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

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Homework Help Overview

The discussion revolves around calculating the power required to pull a body of mass m up a smooth incline at a constant speed Vo. The problem involves understanding the forces acting on the body and the relationship between work, force, and power in the context of inclined planes.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants explore the relationship between power, work, and force, questioning the necessity of specifying the direction of the applied force. There are attempts to clarify the calculations involving force components and the role of angle in determining the power required.

Discussion Status

The discussion is active, with participants providing insights into the calculations and questioning assumptions about the forces involved. Some guidance has been offered regarding the components of forces acting along the incline, and there is a focus on deriving expressions for power in terms of angle and speed.

Contextual Notes

Participants note the importance of considering the angle of the incline and the constant speed condition, as well as the implications of these factors on the forces and power calculations. There is a recognition that the net force must be zero when the object moves at constant velocity.

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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
 
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imy786 said:
Power= mg/ time
mg is the force, not the work done.
 
Power= work done /time
work done= force * distance
Force= mg

power= mgd
 
now you forgot the time element
 
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?
 
Power= work done /time
work done= force * distance
Force= mg

Power= force * distance / time
= mg * d /t
= veloctiy *mg
 
Your answer should be in terms of the angle and the speed.
 
power= vsine mg
 
imy786 said:
power= vsine mg
Right. [itex]P = mg \sin (a) v_0[/itex].
 
  • #10
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
 
  • #11
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 [itex]mg\sin\theta[/itex] 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.
 

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