A girl of mass 40 kg climbs 50 stairs of average height 20 cm each in 50 s. Find the power of the girl. (g = 10  )

CONCEPT:

• Work done (W): When a force is applied on a body and there is a displacement of the body in the direction of force then the work is said to be done by the force. The SI unit of work is Joule.

Work (W) = Force (F) × Displacement (S)

• Potential energy (PE): The energy of a body due to its position is called potential energy.

PE = m g h

Where m is mass, g is the acceleration due to gravity and h is height.

• Power (P): The rate of work done is called power.
  • The SI unit of power is the watt (W).

Power (P) = work done (W) / time (t)   (P = W / t = J / s)

CALCULATION:

Given that:

Mass (m) = 40 kg

Number of stairs (N) = 50

Height of each stairs = 20 cm

Total height (h) = Number of stairs × Height of each stairs = 50 × 20 = 1000 cm = 10 m

Potential energy gained by the girl = PE = m g h = 40 × 10 × 10 = 4000 J

Work done = PE = 4000 J

Power (P) = Work done/Time taken = 4000/50 = 80 Watt

Hence option 3 is correct.