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.
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