A 200-g block is dropped onto a vertical spring with spring constant k =120.0 N/
ID: 1331450 • Letter: A
Question
A 200-g block is dropped onto a vertical spring with spring constant k =120.0 N/m. The block becomes attached to the spring, and the spring compresses 44.4 cm before momentarily stopping. While the spring is being compressed, a) what work is done on the block by its weight?
8.71×10-1 J
b) While the spring is being compressed, what work is done on the block by the spring force?
-1.18×101 J
c) What is the speed of the block just before it hits the spring? (Assume that friction is negligible.)
11.27m/s
d) If the speed at impact is doubled, what is the maximum compression of the spring?
You are correct.Explanation / Answer
(a)
Work done by gravity:
W = m g d
= (0.200 kg ) (9.8 ) ( 0.444 m)
= 0.870 J
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(b)
Work done by spring:
W = - ( 1/2 ) ( k d2)
= - ( 1/2 ) ( 120 ) ( 0.444 m)2
= - 11.8 J
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(c)
If the block had speed V0 initially and rest at finally
Apply work-energy theorem
Wg + WS = - 1/2 . m . V2
0.87 J - 11.8 J = - 1/2 . 0.200 kg . V2
Solve for velocity
V = 10.46 m/s
In 3 significant figures, V = 10.5 m/s
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