A block of mass 10 kg is pushed by a force F on a horizontal rough plane is moving with acceleration 5ms^(-2)…

Q: A block of mass 10 kg is pushed by a force F on a horizontal rough plane is moving with acceleration 5 ms-2. When force is doubled, its acceleration becomes 18 ms-2 . Find the coefficient of friction between the block and rough horizontal plane. (g = 10 ms-2).

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Sol: On a rough horizontal plane, acceleration of a block of mass ‘m’ is given by

$\large a = \frac{F}{m} – \mu_k g $ …..(i)

Initially, a = 5 ms-2

$\large 5 = \frac{F}{10} – \mu_k \times 10 $ …..(ii) (∵ m = 10 kg)

When forced is doubled a = 18 ms-2

$\large 18 = \frac{2F}{10} – \mu_k \times 10 $ …..(iii)

Solving (ii) & (iii)

μk = 8/10 = 0.8.