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A block of mass 2.0 kg is pushed down an...

A block of mass 2.0 kg is pushed down an inclined plane of inclination `37^0` with a force of 20N acting parallel to the incline. It is found that the block moves on the incline with an acceleration of `10 m/s^2`. If the block started from rest, find the work done a. by the applied force in the first second b. by the weight of the block in the first second and c. by the frictional force acting on the block in the first second. Take `g=10 m/s^2`.

Text Solution

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Displacement of block in `1s`
`s=1/2xx10xx1^2=5m`

The work done by the applied force in the first second,
`W_F=vecF*vecs=F*scostheta=20xx5=100J`
The work done by the weight of th block in the first second =Component of weight in the direction of displacement x Displacement
`W_(weight)=(mg sin theta)xxd=(2xx10xx3/5)xx5=60J`
Now we need to calculate friction force acting on block. For this, we need to write
Equation of motion of block, `mgsintheta+F-f=ma`
`2xx10xx3/5+20-f=2xx10impliesf=12N`
The work done by the frictional force acting on the block in the first second,
`W_(f riction)=vecf*vecd=f*dcos180^@=-fxxd=-60J`
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