Find the power needed to accelerate this elevator downward

In summary: Therefore, the ##F_{net}## you should use in the power formula is ##F_{net}=mg-mA-f## In summary, an elevator with mass M is accelerating downward with constant acceleration A. The friction force acting on the elevator is constant and given by f. The objective is to find the power generated by the engine of the elevator, represented by the equation Fnet.v=P. This can be solved by using the equation P=Fnet.v and substituting the value for Fnet, which is mg-mA-f. Then, by finding the relationship between velocity and acceleration and time, the power generated by the engine can be determined. This can be done by replacing velocity v in the power formula with the equation for
  • #1
phase0
6
1
Homework Statement
It is not actually a homework
Relevant Equations
F.V=P
Fnet=ma
An elevator of mass M is accelerating downward with constant acceleration A. Friction force acting on the elevator is constant and given by f (The initial speed of the elevator is zero.). Find the power generated by the engine of the elevator (in terms of M, A, g, f, and time t).

For this question I write this equation Fnet.v=P and Fnet=mg-ma-f but there is time in my question and I think I couldn't use the velocity in an appropriate way.I know that work is equals to change in kinetic energy but I am not sure how can I write an equation which involves both v and t.If you have any idea,please share with me
 
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  • #3
phase0 said:
Fnet.v=P
Fnet=mg-ma-f
"Fnet"? You are trying to find the power generated by the engine. The equations only makes sense if 'Fnet' is the force exerted by the engine, upwards positive.
All you need to add is the relationship between v and a and you have yourself a differential equation.

The benefit of working in terms of energy is usually that it avoids involving time in the first integration step, giving the relationship between velocity and displacement. But of course velocity is dx/dt, so you still get a differential equation in x and t. Having solved that you can find v(t) and hence P(t).

So you can solve it either way, in terms of energy or forces.
 
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  • #4
Lnewqban said:
Please, see:
http://hyperphysics.phy-astr.gsu.edu/hbase/pow.html

The engine or motor, as well as the work of friction, are resisting the free fall of the elevator.
you are right,this was the reason why I wrote down Fnet=mg-ma-f
I thought in free body diagram mg is oppsite direction of ma and f.But it is true that writing Fnet in left hand side of my equation was silly
 
  • #5
Since the acceleration is constant (as it is being given by the problem statement) which is the algebraic equation that relates velocity and acceleration and time?
Use this equation and replace velocity ##v## in the formula for power ##P=F_{net}\cdot v##. Then replace ##F_{net}=mg-mA-f## , do some algebraic manipulation, and you got yourself the answer.

EDIT: @haruspex is right, by ##F_{net}## here we mean the force on the elevator by the engine and not the "classical" ##F_{net}## which is always equal to ##ma##.
 

Related to Find the power needed to accelerate this elevator downward

1. How do you calculate the power needed to accelerate an elevator downward?

To calculate the power needed to accelerate an elevator downward, you need to know the mass of the elevator, the acceleration of the elevator, and the force of gravity. The formula for power is P = F x v, where P is power, F is force, and v is velocity.

2. What is the force of gravity on an elevator?

The force of gravity on an elevator is equal to the mass of the elevator multiplied by the acceleration due to gravity, which is approximately 9.8 meters per second squared on Earth.

3. How does the mass of the elevator affect the power needed to accelerate it downward?

The more massive the elevator is, the more power is needed to accelerate it downward. This is because the force of gravity on the elevator increases with its mass, and according to the formula for power, a greater force requires more power.

4. What is the acceleration of an elevator during downward motion?

The acceleration of an elevator during downward motion is typically the same as the acceleration due to gravity, which is approximately 9.8 meters per second squared on Earth. However, this can vary depending on factors such as the weight of the elevator and any external forces acting on it.

5. How can the power needed to accelerate an elevator downward be reduced?

The power needed to accelerate an elevator downward can be reduced by decreasing its mass or by reducing the acceleration. This can be achieved by using lighter materials for the elevator or by using a slower acceleration rate. Additionally, using regenerative braking systems can also help reduce the power needed for downward acceleration.

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