Question

Mark and David are loading identical cement blocks onto David’s pickup truck. Mark lifts his block straight up from the ground to the truck, whereas David slides his block up a ramp containing frictionless rollers. Which statement is true about the work done on the block–Earth system? (a) Mark does more work than David. (b) Mark and David do the same amount of work. (c) David does more work than Mark. (d) None of those statements is necessarily true because the angle of the incline is unknown. (e) None of those statements is necessarily true because the mass of one block is not given.

Short answer

The correct option is (b): Mark and David do the same amount of work.

Step-by-step solution

Given information

Mark lifts his block straight up from the ground to the truck.

David slides his block up a ramp containing frictionless rollers.

Gravitational potential energy 

When a body of a certain mass is moved in the vertical direction, the change in the energy associated with the body is described as the ‘gravitational potential energy’.

By increasing the mass of the body and the height to which the body is lifted, the value of gravitational potential energy can be increased.

Work done on the block–Earth system

According to the question,Mark lifts his block straight up from the ground to the truck, so the work done on the system by Mark would be equal to theincrease in the gravitational potential energy.

The formula for the work done on the system by Mark to lift the block from the ground is as follows:

$\mathrm{Work}\mathrm{done}\mathrm{by}\mathrm{Mark}=\left(\mathrm{Block}\text{'}\mathrm{s}\mathrm{weight}\right)\times \left(\mathrm{Truck}\text{'}\mathrm{s}\mathrm{height}\mathrm{from}\mathrm{ground}\right)$

David slides his block up a ramp containing frictionless rollers, so there is no change in the kinetic energy while sliding the block up the ramp.

Then, the work done on the system by David will be equal to theincrease in the gravitational potential energy.

$\mathrm{Work}\mathrm{done}\mathrm{by}\mathrm{David}=\left(\mathrm{Block}\text{'}\mathrm{s}\mathrm{weight}\right)\times \left(\mathrm{Truck}\text{'}\mathrm{s}\mathrm{height}\mathrm{from}\mathrm{ground}\right)$

Comparing work done by Mark and David,

$\mathrm{Work}\mathrm{done}\mathrm{by}\mathrm{Mark}=\mathrm{Work}\mathrm{done}\mathrm{by}\mathrm{David}$

Hence, the correct option is (b): Mark and David do the same amount of work.