a- Define I watt of power?
b- A boy of mass 30 kg runs up a staircase of 60 steps each of 25cm in 15s.
A girl of mass 40 kg runs the same distance in 10 sec. Find the ratio of their
work done and the ratio of their power?
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Answer:
1 watt is the amount of Power where 1 J of work is done in a time of 1 second.
Given,
Boy Mass (m₁) = 30 kg
No. of staircase (n) = 60
Height of each staircase (h) = 25 cm
= 0.25 m
Total Height travelled by the boy (d) = [60*0.25] m
= 15 m
Acceleration due to gravity (g) = 9.8 m/s²
Work Done (W₁) = Force*Displacement
= m₁*g*d
= 30*9.8*15 J
= 4410 J
Time (t₁) = 15 s
Power (P₁) = W₁/t₁
= 4410/15 W
= 294 W
Mass of girl (m₂) = 40 kg
d = 15 m
Work Done (W₂) = Force*Displacement
= m₂*g*d
= 40*9.8*15 J
= 5880 J
Time 2 (t₂) = 10 s
Power (P₂) = W₂/t₂
= 5880/10
= 588 J
Ratio of Work Done = W₁:W₂
= 4410:5880
= 441:588
= 147:196
= 21:28
= 3:4
Ratio of Power = P₁:P₂
= 294:588
= 1:2
Ratio of Work Done is 3:4 and Power is 1:2.
I hope this helps.
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