Conservation of Energy — Practice · Grade 8 Science

Chapter: Energy & Heat Transfer

What this practice covers

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

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

Vocabulary used: law of conservation of energy, mechanical energy, energy dissipation, model, evidence, system boundary, assumption.

Problem 1

A ball has 80 J of potential energy at the top of a hill and 0 J of kinetic energy. Ignoring friction, what is its kinetic energy at the bottom?
Answer and explanation

80 J

By conservation of energy, all 80 J of potential energy converts to kinetic energy at the bottom.

Problem 2

A skater has 300 J of potential energy at the top of a ramp. By the bottom, 45 J converts to thermal energy from friction. What is the skater's kinetic energy at the bottom?
Answer and explanation

255 J

300 J − 45 J (lost to friction) = 255 J of kinetic energy.

Problem 3

A roller-coaster car slows as it climbs a hill. According to conservation of energy, its kinetic energy is mainly being
  1. converted into gravitational potential energy
  2. destroyed by the climb
  3. created out of nothing
  4. turned into extra mass
Answer and explanation

converted into gravitational potential energy

Energy is conserved: as the car rises and slows, kinetic energy transforms into gravitational potential energy rather than being destroyed.

Problem 4

A Newton's cradle eventually stops swinging. Does this violate the law of conservation of energy? Explain.
Answer and explanation

No — the energy isn't destroyed. It transforms into small amounts of sound and thermal energy from friction and air resistance at each collision, until almost none of the original energy is left as visible swinging motion.

Problem 5

A 500 J system has 120 J converted to sound and 80 J converted to thermal energy as an object moves. How much energy remains as kinetic energy?
Answer and explanation

300 J

500 − 120 − 80 = 300 J remains as kinetic energy.

Problem 6

An object starts with 100 J of gravitational potential energy. At the bottom it has 75 J of kinetic energy. What happened to 25 J? Explain the reasoning in your own words.
Answer and explanation

25 J transferred into other energy stores or surroundings; it was not destroyed.

Compare starting and final mechanical energies: 100−75=25 J.

Account for transfers through friction, air resistance or deformation.

Response criteria

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

Problem 7

A system starts with 120 J. It retains 45 J and transfers the rest out. Find transferred energy. Show the reasoning, not just the conclusion.
Hints

State where the 55 J went instead of calling it destroyed.

Answer and explanation

120−45=75 J.

Problem 8

A rolling ball loses 10 J of kinetic energy but gains only 7 J of potential energy. Identify a plausible missing transfer.
Hints

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

Answer and explanation

About 3 J can transfer to thermal energy, sound or other accounted outputs, assuming these are the only other changes.

Problem 9

Mechanical energy can decrease while total energy stays accounted forMechanical energy can decrease while total energy stays accounted forFull system includes object, Earth and relevant surroundings.InitialGPE 100 JLaterGPE 30 JKE 50 JThermal 20 JMechanical energy: 100 → 80 J. Total represented energy: 100 → 100 J.
The supplied initial account has 100 J gravitational energy. The later account has 30 J gravitational, 50 J kinetic and 20 J thermal increase, giving the same 100 J total. Mechanical energy, the sum of kinetic and gravitational contributions here, has fallen to 80 J. The bar widths use one common energy scale and the particular values are illustrative.
For this unit’s illustrated case, how much mechanical energy has changed into the represented thermal contribution? Why is conservation of mechanical energy the wrong assumption for this case?
Answer and explanation

20 J. The account explicitly includes a thermal increase from interactions, so mechanical energy alone does not stay constant even though the full stated total does.

Mechanical energy is a subset of an energy account, not another name for every store. Check whether friction and other interactions transfer energy out of that subset before applying a mechanical-conservation shortcut.

20 J. The account explicitly includes a thermal increase from interactions, so mechanical energy alone does not stay constant even though the full stated total does.

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 10

A full supplied energy account starts with 80 J GPE. Later it has 15 J GPE, 45 J KE and 20 J thermal increase. Compare mechanical and total energy before and after.
Answer and explanation

Mechanical energy falls from 80 to 15+45 = 60 J. The stated total stays 80 J once the 20 J thermal increase is included.

Distinguish the mechanical subset from the full account.

Use a common boundary and reference for both states.

Mechanical energy falls from 80 to 15+45 = 60 J. The stated total stays 80 J once the 20 J thermal increase is included.

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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