Conservation of Energy — Drills · Grade 12 Science

Chapter: Work, Energy & Momentum

What these drills covers

By the end of Conservation of Energy you should be able to:

6 questions, numeric, multiple choice and written answer, each with a worked explanation.

Vocabulary used: mechanical energy, conservation of mechanical energy, law of conservation of energy, dissipation, efficiency.

Problem 1

A cart has 75 J of gravitational potential energy at the top of a frictionless ramp and 0 J of kinetic energy. What is its kinetic energy at the bottom?
Answer and explanation

75 J

With no friction, mechanical energy is conserved, so all 75 J of PE becomes kinetic energy at the bottom.

Problem 2

A machine is supplied 250 J of energy and produces 200 J of useful output. Find its efficiency.
Answer and explanation

80 %

Efficiency = (200 ÷ 250) × 100% = 80%.

Problem 3

A 2.0 kg cart reaches the bottom of a frictionless ramp with 100 J of kinetic energy. Find its speed there.
Answer and explanation

10 m/s

100 = ½ × 2.0 × v² = v², so v² = 100 and v = 10 m/s.

Problem 4

In a real machine that has friction, the useful output energy is always…
  1. less than the input energy
  2. greater than the input energy
  3. equal to the input energy
  4. twice the input energy
Answer and explanation

less than the input energy

Some input energy is always dissipated as heat and sound, so useful output is always less than the input — no real machine is 100% efficient.

Problem 5

A real roller coaster loses mechanical energy on every hill. Explain where that energy goes, and whether this breaks the law of conservation of energy.
Answer and explanation

The 'lost' mechanical energy is not destroyed. Friction in the wheels and track and air resistance convert it into thermal energy (warming the parts and the air) and sound. Total energy is still conserved — it has just been dissipated into forms that are spread out and no longer drive the car's motion.

Problem 6

A 4.0 kg cart starts from rest with 200 J of gravitational potential energy at the top of a ramp. Friction dissipates 72 J as it descends. Find its speed at the bottom.
Answer and explanation

8 m/s

Kinetic energy at the bottom = 200 − 72 = 128 J. Then 128 = ½ × 4.0 × v² = 2v², so v² = 64 and v = 8.0 m/s.

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