A block having mass 4 kg is pushed down along an inclined...

A block having a mass of 4 kg is pushed down along an inclined plane of inclination 53° with a force of 40 N 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 initial velocity of the block is zero, then find the work done (a) by the applied force on the block in the 2 seconds from the starting of motion, (b) by the weight of the block in the 2 seconds from the starting of motion, (c) by the frictional force acting on the block in the 2 seconds from the starting of motion.

Transcript

00:01 A block having a mass of 4kg is pushed down along an inclined plane of inclination 53 degrees with a force of 40 newton acting parallel to the incline and it is found that the block moves on the incline with acceleration of 10 m per second square.

00:21 And the initial velocity of block is zero.

00:24 Using this we have to find the work done by applied force on the block in 2 seconds from the starting of the motion.

00:31 So the forces are applied force parallel to the incline.

00:40 Friction force will be opposite to the motion.

00:43 So it will be up the incline and gravitation forces vertically downward.

00:49 Now the displacement of the block is along the incline.

00:56 So the displacement can be found using equation of kinematics.

01:05 So displacement is equal to initial velocity into time t plus half.

01:10 Acceleration into time t square initial velocity is zero acceleration is 10 and time t is two seconds so we get displacement 20 meters so for the first part we have to find the work done by the applied force so applied forces along the incline and displacement is also down the incline so applied force and displacement are in the same direction so angle between them is zero degree so work done by applied force is force times displacement times cost theta force is 40 newton displacement is 20 meters and theta is zero degree so we get the work done 800 jule now for part b we have to find the work done by the weight of the block so weight is mg which is acting in the downward direction vertically downward and displacement is along the incline so angle between the displacement and weight will be alpha and this angle will be equal to 90 degree minus theta so alpha is 90 minus theta theta is angle of incline which is 53 degrees so this is 37 degrees now the angle between displacement and weight is alpha so worked in by the weight is worked in by gravity so this is equal to force m g times displacement times cos alpha where alpha is angle between displacement and force mass is 4 kg g is 9 .8 displacement is 20 meters alpha is 37 degrees so we get 626 j now to find the work done by friction force we will use the work energy theorem...

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