A bench of mass 40 kg is brought from the first floor of the school to the second floor. The height difference between the floors is 3m.

Calculate the work done against the gravitational force when the bench is raised up.

Information from the question:-

Mass of the bench = 40 kg

Height difference or the displacement of the bench = 3 m

Note:- Always try to extract as much as information from the question as you can.

There is also an important thing mentioned in the question, that is we have to find work done against the gravitational force not any other force. So, gravitational force is always acting downward or we can say toward the centre of the earth, so if bench is transferred from one floor to another then it has done work against gravitational force.

Amount of work done = force applied × displacement of the object

We have to find the force applied on the body to find out the amount of work.

As, you know force applied = mass of the body × acceleration of the body

Hence, the body is working against the gravitational pull/force which is acting downward while the body is moving upward, so the acceleration of the body is the negative of the gravitational acceleration. Why negative, because negative sign indicate that the force is applied against the gravity or the motion is against the gravity.

Acceleration of the body = -g {g is gravitational acceleration}

= -9.8 m/s²

Hence

Force applied = 40 × (-9.8)

= -39.2 kg m/s²

Also,

Amount of work done = Force applied × displacement of the object

= 39.2 × 3

= -117.6 kg m²/s²