Question

A man weighing 180 lbf pushes a block weighing 100 lbf along a horizontal plane. the dynamic coefficient of friction between the block and plane is 0.2. assuming that the block moves at a constant speed, how much work is required to move the block 100 ft considering the (a) the block and (b) the man as the system.

Answer 1

To calculate the work required to move the block 100 ft, we need to first find the net force acting on the block. The force of friction is equal to the dynamic coefficient of friction multiplied by the normal force. When considering the block and the man as separate systems, the work required can be calculated using the formula: work = force x distance.

Step-by-step explanation:

To calculate the work required to move the block 100 ft, we need to first find the net force acting on the block. Since the block is moving at a constant speed, the net force must be zero. The force of friction is equal to the dynamic coefficient of friction multiplied by the normal force. The normal force is the weight of the block, which is 100 lbf. So, the force of friction is 0.2 times 100 lbf, which is 20 lbf.

(a) When considering the block as the system, the work done to overcome friction can be calculated using the formula: work = force x distance. The force of friction is 20 lbf and the distance is 100 ft. So, the work required is 20 lbf x 100 ft = 2000 lbf-ft.

(b) When considering the man as the system, we need to take into account both the forces exerted by the man and the force of friction. The man exerts a force of 180 lbf and the force of friction is 20 lbf. Since the block is moving at a constant speed, the work done by the man is equal to the work done against friction. So, the work required is 180 lbf x 100 ft = 18000 lbf-ft.

Answer 2

The first thing you should know is that the work is defined as:
W = F * d
Where
F = force
d = displacement
We have then
(a) the block
F = (0.2) * (100) = 20
d = 100
W = (20) * (100) = 2000 ft.lbf
(b) the man as the system.
F = (0.2) * (100 + 180) = 56
d = 100
W = (56) * (100) = 5600 ft.lbf
answer:
(a) 2000 ft.lbf
(b) 5600 ft.lbf