EnergyEasy

Ball on a slide — work-energy theorem

A ball of m = 0.2 kg starts from rest at the top of a slide h = 3 m high.\nNeglecting friction, calculate the speed at the bottom.

Given data

m = 0.2 kgh = 3 mv₀ = 0g = 9.81 m/s²

Steps

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What is the gravitational potential energy of the ball at the top of the slide?
Write your working — the numerical result must appear in the text J
What is the speed of the ball at the bottom of the slide?

Full worked solution

What is the gravitational potential energy of the ball at the top of the slide?
$U = mgh = 0.2 \cdot 9.81 \cdot 3$
$U = mgh = 0.2 \times 9.81 \times 3 = \mathbf{5.886\,J}$ . This gravitational potential energy is entirely converted into kinetic energy at the bottom, assuming no friction.
What is the speed of the ball at the bottom of the slide?
$v = \sqrt{\dfrac{2U}{m}} = \sqrt{\dfrac{2 \cdot 5.886}{0.2}}$
$v = \sqrt{2gh} = \sqrt{2 \times 9.81 \times 3} = \sqrt{58.86} \approx \mathbf{7.67\,m/s}$ . The speed depends only on $h$ and $g$ , not on the mass — all objects reach the same speed from the same height.

Result:Speed at the bottom: v = √(2gh) ≈ 7.67 m/s. Mass is irrelevant — all objects reach the same speed.

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