Question

in which one of the following situations is zero net work done?
a. a box is pulled across a rough floor at constant velocity.
b. a ball rolls down an inclined plane.
c. a physics student stretches a spring.
d. a projectile falls toward the surface of earth.
e. a child pulls a toy across a rough surface causing it to accelerate.

Explanation:

Step1: Recall work - energy theorem

Work - energy theorem states that net work done on an object is equal to the change in its kinetic energy, $W_{net}=\Delta K$. If $\Delta K = 0$, then $W_{net}=0$.

Step2: Analyze option a

A box is pulled across a rough floor at constant velocity. Since velocity is constant, the kinetic energy $K=\frac{1}{2}mv^{2}$ is constant ($m$ is mass and $v$ is velocity), so $\Delta K = 0$. Thus, $W_{net}=0$.

Step3: Analyze option b

A ball rolls down an inclined plane. Its speed increases as it moves down, so its kinetic energy increases, $\Delta K>0$, and $W_{net}>0$.

Step4: Analyze option c

A physics student stretches a spring. Work is done on the spring to change its elastic - potential energy, and there is a non - zero net work done on the system (the spring). Also, if we consider the spring as the object, its state of motion or configuration changes, and $\Delta K
eq0$ (it gains elastic potential energy which is related to work done on it), so $W_{net}
eq0$.

Step5: Analyze option d

A projectile falls toward the surface of Earth. Its speed increases due to the gravitational force, so its kinetic energy increases, $\Delta K>0$, and $W_{net}>0$.

Step6: Analyze option e

A child pulls a toy across a rough surface causing it to accelerate. Since it is accelerating, its speed is increasing, so its kinetic energy increases, $\Delta K>0$, and $W_{net}>0$.

Answer:

a. A box is pulled across a rough floor at constant velocity.