What is the relation between the net work and kinetic energy?

Question

BlackTom AI · Accepted Answer

We need to evaluate each option about the relation between net work and kinetic energy.

Option a: The net work changes the kinetic energy. This aligns with the work-kinetic energy theorem, which states that the work done by all forces on an object equals the change in its kinetic energy (W_net = ΔK). Therefore, net work indeed changes the kinetic energy, whether increasing or decreasing it.

Option b: The net work may be in opposite direction to the kinetic energy. This statement is conceptually awkward because work is a scalar quantity that changes the kinetic energy by W_net = ΔK. Saying work is in the opposite direction to kinetic energy mixes vector notions (force/velocity) with a scalar energy change. While negative net work can decrease KE, the phrasing about a direction relative to KE is misleading and not a standard way to describe the relationship.

Option c: The net work may increase the kinetic energy but it never decreases it. This is incorrect because net work can be negative, such as when friction or another opposing force reduces the object's kinetic energy (ΔK < 0). Hence net work can decrease KE as well as increase it.

Option d: The net work is parallel to the direction of the kinetic energy. This statement is not meaningful in standard physics terms. KE is a scalar quantity with no direction, so talking about the net work being parallel to the direction of KE is not a valid comparison. W_net depends on forces over displacement and can be positive, negative, or zero independent of any directional alignment with KE.

Summarizing the reasoning across options: option a correctly captures the fundamental relationship W_net = ΔK from the work-kinetic energy theorem, while options b, c, and d misuse or mischaracterize the concepts of work, energy, and direction.

What is the relation between the net work and kinetic energy?Single choice

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