Mechanical work

​Whew. That was hard work. ​ ​You think? What about me then? I take two bales each time, much more work. ​ ​Yeah. But I lift twice as high.

In total, I've probably worked more than you have. ​ ​Yeah right. ​ ​Work is a term we use in everyday language that can mean a lot of different things. There are many ways to do work. A police staking out a criminal in his hideout, a sales rep making a call, a doctor making a note in a patient's journal. But when we talk about work in physics, it has its own special meaning. When Maria and Lina argue over who has worked more, their reasoning sounds pretty close to the physical term.

Let's help them resolve this. In order to carry out work, you need to apply a force to some object so that the force causes it to move. Maria and Lina are lifting hay bales by applying muscle force to them. That force is strong enough to exceed gravity causing the bales to move upward. Force that causes movement.

Maria and Lina are doing work in the physical sense. Who carries out more work? The amount of work is calculated by multiplying the force by the displacement. Work = force x displacement. We can write it as W = F x S Work = force x displacement.

Force. That's the mass of the hay bale times earth's gravity. 15 kg x 9.8 N/kg rounding off to 150. The force required to lift one bale of hay is 150 newton. Maria lifts with a force of 150 newton and Lina lifts with twice that force - 300 newton.

Now displacement. Lena lifted her load of 300 newton 3 meters up. Maria lifted her load of 150 newton 6 meters up. Lina's work is 300 N x 3 m = 900 Nm Maria's work is 150 N x 6 m. Also 900 Nm.

And a newton meter is the same thing as 1 joule. For each lift they make, they carry out the same amount of work. So much work that it's time for a break. Lina gets a tray that she's holding still, 1 meter above the ground. It's pretty heavy.

But is she doing any work? By lifting, Lina is encountering gravity so she exacts an upward force on the tray. But the tray isn't moving upward, so Lina isn't doing any work. How about now? What force is Lina exerting on the tray now?

When Lina is walking at a steady pace there's almost no force at all required to make the tray move forward. But the lifting force is directed upwards and work is only done by force that causes displacement. The upward force does not cause displacement. The force required for the tray to keep moving forward once it has gained speed is nearly 0. The air resistance is so small that we can disregard it.

So at a steady pace and at an even height, no work is done on the tray. What about this? Is this doing work? Yes, pushing the bench through the gravel requires force in order to overcome friction. Maria applies a force to the bench which causes it to displace in the direction of the force.

Say it takes a force of 200 newton to move the bench and Maria moved it 2 meters, then she carried out a work of 200 x 2, 400 Newton meter or 400 joules. Work is measured in joules just like energy, because if you think about it, work is energy created by a force, and energy is capacity to do work. Confused? Don't worry. Even if you master the mathematics of it, it's hard to really understand what energy and work is.