Solutions to Homework #4
Chapter 6
4.
Picture the Problem
: The book slides in a straight line across the top of the tabletop.
Strategy:
The minimum force required to get the book moving is related to the maximum
coefficient of static friction, and the force required to keep the book sliding at constant speed is
equal to the magnitude of the kinetic friction force, from which
µ
k
can be determined.
Solution:
1.
When the book begins sliding,
the applied force equals the maximum
static friction force:
2.
When the book is sliding at constant
speed, the
applied force equals the kinetic friction
force:
Insight:
The coefficient of kinetic friction is usually smaller than the coefficient of static friction.
This is the basic idea behind antilock brakes, which seek to keep the tire of a car rolling so that the
friction between the tire and the road remains in the static regime, where there is a greater force to
stop the car and improved handling during the stop.
10.
Picture the Problem
: The sprinter accelerates in a straight line due to the static friction between
her shoes and the track.
Strategy:
The static friction between her shoes and the track provides the forward force needed to
accelerate the sprinter.
First find her acceleration from equation 212 and then use Newton’s
Second Law to find the minimum coefficient of static friction.
Solution:
1. (a)
Find the sprinter’s
acceleration
from equation 212:
(
29
(
29
2
2
2
2
2
2
0
12 m/s
0
3.6 m/s
2
2
2
20 m
v
v
v
a
x
x


=
=
=
=
∆
∆
2.
Write Newton’s Second Law for the
sprinter:
3.
Solve the equation for
µ
s
:
4. (b)
First, determine the runner’s acceleration from
2
2
0
2
v
v
a x
=
+
∆
. Next, equate the force
associated with this acceleration to the force of static friction between the runner’s shoes and the
track. Solve for
s
μ
.
Insight:
A larger coefficient of friction could produce a larger acceleration, although the sprinter
will likely find the limitations of the human body to exceed the limitations of her shoes!
12 m/s is a
very fast pace, as world class sprinters average about 10 m/s over a 100 m distance (though they
must start from rest, so their final speed is faster than 10 m/s).
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