Question

A man of mass m speeds up while running from rest to a speed v in a straight track along an inclined plane, after rising through a height h.
${W_{gravity}}$= work done by gravity on the man.
${W_{friction}}$​ = work done by gravity on the man.
${W_{man}}$= work done by man.
Which of the following options is correct regarding the various work done?
$
  A.{W_{gravity}} = - mgh \\
  B.{W_{friction}} > 0 \\
  C.{W_{man}} = mgh + \dfrac{1}{2}m{v^2} \\
  D.{W_{friction}} = 0 \\
$

Answer 1

Hint: To get this problem solved we need to know that work done by gravity in going from down to up will be negative and work done by man will be change in total energy and remember total work done is the force multiplied by the displacement of object if the displacement is perpendicular to force then the work done is zero.

Complete step-by-step answer:
This problem will have multiple answers we can from observing options.
Work done by gravity in going from down to up is negative since the force of gravity is directed downwards and the displacement of the body is opposite to the force.

The option A, ${W_{gravity}} = - mgh$ is correct where mg is the force and h is the height body goes up from the ground.

Here work done by man is the change in potential and kinetic energy.
So, the change is potential energy is mgh since earlier height was zero then it is h so the change in potential energy is mgh and that of kinetic energy is $\dfrac{1}{2}m{v^2}$ since it changes speed from 0 to v so the change in KE is $\dfrac{1}{2}m{v^2}$.
So, the option C, ${W_{man}} = mgh + \dfrac{1}{2}m{v^2}$ is the correct option.
Also here work done by friction is zero since there is no frictional force and if there is then there is no displacement in the direction of that force.
So, the option D, ${W_{friction}} = 0$ is correct.

The correct options are A, B and D.

Note – Whenever you face such problems observe the forces and displacement of the body due to those forces and then see the change in work done. Doing this will solve all such types of problems and will give you the right answer.