1
Chap.6
HW1
Questions
1.
In three experiments, three different horizontal
forces are applied to the same block lying on the same
countertop.
The force magnitudes are
F
1
= 12 N,
F
2
= 8
N, and
F
3
= 4 N.
In each experiment, the block remains
stationary in spite of the applied force. Rank the forces
according to
(a) the magnitude
f
s
of the static frictional force on the block from the countertop and
(b) the maximum value
f
s,max
of that force, greatest first.
a)
F
net
=
ma
Since the block is stationary
v
= constant and
a
= 0.
Therefore
F

f
s
= 0
⇒
F
=
f
s
.
and the ranking is
F
1
,
F
2
, and
F
3
b)
f
s,max
=
μ
s
F
N
=
s
mg
in this problem and does not depend on the horizontal force.
Therefore they all tie.
2.
In Figure 614, horizontal force
1
F
v
of magnitude 10 N is
applied to a box on a floor, but the box does not slide.
Then,
as the magnitude of vertical force
2
F
v
is increased from zero,
do the following quantities increase, decrease, or stay the
same: (a) the magnitude of the frictional force
s
f
v
on the
box; (b) the magnitude of the normal force
N
F
v
on the box
from the floor; (c) the maximum value
f
s,max
of the magnitude
of the static frictional force on the box? (d) Does the box
eventually slide?
Hint:
Draw a freebody diagram of the mass.
There will be a total of
four forces.
Now apply Newton’s 2
nd
law.
Note that
in a), b), and c)
the box has constant velocity (actually
v
= 0)so
a
= 0.
a) Applying Newton’s 2
nd
law along x:
F
1
–
f
s
= 0
⇒
F
1
=
f
s
F
2
does not affect
f
S
and so
f
S
stays the same.
b) Applying Newton’s 2
nd
law along y:
F
N
–
F
2
– mg = 0
⇒
F
N
=
F
2
+ mg
Thus as
F
2
increases
F
N
also increases.
c) Since
f
s,max
=
s
F
N
,
f
s,max
increases
d) Since
f
s,max
increases and
f
S
is constant, the box will not move.
6.
In Figure 616, a block of mass m is held stationary on a ramp by the
frictional force on it from the ramp. A force
F
v
, directed up the ramp, is
then applied to the block and gradually increased in magnitude from zero.
During the increase, what happens to the direction and magnitude of the
frictional force on the block?