Question

which best summarizes a concept related to the work-energy theorem?
∘ when work is positive, the environment does work on an object.
∘ when work is negative, the environment does work on an object.
∘ when work is positive, the kinetic energy in a system remains constant.
∘ when work is negative, the kinetic energy in a system remains constant.

Explanation:

1. Recall the work - energy theorem: The work - energy theorem states that the net work done on an object is equal to the change in its kinetic energy, $W=\Delta K = K_f - K_i$.
2. Analyze the sign of work:

• If work is positive ($W>0$), it means that the net work done on the object is positive. This implies that the environment (or the forces from the environment) is doing work on the object. For example, if you push a box and it moves in the direction of your push, you (part of the environment for the box) are doing positive work on the box, and the kinetic energy of the box will increase ($\Delta K>0$).
• If work is negative ($W < 0$), it means that the object is doing work on the environment. For example, if a box is sliding on a rough surface, the frictional force (from the environment) does negative work on the box, and the box is doing work against the friction (on the environment), and the kinetic energy of the box will decrease ($\Delta K<0$).
• Options C and D are incorrect because according to the work - energy theorem, when work is done on a system (positive or negative net work), the kinetic energy of the system changes ($\Delta K=W$), so the kinetic energy does not remain constant. Option B is incorrect because negative work means the object does work on the environment, not the other way around.

Answer:

A. When work is positive, the environment does work on an object.