Question

1. is it possible for the sum of kinetic energy and potential energy of an object to change without work having been done on the object? explain. a. no, because the work-energy theorem states that work done on an object is equal to the change in kinetic energy, and change in ke requires a change in velocity. it is assumed that mass is constant. b. no, because the work-energy theorem states that work done on an object is equal to the sum of kinetic energy, and the change in ke requires a change in displacement. it is assumed that mass is constant. c. yes, because the work-energy theorem states that work done on an object is equal to the change in kinetic energy, and change in ke requires a change in velocity. it is assumed that mass is constant. d. yes, because the work-energy theorem states that work done on an object is equal to the sum of kinetic energy, and the change in ke requires a change in displacement. it is assumed that mass is constant.

Explanation:

The work - energy theorem states that the work done on an object is equal to the change in its kinetic energy ($W=\Delta KE$). Kinetic energy is given by $KE = \frac{1}{2}mv^{2}$, so a change in kinetic energy requires a change in velocity (since mass is assumed constant). For the sum of kinetic and potential energy (mechanical energy) to change, there must be a change in kinetic energy (as potential energy changes can also occur, but the question is about the sum changing without work). Since work done is equal to the change in kinetic energy, if the sum of KE and PE changes, work must be done (or energy transferred in other ways, but in the context of work - energy theorem, work is related to KE change). Option a correctly states that work - energy theorem says work done is $\Delta KE$, and $\Delta KE$ needs $\Delta v$ (mass constant), and the answer to the main question is "No" as per this.

Answer:

a. No, because the work - energy theorem states that work done on an object is equal to the change in kinetic energy, and change in KE requires a change in velocity. It is assumed that mass is constant.