How Can You Calculate the Power Required to Pull a Body Up a Smooth Incline?

[imy786]

Homework Statement

Determine the power required to pull a body of mass m up a smooth plane
inclined at an angle a to the horizontal at a constant speed Vo. Explain why
it is unnecessary to specify the direction in which the applied force is acting.

Homework Equations

Power= work done /time
work done= force * distance
Force= mg

The Attempt at a Solution

Power= mg/ time

 

[Doc Al]

Power= mg/ time

mg is the force, not the work done.

 

[imy786]

Power= work done /time
work done= force * distance
Force= mg

power= mgd

 

[nonequilibrium]

now you forgot the time element

 

[Doc Al]

Do it step by step. If the angle is "a", what force is required to move the body at constant speed? Say you move the object a distance "d" up the incline, how much work is required? How much time is required, if the speed is v0? What's the power required?

 

[imy786]

Power= work done /time
work done= force * distance
Force= mg

Power= force * distance / time
= mg * d /t
= veloctiy *mg

 

[Doc Al]

Your answer should be in terms of the angle and the speed.

 

[imy786]

power= vsine mg

 

[Doc Al]

power= vsine mg

Right. P = mg \sin (a) v_0.

 

[imy786]

doc...can you show me how to arrive to get sin in the solution..i know its by resolving..but can you pelase provide details thanks

 

[Doc Al]

Since the object moves at constant velocity, the net force on it must be zero. Since it moves along the incline, examine forces in that direction. Since the component of gravity parallel to the incline is mg\sin\theta downward, the applied force must have an equal component parallel to the incline pointing upward. Make sense?

Note: Since the object moves parallel to the incline, only force components parallel to the incline contribute to work done.