A block of mass m is being pulled up along the rough incline by an agent delivering constant power P. The coefficient of friction between the block and the incline is µ. The maximum speed of the block during the course of ascent is

Engineering

Physics

Mechanical Power

Motion of Block on Inclined Surface

Static and Kinetic Friction

Question

A block of mass m is being pulled up along the rough incline by an agent delivering constant power P. The coefficient of friction between the block and the incline is µ. The maximum speed of the block during the course of ascent is

$v = \frac{2 P}{mgsinθ + µ mgcosθ}$

$v = \frac{P}{mgsinθ + µ mgcosθ}$

$v = \frac{2 P}{mgsinθ - µ mgcosθ}$

$v = \frac{P}{mgsinθ - µ mgcosθ}$

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Let at any time the speed of the block along the incline upwards be v.

Then from Newton’s second law

$\frac{P}{v}$ – mg sinθ – µmgcosq = $\frac{mdv}{dt}$

the speed is maximum when $\frac{dv}{dt}$ = 0

$∴ v_{\max} = \frac{P}{mgsinθ + µ mgcosθ}$