Laws of Motion

Classical Mechanics Level pending

A block of weight 4 k g 4kg is resting on a smooth horizontal plane. If it is struck by a jet of water at the rate of 2 k g s − 1 2kg{s}^{-1} and at the speed of 10 m s − 1 10 m{s}^{-1} , then find the initial acceleration of the block.

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10m/s^2 2.5m/s^2 15m/s^2 1m/s^2 5 m/s^2

Anandhu Raj by Anandhu Raj , 23, India

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2 solutions

Anandhu Raj
Apr 15, 2016

Force exerted on the block by jet of water, F = d ( m v ) d t = v d m d t = 10 × 2 = 20 N F=\frac{d(mv)}{dt} =v\frac{dm}{dt}=10\times2=20N

∴ \therefore Acceleration, a = F m = 5 m s − 2 a=\frac{F}{m}= 5m{s}^{-2}

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To bring a dm with velocity 10m/s we require dm (10)/dt force for dt time. But dm/dt=2. Thus assuming water to be colliding inelastically , by newtons 3 rd law force on the object is also the same. The acceleration is different because of mass=4kg. Thus it has acceleration 5m/ss.

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