This preview shows pages 1–2. Sign up to view the full content.
Ph 111.01
November 7, 2008
PS 10c (27)
Problem 1 = Walker P. 1325.
The pistons in an internal combustion
engine undergo a motion that is approximately simple harmonic. The
amplitude of motion is
4.1
cm, and the engine runs at
1800
rev/min.
(a) Find the maximum acceleration of the pistons.
m/s
2
(b) Find the maximum speed of the pistons.
m/s
Solution.
We are going to need
ω
,
the angular frequency:
1 min
2 rad1 rev
1800 rev/min
188.5 rad/sec
60 sec
π
==
Now, the equations describing simple harmonic motion are
()
2
2
cos
cos
eq. (13.2)
sin
eq. (13.6)
cos
eq. (13.8)
xA
t A
t
T
vA
t
aA
t
ωω
=−
(a)
The amplitude of the acceleration is seen to be
(
)
2
22
max
0.041 m 188.5 rad/s
1457 m/s
=
(b)
Similarly, the amplitude of the velocity is
( )( )
max
0.041 m 188.5 rad/s
7.73 m/s
=
Problem 2 = Walker P. 1333.
Two people with a combined mass of
139
kg hop into an old car with
worn out shock absorbers. This causes the springs to compress by
8.80
cm. When the car hits a bump
in the road it oscillates up and down with a period of
1.68
s.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Fall '08
 Staff

Click to edit the document details