A boy of mass 50 kg runs up a staircase of 45 steps in 9 s. If the height of each step is 15 cm, find his
power. Take g = 10 m s–2
Answers
Given:-
→ Mass of the boy = 50 kg
→ Number of steps in the staircase = 45
→ Height of each step = 15 cm
→ Value of 'g' = 10 m/s²
To find:-
→ Power of the boy.
Solution:-
Total height climbed by the boy :-
= 45 × 15cm
= 675 cm
= 6.75 m
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Now, we know that :-
P = mgh/t
Where :-
• P is the power.
• m is mass of the body.
• g is acceleration due to gravity.
• h is height.
• t is time taken.
Substituting values, we get :-
⇒ P = 50×10×6.75/9
⇒ P = 3375/9
⇒ P = 375 W
Thus, the power is 375W .
Some Extra Information:-
• Power of a machine is defined as the
rate of work done by a machine. It is a
scalar quantity.
• S.I. unit of power is Watt(W). Another
unit of power is Horse Power (HP).
• If work done by a machine is 1 Joule in a
time of 1 second, then power of the
machine is 1 Watt.
Answer:
The power is 375 W.
Explanation:
Given,
A boy of mass (m) = 50 kg
No. of steps = n = 45
Time taken (t) = 9 s
Height of each step = 15 cm = 15 / 100 m
To find: find his power
Solution:
Concept involved: Power is the rate of doing work.
Total height of staircase = No. of steps * height of each step
or, Total height of staircase = 45 * 15 / 100 = 6.75 m
Work done would be equal to the Potential Energy possessed by the body.
i.e W = mgh
here, m = 50 kg , g = 10 m/s^2, h = 6.75 m
Substituting the values,
W = 50*10*6.75
And, Power = work done / time
or, P = W / t
or, P = 50*10*6.75 / 9
or, P = 375 W
Therefore, The power is 375 W.