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Asked by Harshhacker2580 | 20 Apr, 2020, 04:34: PM
Free body diagram of block of mass m is shown in above figure .
The force acting are normal force N which is due to acceleration of van .

Due to acceleration of van, block of mass m pressing the van with same acceleration that give normal force N = m×a

Velocity of Van as a function of time , v(t) = 9t - t2 + 10

Acceleration of van , a = dv/dt = ( 9 - 2 t )  ...................(1)

Acceleration at time t = 2 s is given by , a = 9 - 2(2) = 5 m/s2

Friction force μN balances the weight mg .

Hence we get , μ N = μ m a =  m g    or  μ a =  g  or  μ =  g / a = 10/5 = 2

static friction force = μ N = μ m a = 100 N

if we substitute μ =2 , a = 5 then  we get,  m = 100 / ( μ a ) = 100 / ( 2× 5 ) = 10 kg
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at t= 3, acceleration of van can be obtained from eqn.(1),  a = 9 - 2(3) = 3 m/s2

friction force  f = μ m a = 2 × 10 × 3 = 60 N

acceleration a' of block is obtained from ,  mg - f = ma'

a' = ( m g - f ) / m  = ( 100 - 60 ) / 10 = 4 m/s2

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Answered by Thiyagarajan K | 20 Apr, 2020, 08:37: PM

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