictorial model.
x
b. Create a physical model with motion
and free-body diagrams.
x a
m A
F T
m Ag
m A
m B
m B
c. What is the acceleration of the smaller
mass?
ma F net where m is the total mass
being accelerated.
F T
m Bg
a
For m A , m A a F T m A g
For m B , m B a F T m B g
F T m B g m B a m B (g a)
Substituting into the equation for
m A gives
m A a m B g m B a m A g
or (m A m B )a (m B m A )g
Therefore a mA m g
B
(9.80 m/s 2 )
2.0 m/s 2 upward
94. Use Models Suppose that the masses in
problem 93 are now 1.00 kg and 4.00 kg.
Find the acceleration of the larger mass.
m B m A
a mA m g
B
(9.80 m/s2
)
1.00 kg 4.00 kg
5.88 m/s 2 downward
95. Infer The force exerted on a 0.145-kg
baseball by a bat changes from 0.0 N to
1.010 4 N in 0.0010 s, then drops back to
zero in the same amount of time. The baseball
was going toward the bat at 25 m/s.
a. Draw a graph of force versus time. What
is the average force exerted on the ball
by the bat?
1.010 4
0.510 4
Force (N) 4.00 kg 1.00 kg
1
Fave F
2 peak
0.0 0.5 1.0 1.5 2.0
(1.0104 1
N)
2
5.010 3 N
m B m A
3.0 kg 2.0 kg
2.0 kg 3.0 kg
Time (ms)
82 Solutions Manual Physics: Principles and Problems
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