Question

When a mass of 2 kg is suspended
slowly by a spring with its upper end
fixed to the ceiling, the spring stretches
by 1 cm. Work done by the spring is
(g=10ms

Answer 1

Given ,

1. Mass suspended = 2 kg
2. spring streaches x = 1 cm = 0.01 m
3. g = 10m/s²

To find : work done by spring " Wsp"

solution :

formula to be used :

1. $f = - kx \: .......(1)$
2. $wext = ∫f \: dx \: .........(2)$
3. Wsp = - Wext .....(3)

From equation 1 and 2 we get

$wext \: = ∫kx \: dx = k \frac{ {x}^{2} }{2} .....(4)$

$mg = kx \: ....(5)$

from equation 4 and 5 we get ,

$wext = \frac{mgx}{2} = \frac{2 \times 10 \times 0.01}{2} = 0.1N/m$

from equation 3 we get ,

Wsp = - 0.1N/m

Hence work done by spring is - 0.1 N/m

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