What is Gravitational Potential Energy?
Gravitational potential energy = energy stored within an object as it is raised to a height against the force of gravity
GPE is alos a way of storing kinetic energy- to lift something, you increase its GPE. This energy is then only released when the object falls, and so is converted into kinetic energy.
Change in GPE (Joules, J) = Weight (Newtons, N) x Change in height (Metres, m)
E.g. A 80kg jumps to a height of 2m on a trampoline. Calculate his change in GPE
(80x10) x 2 = 1,600J (remember, you may need to convert kg in N)
Kinetic energy is the energy of movement i.e. anything moving will have KE
KE depends on both mass and speed, where the greater the objects mass and speed,the bigger its kinetic energy.
KE (J) = 1/2 x Mass (kg) x (Velocity x Velocity)(m/s) <----- i.e. Velocity is squared
Example- A train of mass 235000 kg is travelling at 50 m/s. Calculate its KE:
1/2 x 235000 x (50x50) = 293750000 J
To be able to increase something's KE, it's speed will need to be increased, and the only way to do this is to apply a force to it, meaning you're doing work to it.
i.e. If object X is causing object Y's velocity to increase by exerting a force on it, it's doing work and so increasing object B's KE (although if it doesn't accelerate, then you're not increasing it's KE).
Therefore, Increase in KE = slightly less than the amount of work done (due to friction)
When an object falls, its GPE is converted into KE, meaning the further it falls, the faster it will go (because before the object fell, it must have had a lot of energy stored in it, more so than an object at a lower height).
Although some of the GPE will be dissipated as heat because of air resistance, in the exam, they'll likely to ignore this factor, and so you should say that:
Kinetic energy gained = Potential Energy (i.e. GPE) lost
For example, an object with GPE 300J will fall with 300J of KE
Hard question example:
A 600kg (6000N) Mini is travelling at 50 m/s. What is the maximum height it could climb if all its KE is transferred to GPE?
KE =1/2 x 600 x (50x50) = 750,000 J = GPE gained
GPE = 750,000 J 750,000 = 6000 x Height Height = 750,000/6000 = 125 m