Question

The average power required to lift a 100kg mass through a height of 50 meters in approximately 50 seconds would be (in$$J/s$$ )
A. 50
B. 5000
C. 100
D. 980

Answer 1

Hint: Average Power required to do a certain work in a particular time is given by $P={\displaystyle \frac{W}{t}}$. Here work done can be written as the product of force and displacement $W=F.ds$ . This force in turn can be written as the product of mass and acceleration which leads to the final formula $P={\displaystyle \frac{mgds}{t}}$. Now substitute the corresponding values and calculate the power needed to life the object.

Complete step-by-step answer

The time rate at which the work is done or the energy is transferred is called power. It can also be defined as the ratio of work done to the total time taken to do that particular work. Power expression is given by,
$P={\displaystyle \frac{W}{t}}$
Since work is the product of force and displacement it can be substituted in work’s place,
$W=F.ds$
And we know that Force is a product of mass and acceleration. Here, acceleration is in terms of acceleration due to gravity as the displacement is through height against gravity.
$$\begin{gathered} F=mg \\ P={\displaystyle \frac{mgds}{t}} \end{gathered}$$

Given:
$$\begin{gathered} m=100kg \\ ds=50m \\ t=50s \\ g=9.8m{s}^{-1} \end{gathered}$$
Substitute the values in the above expression.
$$\begin{gathered} P={\displaystyle \frac{100\times 9.8\times 50}{50}} \\ P=980J/s \end{gathered}$$
Therefore, the power required is $$980J/s.$$

The correct option is D.

Note: Power which is the product of force and velocity is called instantaneous velocity power, and average power is force times average velocity. This information is useful to solve the problem alternatively.
Here, v is the average velocity when the force is F .
$P=F.v$
Power is a scalar quantity. Its dimensions are $$J/s$$ i.e also called Watts
Horsepower is another unit of power used in automobiles and motors $1hp=746W$.