Kinetic & Potential Energy — Practice · Grade 12 Science

Chapter: Work, Energy & Momentum

What this practice covers

By the end of Kinetic & Potential Energy you should be able to:

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

Vocabulary used: kinetic energy, gravitational potential energy, elastic potential energy, spring constant (k), reference level.

Problem 1

Find the kinetic energy of a 2.0 kg ball moving at 10 m/s.
Answer and explanation

100 J

KE = ½mv² = ½ × 2.0 × 10² = ½ × 2.0 × 100 = 100 J.

Problem 2

Find the gravitational potential energy of a 0.50 kg ball held 20 m above the ground. (g = 9.8 m/s²)
Answer and explanation

98 J

PE = mgh = 0.50 × 9.8 × 20 = 98 J.

Problem 3

A spring with spring constant k = 500 N/m is compressed 0.20 m. Find the elastic potential energy stored.
Answer and explanation

10 J

PE = ½kx² = ½ × 500 × 0.20² = ½ × 500 × 0.04 = 10 J.

Problem 4

Which has more kinetic energy: a 1,000 kg car moving at 10 m/s, or a 200 kg motorcycle moving at 25 m/s?
  1. The motorcycle (62,500 J)
  2. They are equal
  3. It cannot be determined
  4. The car (50,000 J)
Answer and explanation

The motorcycle (62,500 J)

Car KE = ½ × 1,000 × 10² = 50,000 J. Motorcycle KE = ½ × 200 × 25² = 62,500 J. The motorcycle's higher speed (squared) wins out over its smaller mass.

Problem 5

Explain why gravitational potential energy depends on the reference level you choose, and why that is not a problem in practice.
Answer and explanation

Because PE = mgh measures height h from a chosen zero level, the numerical value of PE changes if you pick a different reference. This is not a problem because only changes in PE (as an object rises or falls) affect motion, and those changes come out the same no matter where you place the reference level.

Problem 6

A 4 kg object moves at 3 m/s. Find KE. Show the reasoning, not just the conclusion.
Hints

Do not add height to speed or confuse their squares.

Answer and explanation

½×4×9=18 J.

Problem 7

At fixed mass, what happens to KE when speed triples?
Hints

State what the supplied observations or conditions establish, and separate that from any assumption.

Answer and explanation

It increases ninefold because of the square dependence.

Problem 8

Spring force and stored elastic energy are different quantitiesSpring force and stored elastic energy are different quantitiesElastic potential energy (J)00.511.5200.050.10.150.2Extension x (m)Us=½kx²; force magnitude is kx, not ½kx².
Calculated linear-spring energy curve, valid only over the stated elastic range.
Interpret the supplied visual. For k=100 N/m and x=0.10 m, find both energy and force magnitude.
Answer and explanation

Us=0.50 J; force magnitude=10 N. Their units and meanings differ.

For an ideal linear spring, elastic potential energy relative to its unstrained state is Us=½kx². This is the area under the balancing force–extension curve, not the endpoint force itself. A spring stretched twice as far stores four times the energy within the same elastic range. Compression can also store energy because x² is positive, while the restoring force reverses direction according to −kx.

Us=0.50 J; force magnitude=10 N. Their units and meanings differ.

Response criteria

  • Interpret labels, structures, axes, units and directions correctly.
  • Explain the physical or environmental relationship or mechanism.
  • Respect stated assumptions and distinguish observation from inference.

Problem 9

A 1.5 kg cart has speed 4 m/s. It compresses a loss-free spring with k=600 N/m on a level track. Find initial K and maximum compression.
Answer and explanation

K=½×1.5×16=12 J. Set 12=½×600x², giving x=0.20 m within the spring’s assumed elastic range.

K=½×1.5×16=12 J.

Set 12=½×600x², giving x=0.20 m within the spring’s assumed elastic range.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the physical or environmental mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

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