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

Study Guide

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Author

Leander Oates

Expertise

Physics

Calculating power

Power is defined as:

The rate at which energy changes with respect to time

The energy change could be:
- a transfer of energy into or out of a system
- a conversion from one energy type to another within a system
Average power is the amount of energy being transferred or converted, divided by the time taken for the transfer or conversion to occur

$P_{a v g} = \frac{∆ E}{∆ t}$

Where:
- $P_{a v g}$ = average power, measured in $W$
- $∆ E$ = change in energy, measured in $J$
- $∆ t$ = change in time, measured in $s$
The unit of power is the watt
- $1 W = 1 J / s$
Since work done, $W$ , is equal to the change in energy of an object or a system due to a force, average power can also be calculated using:

$P_{a v g} = \frac{W}{∆ t}$

Worked Example

A warehouse worker is stacking boxes on a shelf. They lift a box of mass $18 kg$ to a shelf of height $1.4 m$ over a time interval of $3 s$ . Which of the following is the average power output of the worker lifting the box?

A: $48 W$

B: $64 W$

C: $84 W$

D: $86 W$

The correct answer is C

Answer:

Step 1: List the known quantities

Mass, $m = 18 kg$
Height, $∆ y = 1.4 m$
Change in time, $∆ t = 3 s$

Step 2: State equation for average power

$P_{a v g} = \frac{∆ E}{∆ t}$

The energy transferred to the box is gravitational potential energy, therefore:

$P_{a v g} = \frac{m g ∆ y}{∆ t}$

Step 3: Substitute in the known values to calculate

$P_{a v g} = \frac{18 \cdot 10 \cdot 1.4}{3}$

$P_{a v g} = 84 W$

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