Chapter 13 Solutions - Mosinee School District

Chapter 13
1
(b) The maximum speed occurs at the equilibrium position where PE s = 0. Thus, E mv
2
2 max
, or
v
max
2 E k
250 N m
A 0.035 m 0.78 m s
m m
0.50 kg
(c) The acceleration is a F/ m kx/
m . Thus, a = a max at x = x max = A.
a
max
k A k
m m
A
250 N m 0.035 m 18 m s
0.50 kg
2
13.19 The maximum speed occurs at the equilibrium position and is
v
max
k
m
A
Thus,
m
kA
v
2
2
max
16.0 N m 0.200 m
0.400 m s
2
2
4.00 kg ,
and
Fg
mg
4.00 kg 9.80 m s2
39.2 N
13.20
k
v A x
m
2 2
10.0 N m
50.0 10
-3
kg
2 2
0.250 m 0.125 m 3.06 m s
13.21 (a) The motion is simple harmonic because the tire is rotating with constant velocity and you are looking at the
uniform circular motion of the “bump” projected on a plane perpendicular to the tire.
(b)
Note that the tangential speed of a point on the rim of a rolling tire is the same as the translational speed of the
axle. Thus, v v 3.00 m s and the angular velocity of the tire is
t
car
v t
r
3.00 m s
0.300 m
10.0 rad s
Therefore, the period of the motion is
T
2 2
10.0 rad s
0.628 s
Page 13.8