Question about gravitational potential energy

[scott22]

I am wondering how this all works and am hoping to get some guidance. If a 1000 lb weight freefalls vertically from 660 ft the energy is 894,289 joules. If the fall is down a 30 degree slope that is 1300 ft long, then it takes 17 seconds and the potential energy can be said to be 53 KW. If, and I really mean if, I did that math right then my question has to do with converting that 53KW into kinetic energy. If the 1000 lb. weight is brought to a stop by a mechanical device, rather than impacting the earth, does the 53KW transfer to the mechanical device? If so does all or most of it transfer? Secondly, if the mechanical device takes longer than the 17 seconds of freefall to bring the weight to a stop is the 53KW of potential energy still available? My guess is that no matter how long the mechanical device takes to bring the weight to a stop the potential energy, of 53KW, would remain the same.

 

[Khashishi]

Be careful with terminology: "potential energy can be said to be 53 KW" makes no sense. You mean, the average power is 53 kW. Energy is measured in joules. Energy is conserved and power is not. If you take the same energy and spread it over a longer time, the power will decrease. So your last sentence is totally wrong.

Depending on how efficient the mechanism is, almost all of the 894289 joules can be recovered by the machine. Of course there's always some inefficiency, but there's no hard limit on efficiency like there is in a heat engine.

 

[Electric Red]

You are talking about a potential energy of 53 KW, energy is measured in Joules, not in Joules per second, which is W.
And if I understand your question correct, yes most of the energy gets converted into mechanical energy but there will also be a not neglible amount of heat after the collision.

Does that answer your question a little bit?

 

[PhanthomJay]

If a problem is stated in pounds and feet, please stick with those units when calculating potential energy in foot-pounds.

 

[PJC01]

Yes, you are correct in your calculations and understanding of the potential energy and its conversion to kinetic energy in this scenario. When the 1000 lb weight freefalls vertically, its potential energy is converted to kinetic energy until it reaches the bottom of the 30 degree slope. At this point, the potential energy is 0 and the kinetic energy is at its maximum. If a mechanical device is used to stop the weight before it reaches the bottom, the kinetic energy will be converted back into potential energy, which can then be used to do work on the mechanical device. The amount of potential energy transferred to the mechanical device will depend on the efficiency of the device and any external factors that may affect the transfer.

In terms of the time it takes for the mechanical device to bring the weight to a stop, the potential energy will remain the same regardless of the duration. This is because potential energy is determined by the height and mass of the object, not the time it takes to convert it into kinetic energy. However, the rate at which the potential energy is converted to kinetic energy may vary depending on the speed at which the mechanical device can operate.

Overall, the potential energy can be transferred to a mechanical device and converted into kinetic energy, but the efficiency and external factors will affect the amount of energy transferred. I hope this helps guide you in your understanding of gravitational potential energy.