A dog picks up a 0.2kg bone 0.40m and carries it 3m down the hallway at a constant velocity. Then he sets it back down 0.40m to the ground. What is...

Hello!

Denote the mass of a bone as `m,` the height on which it was lifted as `h` and the distance it was carried as `d.`

The force against which a dog performs work is the gravity force. It acts downwards and is equal to `mg,` where `g=9.8 m/s^2` is the gravity acceleration. Therefore a dog's force is `mg` upwards.

At the first stage, the displacement and the force have the same direction and the work is the product of them, `W_1=mgh approx 0.78 (J).` At the second stage, the displacement and the force are perpendicular, and the work `W_2` is zero. At the third stage, the displacement and the force have opposite directions and the work `W_3=-W_1 approx -0.78 J.`

I suppose that a hallway is level.

The same results may be obtained by considering the difference `mgh` between potential energies (kinetic energy is the same at the beginning and at the end of any stage).