Energy, Year 10: energy stores, kinetic and gravitational energy

A system

HintThe solar ______ and the digestive ______ use the same word for a set of parts treated as one thing.

The whyBefore any energy calculation you decide what is inside your boundary: the kettle and its water, say, or a ball and the Earth. When the chosen set of objects changes, the way its energy is stored changes too. AQA opens the Energy topic with this idea.

The thermal store of the brakes (and then the surroundings)

HintThink about what you would notice if you could touch the discs just after a hard stop.

The whyFriction between the pads and the discs does work on the car, emptying its kinetic store. The same amount of energy raises the temperature of the brakes, which then warm the air around them. A vehicle slowing down is one of the situations AQA expects pupils to describe.

15

HintWith nothing lost to the air, the two stores must always add up to what the ball set off with.

The whyThe system is the ball and the Earth, and no energy leaves it, so the total stays at 60 J. If 45 J has moved into the gravitational potential store, 60 − 45 is left in the kinetic store. Putting both stores on one scale like this is how AQA wants energy changes shown.

heating; forces

HintOne is what a flame does to a pan of water; the other is a push or pull moving something along.

The whyEach way has its own equations later in the course: specific heat capacity for a temperature change, force × distance for mechanical work, and the electrical equations for work done in a circuit. Recognising which of the three is happening tells you which equation to reach for.

By the force doing work on the sledge

HintA push that moves something along is achieving more than just pressing on it.

The whyWhenever a force moves an object through a distance, work is done and energy is transferred. Here that energy fills the sledge's kinetic store, which is why the sledge gets faster for as long as the push continues. An object accelerated by a constant force is one of AQA's named situations.

speed

HintOf the two things that decide how hard a moving object hits, this is the one that counts twice over.

The whyIn symbols, Ek = ½ m v², with Ek in joules, m in kilograms and v in metres per second. Only the v is squared, so work out v² first and then multiply by the mass and by a half. AQA expects this equation to be recalled; it is not on the equation sheet.

18

HintSquare first, then deal with the half and the 4 kg.

The whyEk = ½ × m × v² = 0.5 × 4 × 3² = 0.5 × 4 × 9. Squaring the speed before anything else avoids the most common slip. The equation must be recalled.

It becomes four times as large

HintLook at what the equation does to the quantity that has changed.

The whyKinetic energy depends on speed squared, so doubling the speed multiplies the energy by 2², and trebling it would multiply the energy by 9. This is why a small rise in speed makes a crash so much more severe and a braking distance so much longer.

10 m/s

HintUndo the equation one step at a time; the last step is a root.

The whyRearranging Ek = ½ m v² gives v² = 2 × Ek ÷ m = 2 × 100 ÷ 2 = 100, so v is the square root of 100. Pupils are expected to recall the equation and rearrange it for any of its three quantities.

They are equal — 200 000 J each

HintWork both out before trusting your instinct about the heavier vehicle.

The whyCar: 0.5 × 1000 × 20² = 200 000 J. Lorry: 0.5 × 4000 × 10² = 200 000 J. The lorry has four times the mass, but the car has twice the speed, and because speed is squared that also counts four times.

Gravitational potential energy

HintIt is named after the force you have to work against to lift anything.

The whyLifting an object means doing work against its weight, and that energy is stored because of the object's raised position. Let the object fall and the store empties again as it speeds up. Its short form is g.p.e., or Ep in equations.

g.p.e. = mass × gravitational field strength × height

HintThree things multiply together: how much stuff, how hard the planet pulls on each kilogram, and how far up.

The whyIn symbols, Ep = m g h, with Ep in joules, m in kilograms, g in newtons per kilogram and h in metres. AQA expects this equation to be recalled, and says the value of g will always be given in the question.

29.4

HintMultiply all three numbers in the question together.

The whyEp = m × g × h = 2 × 9.8 × 1.5. The value of g is given, as AQA says it always will be. The answer is also the work done in lifting the book.

50 m

HintRearrange so the unknown stands alone, then divide the energy by the other two multiplied together.

The whyRearranging Ep = m g h gives h = Ep ÷ (m × g) = 24 500 ÷ (50 × 9.8) = 24 500 ÷ 490. Dividing by the mass and the field strength together, rather than one at a time, saves a slip.

10 m/s

HintAll the energy it had because of its position has become energy of movement by the bottom.

The whyg.p.e. at the top = 0.5 × 10 × 5 = 25 J, and with no air resistance all of it is in the kinetic store at the bottom. Then v² = 2 × 25 ÷ 0.5 = 100, so v is the square root of 100. Following energy from a gravitational store to a kinetic store is an investigation AQA suggests for this section.