Question

If it takes 726 watts of power to move an object 36 m in 14 s, what is the mass of the object?

Answer 1

To determine the mass of the object, we can use the relationship between power, work, and motion. The power \( P \) is given by the formula:

\[
P = \frac{W}{t}
\]

where \( W \) is the work done and \( t \) is the time. Work \( W \) can also be expressed in terms of the force \( F \) and the distance \( d \):

\[
W = F \cdot d
\]

Putting it all together, we can express power as:

\[
P = \frac{F \cdot d}{t}
\]

Given that we know the power \( P = 726 \) watts, the distance \( d = 36 \) m, and the time \( t = 14 \) s, we can rearrange the power formula to solve for force \( F \):

\[
F = \frac{P \cdot t}{d}
\]

Now substituting the known values:

\[
F = \frac{726 \text{ W} \times 14 \text{ s}}{36 \text{ m}}
\]

Calculating the force:

\[
F = \frac{10164 \text{ W}\cdot \text{s}}{36 \text{ m}} = 282.33 \text{ N}
\]

Now, knowing that the force \( F \) is also related to mass \( m \) and gravitational acceleration \( g \) (approximately \( 9.81 \text{ m/s}^2 \)), we can find the mass using:

\[
F = m \cdot g
\]

Rearranging to solve for mass \( m \):

\[
m = \frac{F}{g}
\]

Substituting for \( F \):

\[
m = \frac{282.33 \text{ N}}{9.81 \text{ m/s}^2}
\]

Calculating the mass:

\[
m \approx 28.8 \text{ kg}
\]

So, the mass of the object is approximately **28.8 kg**.