AP Physics C: Mechanics Practice Quiz: Power

Correct Answer: B

Based on the provided content, "Average power is the amount of energy being transferred or converted, divided by the time it took for that transfer or conversion to occur." This describes a rate of energy transfer.

Correct Answer: A

Using the equation for average power, $P_{avg}=\frac{\Delta E}{\Delta t}$. Here, $\Delta E = 1200$ J and $\Delta t = 6$ s. So, $P_{avg} = \frac{1200 \text{ J}}{6 \text{ s}} = 200$ W.

Correct Answer: C

The instantaneous power delivered by a constant force is given by $P_{inst}=\vec{F}\cdot\vec{v}$. Since the force and velocity are in the same direction, the dot product simplifies to $P_{inst} = Fv$. Therefore, $P_{inst} = (20 \text{ N})(5 \text{ m/s}) = 100$ W.

Correct Answer: C

The energy transferred is given as $\Delta E = 10,000$ J, and the time taken is $\Delta t = 20$ s. Using the average power equation, $P_{avg}=\frac{\Delta E}{\Delta t} = \frac{10000 \text{ J}}{20 \text{ s}} = 500$ W.

Correct Answer: C

Instantaneous power is given by $P_{inst}=\vec{F}\cdot\vec{v}$. The dot product is zero when the two vectors are perpendicular. If the force is perpendicular to the velocity, the component of the force parallel to the velocity is zero, and thus no power is delivered by that force.

Correct Answer: D

The equation $P_{inst}=\frac{dW}{dt}$ explicitly shows that instantaneous power is the time derivative of work ($W$). It represents the rate at which work is being done at a specific moment in time.

Correct Answer: A

The instantaneous power is delivered by the component of the force parallel to the velocity, as described by $P_{inst}=\vec{F}\cdot\vec{v} = Fv\cos\theta$. The component of force parallel to the velocity is $F\cos\theta$. So, $P_{inst} = (50 \text{ N})(2 \text{ m/s})\cos(60^{\circ}) = (100)(0.5) = 50$ W.

Correct Answer: B

The instantaneous power is $P_{inst} = \vec{F}\cdot\vec{v}$. Since the net force $F$ is constant, the acceleration $a$ is also constant. The velocity of the object starting from rest is given by $v = at$. Substituting this into the power equation gives $P_{inst} = F(at) = (Fa)t$. Since $F$ and $a$ are constants, the power $P$ is directly proportional to time $t$, meaning it increases linearly.

Correct Answer: A

Both students transfer the same amount of energy to the boxes ($\Delta E$) because the boxes are identical and lifted to the same height. Average power is $P_{avg}=\frac{\Delta E}{\Delta t}$. Since Alex took half the time ($\Delta t$) to transfer the same energy, his average power is twice as great as Ben's. $P_{Alex} = \frac{\Delta E}{2}$ and $P_{Ben} = \frac{\Delta E}{4}$, so $P_{Alex} = 2 \times P_{Ben}$.

Correct Answer: D

The equation for average power is $P_{avg}=\frac{\Delta E}{\Delta t}$. Energy ($\Delta E$) is measured in Joules (J) and time ($\Delta t$) is measured in seconds (s). Therefore, the unit for power is Joules per second (J/s), which is also known as a Watt (W).