PHY2053 RECITATIONS, SPRING 2011
Recitation 8
(Chapters 67) Feb. 14Mar. 18
52. Starting from rest, a 93kg firefighter slides down a fire pole. The average frictional force
exerted on him by the pole has a magnitude of 810 N, and his speed at the bottom of the pole is
3.4 m/s. How far did he slide down the pole?
REASONING
As the firefighter slides down the pole from a height
h
0
to the ground (
h
f
= 0 m), his
potential energy decreases to zero. At the same time, his kinetic energy increases as he speeds
up from rest (
v
0
= 0 m/s) to a final speed
v
f
,.
However, the upward nonconservative force of
kinetic friction
f
k
, acting over a downward displacement
h
0
, does a negative amount of work on
him:
(
29
nc
k
0
k 0
cos180
W
f
h
f h
=
= 
o
(Equation 6.1). This work decreases his total mechanical
energy
E
. Applying the workenergy theorem (Equation 6.8), with
h
f
= 0 m and
v
0
= 0 m/s, we
obtain
(
29
(
29
2
2
1
1
nc
f
f
0
0
2
2
W
mv
mgh
mv
mgh
=
+

+
(6.8)
{
(
29
(
29
nc
0
f
2
2
1
1
k 0
f
0
f
0
2
2
0 J
0 J
W
E
E
f h
mv
mgh
mv
mgh

=
+

+
=

1 4 2 4 3
1 442 4 43
(1)
SOLUTION
Solving Equation (1) for the height
h
0
gives
(
29
(
29
2
2
2
f
1
1
0
k 0
f
0
k
f
0
2
2
k
or
or
2
mv
mgh
f h
mv
h mg
f
mv
h
mg
f

=

=
=

The distance
h
0
that the firefighter slides down the pole is, therefore,
(
29
(
29
(
29
(
29
2
0
2
93 kg
3.4 m/s
5.3 m
2
93 kg
9.80 m/s
810 N
h
=
=

61. A truck is traveling at 11.1 m/s down a hill when the brakes on all four wheels lock. The hill
makes an angle of 15.0° with respect to the horizontal. The coefficient of kinetic friction
between the tires and the road is 0.750. How far does the truck skid before coming to a stop?
REASONING
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 Spring '08
 Staff
 Energy, Force, Friction, Potential Energy, Wnc

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