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Question
Solve the following problem.
Derive the expression for power in terms of F, m, and t.
Solution
- A constant force F is applied to a body of mass (m) initially at rest (u = 0).
- We have, v = u + at
∴ v = 0 + at
∴ v = at ....(1) - Now, power is the rate of doing work,
∴ P = `"dW"/"dt"`
∴ P = `"F"*"ds"/"dt" ....[because "dW" = "F"*"ds"]` - But `"ds"/"dt" = "v"`, the instantaneous velocity of the particle.
∴ P = F·v ....(2) - According to Newton’s second law,
F = ma .....(3) - Substituting equations (1) and (3) in equation (2)
P = (ma)(at)
∴ P = ma2t
∴ P = `("m"^2"a"^2)/"m" xx "t"`
∴ P = `"F"^2/"m" "t"` - As F and m are constant, therefore, P ∝ t.
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