Question

girl of mass 40 kg runs up a staircase of 30 steps in 10 s. If the height of each step is 0.1 m, find the power developed by her. Take g = 10 \small ms^{-2}

112 W
1200 W
120 W
133 W​

Answer 1

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Answer :

• Mass = 40 kg
• Number of steps = 30
• Time = 10 sec
• Height of each step = 0.1 m
• Power = ?

$\displaystyle\underline{\bigstar\:\textsf{According to the Question :}}$

• Here we shall first find the Work done by the body. Work done by the girl is equal to the potential energy she has. Potential energy is given by the product of the mass, the acceleration and the height of the body.

⇒ Work = Potential Energy

⇒ Work = mgh

• Mass = 40 kg
• Gravitational Acceleration = 10 m/s²
• Height = 0.1 × 30 = 3 m

⇒ Work = 40 × 10 × 3

⇒ Work = 1200 J

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• Now that we have the work done, the power given by the ratio of the work done and the time taken

⇒ Power = Work/Time

⇒ Power = 1200/10

⇒ Power = 120 W

∴ The power in this case is 120 W

Answer 2

Given:-

✦ A girl of mass 40 kg runs up a staircase if 30 steps in 10 seconds

✦ The height of each step is 0.01 m

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To Prove:-

✦ The power developed by the girl ?..

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Solution:-

✦ To Find Work done:-

✦ Using Formula,

➸ Work done = Mass × Gravity × Height

✦ Substitute the value given in the question..

➸ Work done = 40 × 10 × 3

➸ Work done = 1200 J

━━━━━━━━━━━━━━━━

✦ To Find Power:-

✦Using Formula,

➸ Power = Work done / Time taken

✦ Substitute the value given in the question...

➸ Power = 1200 / 10

➸ Power = 120 W

━━━━━━━━━━━━━━━━

➸ Hence the power developed by girl is 120 W