A person lifts a 6.5 kg box of bricks a vertical distance of 1.20 m and then carries the box horizontally a distance of 13.30 m.

Question

(a) How much work is done by the person in the process?

(b) How much work is done by gravity in the process?

Answer 1

Recall that the Work = change in KE. When mechanical energy is conserved, and the only energy are KE and PE, then Work =-change in PE.

When a person lifts the block, the block has more potential energy. Therefore, the person does positive work on the block.

work = m g h = (6.5 kg) (9.81 m/s^2) (1.2 m) work = 76.518 joules. Do not forget to account for significant digits in your final answer!

When the block is being raised, the force of gravity opposes the motion. Therefore the force of gravity does negative work on the block. work = - (force) (h) work = - m g h work = -(6.5 kg) (9.81 m/s^2) (1.2 m) work = -76.518 joules. Do not forget to account for significant digits in your final answer!

Note that when the block is moved horizontally, the potential energy does not change. Therefore, there is no work done on the block when it moves horizontally. This does not mean that at all times the work is zero. It won't be -- we will be doing work to get the object to move and then will be doing work to get the object to slow down to a stop. But these two works will cancel out!

Answer 2

Gravity is what is called a "conservative force". This means the total work done on an object between two points is independent of the path taken. Gravity always points downwards so any horizontal components of displacement don't contribute to the total work done since W=Fdcosθ and cos(90)=0. This means the gravitational work done only depends on the vertical displacement. The exact equation for the total work done by gravity is W=-mgh where h is the total vertical displacement. In this scenario, the block is lifted a vertical distance of 1.20m so the total work done by gravity is

W_grav=-(6.5 kg)(9.8 m/s^2)(1.20 m)

W_grav= -76.44 J

so the answer for b) is -76.44J

Gravity does negative work on the object since the force acts in the opposite direction of the displacement. This means that the person has to exert the same amount of work in the positive direction to keep the box in equilibrium. So a) is also 76.44J

Another way to understand why the answer for a) is the same as b) is because the person applies an upwards force which will act as the box's normal force. It's magnitude must be equal in magnitude and opposite in direction to the gravitiational force to make sure the box doesn't accelerate. From this it should follow that the work is equal in magnitude but of opposite sign