How is the power related to the speed at which a body can be lifted? How many kilograms will a man working at the power of 100 W, be able to lift at a constant speed of $1 m s^{- 1}$ vertically? (g = $10 m s^{- 2}$ )

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Solution

Step 1: Given data:
Power, $P = 100 w a t t$
Speed, $v = 1 m / s$ .
Acceleration due to gravity, $g = 10 m / s^{2}$
Step 2: How the power is related to the speed,
Power:
Power is a scalar quantity. The time rate of change in work done is called power.
Power, $P = \frac{W}{t}$ , where $W$ is the necessary work done to lift a body against gravity.
Relation between power and speed:
The necessary work done to lift a body up to height $h$ , is $W = m g h$ , where $m$ is the mass of the body and $g$ is the acceleration due to gravity.
Now, power,
$P = \frac{W}{t} = \frac{m g h}{t} = m g \frac{h}{t} .$
or $p = w v$ , where, $\frac{h}{t} = v$ is the speed and $w = m g$ is the weight of the lift.
So, power is the product of the weight and speed of a running lift.
Step 3: Find the mass:
From the equation of power in terms of mass, height and time,
$m = \frac{P t}{g h} = \frac{P}{g v} = \frac{100}{10 \times 1} = 10 K g$ . [where $\frac{h}{t}$ = speed]
Therefore, the required mass is 10 kg.

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