Solved Conservation of Energy Worksheet Name: PEKE = PEKE PE ... - Free Printable

Let’s solve this step by step. We’re using conservation of energy:
Total Energy before = Total Energy after
That means:
PE_before + KE_before = PE_after + KE_after

We’re given:
- Mass (m) = 100 kg
- Initial speed at top of first hill (v₀) = 2 m/s
- Height of first hill (h) = 20 meters
- g = 9.81 m/s²

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Step 1: Find total energy at initial point (top of first hill)

At the start, the roller coaster has both potential energy (because it’s high up) and kinetic energy (because it’s moving).

Potential Energy (PE) = mgh
= 100 kg × 9.81 m/s² × 20 m
= 19620 Joules

Kinetic Energy (KE) = ½mv²
= ½ × 100 kg × (2 m/s)²
= 50 × 4
= 200 Joules

→ Total Energy = PE + KE = 19620 + 200 = 19820 J

✔ So, total energy is always 19820 J unless friction or air resistance acts — but we ignore those here.

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Step 2: Find potential energy at point A

Looking at the diagram, point A is at the same height as the first hill → so h_A = 20 m

So PE at A = mgh = 100 × 9.81 × 20 = 19620 J

(Same as initial PE — makes sense!)

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Step 3: Use conservation of energy to find KE at point B

Point B is at height h/2 = 20 / 2 = 10 meters

So PE at B = mgh_B = 100 × 9.81 × 10 = 9810 J

Total energy is still 19820 J.

So:
KE at B = Total Energy – PE at B
= 19820 – 9810 = 10010 J

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Step 4: Find potential energy at point C

Point C is at ground level → height = 0

So PE at C = mg×0 = 0 J

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Step 5: Use conservation of energy to find KE at point C

Total energy = 19820 J
PE at C = 0 J

So KE at C = 19820 – 0 = 19820 J

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Step 6: Use KE at C to find velocity at point C

KE = ½mv²
So:
19820 = ½ × 100 × v²
19820 = 50 × v²
v² = 19820 ÷ 50 = 396.4
v = √396.4 ≈ 19.91 m/s

(Rounded to two decimal places)

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Final Answer:

1) Total energy at initial point: 19820 J
2) Potential energy at point A: 19620 J
3) Kinetic energy at point B: 10010 J
4) Potential energy at point C: 0 J
5) Kinetic energy at point C: 19820 J
6) Velocity at point C: 19.91 m/s