What power is needed to create such a constant force?

[Piewie]

Maybe this problem is easy to solve, but I can't find a way out.

I need to know what power is needed to create an acceleration of 9.81 m/s^2.
For an object with a mass of 1 kg.

A constant force of 9.81 N is needed (that's easy ).

But what power is needed to create such a constant force?
There is no friction.


Thanx 4 your help,
Pieter

 

[Doc Al]

If a force of 9.81 N is applied to a 1 kg object, it will accelerate. The power required to maintain that force on the object will depend on the speed of the object: P = Fv. (Power is the rate at which work is done or energy is transferred.)

 

[spacetime]

If you are keeping the force constant, you'll have to put in more and more power as time passes.

You can calculate it from:

$$P = \vec{F} \cdot \vec{v}$$

at any time when the velocity is v.

So, basically at any time t,

$$P = F \times a \times t$$


spacetime
www.geocities.com/physics/index.html

 

[Piewie]

Thanx a lot, but unfortunately these answers only solve a part of my problem.

The actual question is: what power must a rocket deliver so that its upward force equals the gravitational force. So the rocket will 'float' above the launch platform.

There is no upward or downward speed, except for the exhaust products.

Pieter

 

[HallsofIvy]

In order for the rocket to "float" above a platform, the upward force must be exactly the same as the gravitational force: gm. I don't see what that has to do with "power" (work done per second). You could for example, "float" the rocket by putting it on a table which would exert the correct force while doing no work at all.

 

[sal]

Thanx a lot, but unfortunately these answers only solve a part of my problem.

The actual question is: what power must a rocket deliver so that its upward force equals the gravitational force. So the rocket will 'float' above the launch platform.

There is no upward or downward speed, except for the exhaust products.

Pieter

zero
Intentional or otherwise, this is a "trick question". A stationary rocket motor delivers zero power to the rocketship. As someone already said in this thread, w=f*v and when v=0, w=0.

Now, if you want to figure out how much power is being delivered to the exhaust, that will be nonzero. However, there's no single answer. If the thrust (force) needed is f then

$$f = v_{exhaust} \cdot \frac{dm}{dt}$$

as you probably already know. But you can achieve the needed f value with many different combinations of v_e and dm/dt, and each different combination will yield a different rate of energy transfer into the exhaust.

If one packet of exhaust is dm, and exhaust velocity is v_e, then one packet of energy into the exhaust is

$$dE = \frac{1}{2} \cdot dm \cdot v_e^2$$

Divide through by dt and you've got power.

 

[pmb_phy]

Thanx a lot, but unfortunately these answers only solve a part of my problem.

The actual question is: what power must a rocket deliver so that its upward force equals the gravitational force. So the rocket will 'float' above the launch platform.

There is no upward or downward speed, except for the exhaust products.

Pieter

The question is quite literally meaningless. Work is not being done on such a rocket so the time rate of change of the energy of the rocket is zero. Power is the rate at which work is being done and in this case there is no work being done. E.g. it takes zero energy to let a rocket stay at a given location such as sitting on the ground on the launch pad.

However, rocket fuel is being burned and energy is being changed from one form to another at a given rate. This energy goes into the chaging the kinetic energy of the gas particles and thus giving them momentum. This momentum serves to impress a force on the rocket. But there is no direct relationship between this rate and the weight of the rocket since some fuels will be more efficient than others. This is akin to saying "How much energy do I need to expend in order to hold up a bucket full of water?" The work done on such a bucket, while holding it at a particular height, is zero. But energy is being burnt by your body in order to accomplish this.

Pete