How to Calculate the Work Required to Move a Block at a Constant Speed?

The work required to move the block at a constant speed when the man is pushing it can be calculated by determining the force needed to overcome friction and the distance the block is moved. Given that the block is moving at a constant speed, the work done on the block is zero.

Calculating the Work done by the Man:

Firstly, we need to calculate the force of friction between the block and the horizontal plane using the formula f = µN, where N is the normal force and µ is the coefficient of friction. Since the block is moving horizontally, the normal force is equal to the weight of the block, N = mg = 45 kg x 9.8 m/s² = 441 N. Therefore, the force of friction is f = 0.2 x 441 N = 88.2 N.

Assuming the block is moving at a constant speed means that the man is exerting a force equal to the frictional force. The work done by the man in pushing the block can be calculated using the formula W = Fd, where F is the force applied and d is the distance moved. Therefore, the work done by the man is W = f x d = 88.2 N x 30 m = 2646 J.

Work done on the Block as the System:

Since the block is moving at a constant speed, its kinetic energy remains constant, and therefore the work done on the block is zero. This is because the net work done on an object moving at a constant speed is zero, meaning the block's kinetic energy does not change.

In conclusion, the work required to move the block at a constant speed when considering the man and the block as separate systems is 2646 J.