Question

Develop a model (diagram) that shows how different amounts of gravitational potential energy (GPE) are stored in the earth-ball system when the ball is raised to different heights on the ramp.

Answer 1

The gravitational potential energy of the ball can be modelled in

relation to the velocity attained by the ball rolling down the ramp.

A model of the GPE of the ball is as follows;

• The height of ball is directly proportional to the square of the velocity the ball reaches while rolling down the ramp. h ∝ v²

Which is the method used to obtain the model for the GPE of the ball?

The gravitational potential energy, GPE, is given as follows;

GPE = m·g·Δh

Where;

m = The mass of the ball

g = The acceleration due to gravity

Δh = The change in elevation of the ball

The gravitational energy of the ball at the starting (lowest) part of the

ramp, where Δh = 0, is 0.

When a small amount of energy is applied to the ball by moving it with a

slow speed, the ball moves some distance up the ramp then stops.

When a higher amount of energy is applied to the ball, the ball moves to

a higher point on the ramp.

When energy is applied to the ball, the energy is converted into

gravitational potential energy such that the height the ball reaches,

indicates the amount of gravitational potential energy in the ball.

Based on the model, we have;

Kinetic energy K.E. applied = GPE gained

Which gives;

$\dfrac{1}{2} \cdot m \cdot v^2 = \mathbf{m \cdot g \cdot h}$

$v^2 = 2 \cdot g \cdot h$

• $h \propto v^2$

• The height of the ball is directly proportional to the square of the velocity

Learn more about gravitational potential energy here:

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