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Question
A block of mass 5 kg is suspended from the end of a vertical spring which is stretched by 10 cm under the load of the block. The block is given a sharp impulse from below, so that it acquires an upward speed of 2 m/s. How high will it rise? Take g = 10 m/s2.
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Solution
Given,
Mass of the block, m = 5 kg
Compression in the string with the load, x = 10 cm = 0 . 1 m
Initial speed in upward direction, ν = 2 m/s,
h = ?, g = 10 m sec2
So, F = kx = mg
⇒`k = (mg)/x`
⇒ `50/0.1 = 500` N/m
Total energy just after the impulse,
`E = 1/2 mv^2 + 1/2 kx^2` ...(i)
Total energy at a height h
= `1/2 k(h - x)^2 + mgh`
On solving, we get:
h = 0.2 m
h = 20 cm
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