To launch a 100-g toy car so it has a speed of 1 m/s when it is just launched, a
ID: 1606080 • Letter: T
Question
To launch a 100-g toy car so it has a speed of 1 m/s when it is just launched, a spring with an appropriate spring constant is used. This spring will be compressed 10-cm from its natural length when it is ready to launch. The stage is oriented at an angle of 45° above the horizontal. Determine the spring constant. Show work.
A) 23.9 N/m
B) 10.0 N/m
C) 1.0 N/m
D) 13.9 N/m
E) 3.9 N/m
Initial state: Final state: Spring is compressed Spring is released Car is at rest. y and launches car off ramp EarthExplanation / Answer
Applying work - energy theorm ,
Net worl done on car = change in KE
work done by spring force + work done by gravity = change in KE
(k x^2 / 2) + (- m g x sin45) = m v^2 /2 - 0
k (0.10^2) + (- 2 x 0.100 x 9.8 x 0.10 x sin45) = 0.100 x 1^2 / 2
0.01 k = 0.239
k = 23.9 N/m
Ans(A)
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