387
Chapter 5
Additional Applications of Newton’s Laws
Conceptual Problems
1
•
[SSM]
Various objects lie on the bed of a truck that is moving along
a straight horizontal road. If the truck gradually speeds up, what force acts on the
objects to cause them to speed up too? Explain why some of the objects might
stay stationary on the floor while others might slip backward on the floor.
Determine the Concept
Static and kinetic frictional forces are responsible for the
accelerations. If the coefficient of static friction between the truck bed and the
object is sufficiently large, then the object will not slip on the truck bed. The
larger the acceleration of the truck, the larger the coefficient of static friction that
is needed to prevent slipping.
2
•
Blocks made of the same material but differing in size lie on the bed of
a truck that is moving along a straight horizontal road.
All of the blocks will slide
if the truck’s acceleration is sufficiently great. How does the minimum
acceleration at which a small block slips compare with the minimum acceleration
at which a much heavier block slips?
Determine the Concept
The forces
acting on an object are the normal force
exerted by the floor of the truck, the
gravitational force exerted by Earth,
and the friction force; also exerted by
the floor of the truck. Of these forces,
the only one that acts in the direction of
the acceleration (chosen to be to the
right) is the static friction force. Apply
Newton’s second law to the object to
determine how the critical acceleration
depends on its weight.
x
y
n
F
r
g
F
r
s
f
r
Taking the +
x
direction to be to the
right, apply
Σ
F
x
=
ma
x
to the object:
x
ma
mg
F
f
=
=
=
s
g
s
s
μ
⇒
g
a
x
s
=
Because
x
a
is independent of
m
and
F
g
, the critical accelerations are the same.
3
•
A block of mass
m
rests on a plane that is inclined at an angle
θ
with
the horizontal. It follows that the coefficient of static friction between the block
and plane is (
a
)
s
≥
g
, (
b
)
s
= tan
, (
c
)
s
≤
tan
, (
d
)
s
≥
tan
.
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388
Determine the Concept
The forces
acting on the block are the normal force
n
F
r
exerted by the incline, the weight of
the block
g
F
r
exerted by Earth, and the
static friction force
s
f
r
also exerted by
the incline. We can use the definition of
μ
s
and the conditions for equilibrium to
determine the relationship between
s
and
θ
.
s
f
r
g
F
r
n
F
r
x
y
Apply
x
x
ma
F
=
∑
to the block:
0
sin
g
s
=
−
F
f
or, because
F
g
=
mg,
0
sin
s
=
−
mg
f
(1)
Apply
y
y
ma
F
=
∑
in the
y
direction:
0
cos
n
=
−
mg
F
(2)
Divide equation (1) by equation (2)
to obtain:
n
s
tan
F
f
=
Substitute for
f
s
(
≤
s
F
n
) and simplify
to obtain:
s
n
n
s
tan
=
≤
F
F
and
)
(
d
is correct.
4
•
A block of mass
m
is at rest on a plane that is inclined at an angle of
30º with the horizontal, as shown in Figure 556. Which of the following
statements about the magnitude of the static frictional force
f
s
is necessarily true?
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 Spring '09
 Force, Friction

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