A 0.5 kg ball of negligible size is fired up a vertical
track of radius 1.5 m using a spring plunger with k =
500 N/m.
The plunger keeps the spring compressed
0.08 m when s = 0 (i.e., after the ball leaves the spring
is still compressed 0.08 m). What is the distance
s
the
plunger must be pulled back and released so the ball
will begin to leave the track when θ = 135°.
What is your first step?
IC8.1 Pinball
Solution:
Problem Type:
Find:
Given:
m = 0.5 kg, k=500N/m, r=1.5m, Plunger keeps spring
compressed 0.08m when handle is not pulled.
s, so that ball leaves track at θ=135º
Work Energy and F=ma to determine ball leaving track
Draw FBD and MAD at θ=135º
T
1
+ V
1e
+ V
1g
+ U
12
= T
2
+ V
2e
+ V
2g
Which are zero?
0
0
J
V
V
mgh
V
g
g
g
56
.
12
)
45
sin
5
.
1
5
.
1
(
81
.
9
5
.
0
2
2
2
=
°
+
=
=
Apply Equations of motion in the Normal direction
In order to find the initial spring compression to give this speed we need to use Work
Energy. Add a datum to the figure and write out the WE equation
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 Spring '05
 staff
 Force, Friction, Normal Force, ball, 1.5 m, 0.08M

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