How Is Kinetic Energy Calculated and Converted into Electrical Energy?

[mailhiot]

If a metal sphere that weights 1.006 kg is dropped from 2.5 meters, what is it's kinetic energy when it hits the ground?

Is this kinetic energy the same value as mechanical energy?

If this kinetic energy was converted in electrical energy by a 1000 watt electric generator that was 95% efficient, how much mechanical energy (in joules) is required? In other words, does a 1000 watt generator require 1000 joules of mechanical energy?

 

[Thundagere]

If a metal sphere that weights 1.006 kg is dropped from 2.5 meters, what is it's kinetic energy when it hits the ground?

Is this kinetic energy the same value as mechanical energy?

If this kinetic energy was converted in electrical energy by a 1000 watt electric generator that was 95% efficient, how much mechanical energy (in joules) is required? In other words, does a 1000 watt generator require 1000 joules of mechanical energy?

In this case, what you want to do is apply conservation of energy—in other words, total mechanical energy will always be conserved. Use that principal, and potential & kinetic energy to answer your question.

 

[mailhiot]

Thank you for the answer, but I am not a physics person so don't really understand the answer. So in my question, with a metal sphere that is 1.006 kg dropped from 2.5 meters, what is the potential energy, kinetic energy, and mechanical energy? I need to know this value because I need to know how many spheres need to be dropped per second to power a 1000 watt electric generator. THANKS!

 

[Thundagere]

OK, some background info then.
The mechanical energy is the total energy the object posseses from position and from motion. This will always be conserved.

Potential energy is energy from position. GRAVITATIONAL potential energy is the potential energy that gravity causes, and is given by PE= mgh, where m is the mass, g is the acceleration due to garvity (9.8 m/s^2), and h is the height. You have all these values.

Kinetic energy is the energy due to motion, and is given by KE= 0.5 m v^2, where m is mass and v is velocity.

Now ask yourself, before the sphere is dropped, what is it's kinetic energy? Since it's velocity is 0, logically it has no kinetic energy. However, it has gravitational potential energy, which you can calculate.
Since mechanical energy is potential energy and kinetic energy. then the GPE in this scenario makes up all the mechanical energy.

Remember that all the mechanical energy will be conserved. At 0 m, all of it will be kinetic energy.
Hopefully, I've given you something to think about!

 

[PJC01]

I can confirm that the kinetic energy of the metal sphere can be calculated using the formula KE = 1/2 mv^2, where m is the mass of the sphere and v is its velocity. In this case, the kinetic energy of the sphere when it hits the ground can be calculated as follows:

KE = 1/2 (1.006 kg) (9.8 m/s^2)^2 = 48.9 joules

It is important to note that kinetic energy and mechanical energy are not the same values. Kinetic energy is a type of mechanical energy, but mechanical energy includes other forms such as potential energy and thermal energy. Therefore, the kinetic energy of the sphere is only a part of its total mechanical energy.

In terms of the electrical energy conversion, a 1000 watt electric generator that is 95% efficient means that 95% of the mechanical energy used to power the generator is converted into electrical energy. Therefore, the amount of mechanical energy required to produce 1000 watts of electrical energy would be calculated as follows:

ME = (1000 watts) / (95% efficiency) = 1052.6 watts

This means that the generator would require 1052.6 joules of mechanical energy to produce 1000 watts of electrical energy. So, the generator does not require exactly 1000 joules of mechanical energy, but it is very close to that value. Overall, the conversion of energy from mechanical to electrical forms is not a perfect process and some energy is lost in the conversion.