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

In summary, the power required to pull a body up a smooth inclined plane at a constant speed is equal to the force applied multiplied by the distance traveled divided by the time taken. The force required can be found by multiplying the mass of the body by the acceleration due to gravity, and the work done can be found by multiplying the force by the distance traveled. The time element is not necessary in this calculation. The force required can also be expressed as the product of the object's velocity, the angle of the incline, and the force of gravity. This is due to the fact that for the object to move at a constant speed, the net force acting on it must be zero. Therefore, the component of gravity parallel to the incline
  • #1
imy786
322
0

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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  • #2
imy786 said:
Power= mg/ time
mg is the force, not the work done.
 
  • #3
Power= work done /time
work done= force * distance
Force= mg

power= mgd
 
  • #4
now you forgot the time element
 
  • #5
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?
 
  • #6
Power= work done /time
work done= force * distance
Force= mg

Power= force * distance / time
= mg * d /t
= veloctiy *mg
 
  • #7
Your answer should be in terms of the angle and the speed.
 
  • #8
power= vsine mg
 
  • #9
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.
 

1. What is power in physics?

Power in physics is the rate at which work is done or energy is transferred. It is measured in watts (W) and is calculated by dividing the amount of work or energy by the time it takes to do it.

2. How is power related to force and velocity?

Power is directly proportional to both force and velocity. This means that an increase in force or velocity will result in an increase in power. The formula for power is P = F x v, where P is power, F is force, and v is velocity.

3. What is the difference between average power and instantaneous power?

Average power is the amount of power used or produced over a period of time, while instantaneous power is the power used or produced at a specific moment in time. Average power is calculated by dividing the total work or energy by the total time, while instantaneous power is calculated by dividing the change in energy by the change in time.

4. How does power relate to energy?

Power and energy are closely related, as power is the rate at which energy is transferred or used. This means that the more power is used or produced, the more energy is transferred or used over a given time period. The unit of energy, joules (J), is also equal to a watt-second (W·s).

5. Can power be negative?

Yes, power can be negative. This occurs when work or energy is being transferred in the opposite direction, such as when an object is slowing down or when energy is being absorbed instead of produced. In these cases, the power is considered to be negative because the energy is decreasing instead of increasing.

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