Question Video: Finding the Mass of a Body given the Work Done by a Force Mathematics

Video Transcript

A construction worker of mass 100 kilograms is carrying some bricks up a ladder of height 15 meters. If the work done by the construction worker in climbing the ladder is 20,433 joules, find the mass of the bricks. Take 𝑔 to equal 9.8 meters per second squared.

Okay, so let’s say that this is our ladder, which we’re told has a height we’ll call ℎ of 15 meters, and that on this ladder there’s a construction worker with a mass we’ll call 𝑚 sub 𝑐, who has climbed all the way to the top carrying a load of bricks with a mass we’ll call 𝑚 sub 𝑏. Knowing that this construction worker did 20,433 joules of work in climbing this ladder with this load of bricks, we want to determine the mass of the bricks, 𝑚 sub 𝑏.

If we think about the combined mass involved, the mass of the bricks plus the mass of the construction worker, we know that this total mass multiplied by the acceleration due to gravity is equal to the weight force that acts on this worker. But then, over against this force, the construction worker is able to climb up a height of 15 meters. We can say then that the magnitude of the force the construction worker exerts, we’ll call it 𝐹 sub 𝑐, is equal to this total mass times 𝑔.

At this point, we can recall that the work done by a given force 𝐹 is equal to that force multiplied by the displacement of an object on which the force acts. In our case, our body’s displacement is the height of our ladder ℎ, while the force involved is the sum of the masses of the bricks and the construction worker times 𝑔. Therefore, we can write this expression for the work done by the construction worker. Recalling that it’s 𝑚 sub 𝑏 that we want to solve for, we divide both sides of the equation by 𝑔 times ℎ. Those factors then are canceled on the right. And following that, we subtract 𝑚 sub 𝑐, the mass of the construction worker, from both sides. That results in this equation for the mass of the bricks. When we plug in for the values of 𝑊, 𝑔, ℎ, and 𝑚 sub 𝑐, we obtain a result of 39 kilograms. This is the mass of the bricks the worker carried to the top of the ladder.