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PHYSICS · Stage 7 · Chapter 1: Energy

Physics 1.5 Gravitational potential energy and kinetic energy

5 min read 5 parts Lesson 5 of 8

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1.5 Gravitational potential energy and kinetic energy — Alhussan International Academy — Physics (Stages 7–9) notes: Describe the factors that affect gravitational potential energy and kinetic energy and the energy changes between them, including dissipation.GPE = the energy some…

  • Rearranging
  • Stationary
  • Ball thrown upwards
  • Entering water
  • Bouncing ball
  • Pulling back

Part 1 of 5Gravitational potential energy (GPE)

  • GPE = the energy something has because of its position, another term for energy in a gravity store or energy stored gravitationally.
  • Height — GPE depends on distance from the centre of the Earth, so moving up two floors gains twice as much GPE as moving up one floor.
  • Mass — it also depends on mass, so a mother with twice the mass of her son gains twice as much GPE going up one floor.
  • Formula — GPE = mass × gravitational field strength × height, E = m × g × h.
    • On Earth g = 10 N/kg, and height must be in metres and mass in kilograms.
    • A 2 kg book on a shelf 1.5 m high has 30 J of GPE.
  • Rearranging — h = GPE ÷ (m × g) and m = GPE ÷ (g × h).
  • Graph — a graph of GPE against height is a straight line through the origin, with gradient m × g.

Part 2 of 5Kinetic energy (KE)

  • KE = the energy something has when it is moving, another term for energy in a kinetic store or energy stored kinetically.
  • Mass — if a lion and an antelope move at the same speed, the lion has more kinetic energy because it has more mass.
  • Speed — two lions of the same mass running at different speeds have different kinetic energy, and the faster lion has more.
    • Doubling the speed makes the kinetic energy four times as large.
  • Formula — KE = ½ × m × v2.
  • Stationary — a stationary object has zero KE.

Part 3 of 5Up and down

  • Ball thrown upwards — it slows down, stops for an instant, then speeds up as it falls.
    • On the way up, energy moves from the kinetic store to the gravitational store.
    • The increase in GPE equals the decrease in kinetic energy.
    • On the way down, energy is transferred from the gravitational store to the kinetic store.
  • Dissipation — a very small amount of energy is transferred to the surroundings because of air resistance.
  • Diver — at the top of the board GPE is greatest and KE is zero, halfway they have equal amounts, and just above the water GPE is smallest and KE is greatest.
PositionGPEKE
TopMaximumZero
HalfwayHalfHalf
Just above the ground or waterMinimumMaximum
  • Entering water — KE is transferred to the kinetic energy of the water, thermal energy and sound.
  • Bouncing ball — it converts between KE and GPE but loses a little energy to thermal and sound on each bounce, so each bounce is lower.

Part 4 of 5Back and forth: the pendulum

  • Pendulum = a ball on a string that swings backwards and forwards.
  • Pulling back — when you pull the pendulum back you also pull it up, so its GPE increases.
  • Letting go — it falls and energy is transferred to a kinetic store.
  • Swinging up — energy is transferred back to a gravity store.
    • At the highest point of the swing there is no kinetic energy and GPE is a maximum.
    • At the lowest point KE is a maximum and GPE is a minimum.
  • Swing — a child on a swing behaves like a pendulum.
    • If the father stops pushing, she does not swing so high, because friction warms parts of the swing and air resistance heats the air.
    • Kinetic energy is transferred to the thermal store of the surroundings, which is dissipation.

Part 5 of 5Rollercoasters

  • Design — engineers think carefully about kinetic energy and GPE to know how much energy is needed for passengers to reach the top of the hills.
  • Lifting — the ride lifts people up high so they can move fast on the way down.
  • Calculation — a 500 kg car lifted 20 m gains 100 000 J of GPE.
    • Ignoring friction, all of this becomes KE at the bottom of the first drop, where the car reaches its top speed.
  • Dissipation — friction and air resistance mean the car has less KE than expected, so later hills must be lower than the first.
  • Ordering GPE — compare mass × height, using consistent units.

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