Three masses setat rest on a frictionless surface are connected by identical spr

Question

Three masses setat rest on a frictionless surface are connected by identical springs of force constant 100N/m. The right most block is acted upon by a constant 20N force. Starting at time t0. The block no longer oscillate after 10 seconds.

Which of the following will be true after 10seconds

a The reight spring will be stretch twice as far as the left spring

b the left spring will be stretch twice as far as the right spring

c: the right spring will store twice as much potential energy as the left spring

Explanation / Answer

a The reight spring will be stretch twice as far as the left spring

because the acceleration of blocks, a = F/(m1+m2+m3)

= 20/(1+2+2)

= 4 m/s^2

Force exrted by right spring, FR = (m2+m3)*a

= (2+2)*4

= 16 N

Force exerted by left spring, FL = m3*a

= 2*4

= 8 N

we know, extenion is direclty proportional to force exerted by the spring.

so, here, FR = 2*FL

so, extension of right spring = 2*extension of left spring.

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