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Mechanics

Kinetic and gravitational potential energy

  • 2 things to know
  • Papers 1 and 3

Overview

Recall questions on the two energy equations, why doubling speed quadruples kinetic energy, and why the potential energy formula only holds near the Earth's surface.

What you need to know

Answer each one before you reveal it.

Your recallNot started
Numbers

What is the equation for kinetic energy, what happens to it if speed doubles, and what does negative work mean?

Numbers

How is the change in gravitational potential energy calculated, and why does the path taken to a summit not matter?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    State the equation for the kinetic energy of a moving body:

    Model answer

    The kinetic energy is Eₖ = ½mv².

  2. 2

    What happens to the kinetic energy of a car if its speed doubles?

    Model answer

    It becomes four times as large, because kinetic energy is proportional to the square of the speed.

  3. 3

    What is the kinetic energy of a car of mass 1200 kg travelling at 25 m s⁻¹?

    Model answer

    Eₖ = ½ × 1200 × 25² = 3.75 × 10⁵ J.

  4. 4

    State the equation for the change in gravitational potential energy near the Earth's surface:

    Model answer

    The change is ΔEgrav = mgΔh.

  5. 5

    Why is ΔEgrav = mgΔh valid only near the Earth's surface?

    Model answer

    It assumes that g is constant, which holds only for height changes that are small compared with the radius of the Earth.

  6. 6

    Two walkers of equal mass reach the same summit, one by a steep direct path and the other by a longer zigzag. Why is their gain in gravitational potential energy the same?

    Model answer

    The change in gravitational potential energy depends only on the vertical height gained, not on the path taken to gain it.

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