259
Chapter 5
Applications of Newton’s Laws
Conceptual Problems
1
•
Determine the Concept
Because the
objects are speeding up (accelerating),
there must be a net force acting on them.
The forces acting on an object are the
normal force exerted by the floor of the
truck, the weight of the object, 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 in the free-body
diagram) is the friction force.
.
accelerate
object to
the
causes
that
force
the
be
must
truck
the
of
floor
the
and
object
e
between th
friction
of
force
The
*2
•
Determine the Concept
The forces acting
on an object are the normal force exerted
by the floor of the truck, the weight of the
object, 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 in
the free-body diagram) is the friction force.
Apply Newton’s 2
nd
law to the object to
determine how the critical acceleration
depends on its weight.
Taking the positive
x
direction to be
to the right, apply
Σ
F
x
=
ma
x
and
solve for
a
x
:
f
=
µ
s
w
=
µ
s
mg
=
ma
x
and
a
x
=
µ
s
g
same.
the
are
ons
accelerati
critical
the
and
of
t
independen
is
Because
w,
m
a
x

This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*
Chapter 5
260
3
•
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
r
m
exerted by the earth, and the
static friction force
s
f
r
exerted by an
external agent. We can use the definition of
µ
s
and the conditions for equilibrium to
determine the relationship between
µ
s
and
θ
.
Apply
x
x
ma
F
=
∑
to the block:
f
s
−
mg
sin
θ
= 0
(1)
Apply
y
y
ma
F
=
∑
in the
y
direction:
F
n
−
mg
cos
θ
= 0
(2)
Divide equation (1) by equation (2)
to obtain:
n
s
tan
F
f
=
θ
Substitute for
f
s
(
≤
µ
s
F
n
):
s
n
n
s
tan
µ
µ
θ
=
≤
F
F
and
correct.
is
)
(
d
*4
•
Determine the Concept
The block is in
equilibrium under the influence of
,
n
F
r
,
m
g
r
and
;
s
f
r
i.e.,
n
F
r
+
g
r
m
+
s
f
r
=
0
We can apply Newton’s 2
nd
law in the
x
direction to determine the relationship
between
f
s
and
mg
.
Apply
0
=
∑
x
F
to the block:
f
s
−
mg
sin
θ
= 0
Solve for
f
s
:
f
s
=
mg
sin
θ
and
correct.
is
)
(
d