Kinetic & Potential Energy — Practice · Grade 8 Science

Chapter: Energy & Heat Transfer

What this practice covers

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

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

Vocabulary used: energy, kinetic energy, potential energy, joule (J), model, evidence, system boundary, assumption.

Problem 1

Find the kinetic energy of a 4 kg cart moving at 5 m/s.
Answer and explanation

50 J

KE = ½mv² = ½ × 4 × 5² = ½ × 4 × 25 = 50 J.

Problem 2

A 10 kg object sits on a shelf 2 m high. Find its gravitational potential energy. (g = 9.8 m/s²)
Answer and explanation

196 J

PE = mgh = 10 × 9.8 × 2 = 196 J.

Problem 3

If you double an object's speed, its kinetic energy…
  1. doubles
  2. triples
  3. quadruples (×4)
  4. stays the same
Answer and explanation

quadruples (×4)

Since KE = ½mv², speed is squared, so doubling speed multiplies KE by 2² = 4.

Problem 4

Find the kinetic energy of a 1 kg ball moving at 6 m/s.
Answer and explanation

18 J

KE = ½mv² = ½ × 1 × 6² = ½ × 1 × 36 = 18 J.

Problem 5

Explain why a roller coaster car has the most kinetic energy at the bottom of the first hill and the most potential energy at the top.
Answer and explanation

At the top, the car is high up and barely moving, so it has maximum potential energy and almost no kinetic energy. As it drops, that potential energy converts into kinetic energy, so by the bottom it's moving fastest (maximum kinetic energy) but has almost no height left (minimum potential energy).

Problem 6

A 3 kg object has 96 J of kinetic energy. What is its speed?
Answer and explanation

8 m/s

96 = ½ × 3 × v², so 96 = 1.5v², giving v² = 64, so v = 8 m/s.

Problem 7

Using g=10 N/kg, find the potential-energy gain of a 2 kg book raised 1.5 m. Explain the reasoning in your own words.
Answer and explanation

The book–Earth system gains 30 J of gravitational potential energy.

Use change in GPE=mgh.

Substitute 2×10×1.5=30 J.

Response criteria

  • Use the stated conditions.
  • Show the evidence or calculation.
  • Explain the conclusion and any stated limitation.

Problem 8

A 3 kg object is raised 2 m. Use g=10 N/kg to find gravitational potential-energy increase. Show the reasoning, not just the conclusion.
Hints

Square the speed before multiplying.

Answer and explanation

ΔPE=mgh=3×10×2=60 J.

Problem 9

Two equal-speed carts have masses 2 kg and 6 kg. Compare their kinetic energies.
Hints

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

Answer and explanation

The 6 kg cart has three times the KE because energy is proportional to mass at fixed speed.

Problem 10

An energy value needs its system and referenceAn energy value needs its system and referenceObject + EarthGPE reference neededMoving objectKE depends on frameEnergy comparisons require a receiving system, reference level and conditions.A height zero and a motion reference are choices used to organize the account.
Gravitational energy is associated with the interacting object–Earth arrangement and is quoted relative to a chosen zero height. Kinetic energy describes motion relative to a chosen reference frame. The boxes organize which system/reference a number belongs to; they do not imply that energy is a material stored inside each box or that absolute values are meaningful without those choices.
For this unit’s illustrated case, why can shifting the zero-height reference change a quoted GPE without changing a predicted energy gain during the same rise?
Answer and explanation

It changes both absolute values by the same reference offset, leaving the height difference and therefore the physical energy change unchanged.

Reference means the agreed comparison used to quote a quantity. State it so two people calculate the same question. For changes, compare the same system and reference in both states rather than mixing unrelated totals.

It changes both absolute values by the same reference offset, leaving the height difference and therefore the physical energy change unchanged.

Response criteria

  • Use the named labels, directions or supplied quantities accurately.
  • Connect the visual evidence to the scientific mechanism or calculation.
  • State the relevant model conditions or limitation.

Problem 11

A supplied 2 kg object moves at 3 m/s and then at 6 m/s in the same reference frame. Compare kinetic energies and say whether doubling speed doubles kinetic energy.
Answer and explanation

KE values are 9 J and 36 J, so doubling speed quadruples KE in this fixed-mass model.

Use ½mv² with the same mass and units.

Compare the ratio after squaring both speeds.

KE values are 9 J and 36 J, so doubling speed quadruples KE in this fixed-mass model.

Response criteria

  • Use the named labels, directions or supplied quantities accurately.
  • Connect the visual evidence to the scientific mechanism or calculation.
  • State the relevant model conditions or limitation.

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