Power – problems and solutions

1. A 50-kg person runs up the stairs 10 meters high in 2 minutes. Acceleration due to gravity (g) is 10 m/s². Determine the power.

Known :

Mass (m) = 50 kg

Height (h) = 10 meters

Acceleration due to gravity (g) = 10 m/s²

Time interval (t) = 2 minute = 2 (60) = 120 seconds

Wanted : Power (P)

Solution :

Formula of power :

P = W / t

P = power, W = work, t = time

Formula of Work :

W = F s = w h = m g h

W = work, F = force, w = weight, d = displacement, h = height, m = mass, g = acceleration due to gravity

W = m g h = (50)(10)(10) = 5000 Joule.

P = W / t = 5000 / 120 = 41.7 Joule/second.

2. Calculate the power required of a 60-kg person climbs a tree 5 meters high in 10 seconds. Acceleration due to gravity is 10 m/s².

Known :

Mass (m) = 60 kg

Height (h) = 5 meters

Acceleration due to gravity (g) = 10 m/s²

Time interval (t) = 10 seconds

Wanted : Power

Solution :

Work :

W = m g h = (60)(10)(5) = 3000 Joule

Power :

P = W / t = 3000 / 10 = 300 Joule/second.

3. A rotary comedy with power of 300 watts and period 5 minutes rotates 5 rounds. The energy it uses is ….

A. 15 kJ

B. 75 kJ

C. 90 kJ

D. 450 kJ

Known :

Power (P) = 300 Watt = 300 Joule/second

Period (T) = 5 minutes = 5 (60 seconds) = 300 seconds

Number of rotation = 5

Wanted: Energy used by the rotary comedy

Solution :

The correct answer is D.

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