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.
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 Fall '08
 Staff
 Energy, Force, Internal combustion engine, pistons

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