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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 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;
[tex]\dfrac{1}{2} \cdot m \cdot v^2 = \mathbf{m \cdot g \cdot h}[/tex]
[tex]v^2 = 2 \cdot g \cdot h[/tex]
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