Power (College Board AP® Physics 1: Algebra-Based): Exam Questions

Figure 1

A microlight is a small airplane powered by a gasoline engine. Figure 1 shows the flight path of a short horizontal training flight, AB, which has a displacement of $∆x$.

On its outbound journey, the resultant velocity of the microlight is $v$ at an angle $\theta$ west of due north. The work done by the engine is $W$ over it's flight path AB.

Derive an expression for the force exerted by the engine of the aircraft on its outbound journey as it travels at speed $v$. Express your answer in terms of $P$, $v$, and $\theta$. Begin your derivation by writing a fundamental physics principle or an equation from the reference booklet.

A box of mass $m$is pushed across a rough wooden floor with a constant force $F$ applied parallel to the displacement of the box, such that the power $P$ delivered to the box maintains a constant speed $v$.

Determine an expression for the magnitude of the coefficient of kinetic friction $\mu$. Express your answer in terms of $P$, $v$, $m$ and physical constants as appropriate.

A crate of mass $m$ is pulled along a rough horizontal surface using a rope attached at an angle $\theta$ with respect to the displacement of the crate, where $\theta <90°$. The crate is displaced by an amount $∆x$ in time $∆t$ at speed $v$by the rope with a constant tension force $F_T$. The coefficient of kinetic friction between the crate and the surface is ${\mu }_k$.

Determine an expression for the average power $P_{avg}$ delivered by the rope during the crate's period of motion. Express your answer in terms of $m$, $v$, $F_T$, ${\mu }_k$, $\theta$, and physical constants as appropriate.

A container of mass $m$ is pulled up a incline of angle $\theta$ with respect to the horizontal, by a chain attached to the container and parallel to the incline. The coefficient of kinetic friction between the container and the inclined surface is ${\mu }_k$. At a specific instant $t_1$, the container is moving with speed $v$ and acceleration $a$.

Determine an expression for the instantaneous power delivered by the rope at time $t_1$. Express your answer in terms of $m$, $\theta$, ${\mu }_k$, $v$, $a$, and physical constants as appropriate.