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

A system

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

为什么Before 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)

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

为什么Friction 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

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

为什么The 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

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

为什么Each 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

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

为什么Whenever 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

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

为什么In 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

提示Square first, then deal with the half and the 4 kg.

为什么Ek = 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

提示Look at what the equation does to the quantity that has changed.

为什么Kinetic 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

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

为什么Rearranging 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

提示Work both out before trusting your instinct about the heavier vehicle.

为什么Car: 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

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

为什么Lifting 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

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

为什么In 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

提示Multiply all three numbers in the question together.

为什么Ep = 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

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

为什么Rearranging 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

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

为什么g.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.