Work, Energy and Power

Question

A person A pushes a body of 5 kg placed on rough surface of coefficient of friction 0.3 by a distance of 4m in 15 seconds. Another person B pushes the body of 7 kg on same surface by a distance of 3m in the same time. Who has done more work and has more power?

Solution

Person A:
Mass of body,

straight m subscript 1 space equals space 5 space kg

Coefficient of friction,

space space space straight mu equals 0.3

∴ The force of friction,

straight F subscript 1 equals μm subscript 1 straight g equals 0.3 cross times 5 cross times 10 equals 15 straight N

Displacement,

straight s subscript 1 equals 4 straight m

Therefore,
Work done,

straight W subscript 1 equals 15 cross times 4 equals 60 straight J

Time taken,

straight t subscript 1 equals 15 space sec

∴ Power,

straight P subscript 1 equals 60 over 15 equals 4 straight W

Person B:
Mass of body,

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Coefficient of friction,

space space straight mu equals 0.3 space

∴ Force of friction,

straight F subscript 2 equals μm subscript 2 straight g equals 0.3 cross times 7 cross times 10 equals 21 straight N

Displacement,

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∴ Work done,

straight W equals 21 cross times 3 equals 63 straight J

Time taken,

straight t subscript 2 equals 15 space sec

∴ Power,

straight P subscript 2 equals 63 over 15 equals 4.2 space straight W

Thus, the person B has more energy and power.

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Work, Energy And Power

A person A pushes a body of 5 kg placed on rough surface of coefficient of friction 0.3 by a distance of 4m in 15 seconds. Another person B pushes the body of 7 kg on same surface by a distance of 3m in the same time. Who has done more work and has more power?

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