Coaching Centre
Work and energy in motion
Kinetic energy and its dependence on speed squared, gravitational and elastic potential energy, work done by a force, the law of conservation of energy, efficiency of bouncing balls, energy transformations in sport, and the woomera as a way of doing more work on a spear.
In televised cricket, "Snicko" listens for the tiny click when the ball brushes the edge of the bat, and "Hot Spot" uses an infrared camera to see a bright patch where the ball warmed the bat. Both work because a collision never transfers all of the kinetic energy: a little always turns into sound and heat.
Kinetic energy
Every moving object has kinetic energy (KE). The more mass and the more speed, the more kinetic energy.
kinetic energy = ½ × mass × velocity²
KE = ½ m v² (J, kg, m/s)
Because the speed is squared, speed matters far more than mass. Double the mass and the KE doubles; double the speed and the KE becomes four times as big. Triple the speed and the KE is nine times as big.
A 1400 kg car travels at 40 km/h. 40 ÷ 3.6 = 11.11 m/s.
KE = ½ × 1400 × 11.11² = 0.5 × 1400 × 123.4 = 86 400 J ≈ 86 kJ.
At 80 km/h (22.22 m/s): KE = ½ × 1400 × 22.22² ≈ 346 kJ, four times as much.
All of this energy must be removed to stop the car, either by the brakes (as heat) or, in a crash, by crushing metal and bodies. That's why speed is so dangerous (5I).
Potential energy
Gravitational potential energy (GPE) is stored when an object is lifted against gravity.
GPE = mass × g × height GPE = m g h (J, kg, 9.8 N/kg, m)
Lifting a 100 g apple (weight about 1 N) up 1 m gives it about 1 J of GPE. Climbing 2 m of stairs, a 60 kg student gains 60 × 9.8 × 2 = 1176 J, about 1.2 kJ.
Elastic potential energy (EPE) is stored when something is stretched or squashed: a bow, a trampoline, a compressed tennis ball. The stiffer the object and the more it is distorted, the more energy it stores.
Work
In physics, work is done when a force moves an object in the direction of the force. Work is a transfer of energy, so it is measured in joules.
work = force × distance moved W = F × d (J, N, m)
If you push a wall and it doesn't move, you do no work on it (though your muscles still use energy). When a net force does work on an object, its kinetic energy increases by exactly that amount; when a force such as friction acts against the motion, it does negative work and takes kinetic energy away.
A force of 200 N moves a heavy box 3 m. W = 200 × 3 = 600 J.
800 J of work is done using a 250 N force. d = W ÷ F = 800 ÷ 250 = 3.2 m.
Lifting a 0.1 kg object 1 m needs a force equal to its weight, 0.98 N. W = 0.98 × 1 = 0.98 J, which becomes 0.98 J of GPE.
In Year 7 you saw how the woomera (spear-thrower), developed by Aboriginal peoples across much of Australia, works as a lever. Work and energy explain why it is so effective. The woomera's hook holds the end of the spear, effectively lengthening the thrower's arm. During the throw, the thrower's force acts on the spear over a much longer, faster arc than the hand alone could manage, so more work is done on the spear and it leaves with much more kinetic energy, travelling faster and further. Many woomeras are also multi-purpose tools, used for making fire, cutting, mixing ochre and carrying.
Conservation of energy
Law of conservation of energy: energy cannot be created or destroyed. It can only be transferred or transformed, so the total amount of energy stays the same.
A ball thrown straight up shows this clearly. It leaves your hand with KE. As it rises it slows down, and its KE becomes GPE. At the top it momentarily stops: all the KE has become GPE. As it falls, the GPE turns back into KE. Ignoring air resistance, it arrives back at your hand with the same speed it left with.
When an object falls from rest, the GPE lost equals the KE gained, so m g h = ½ m v². The mass cancels, giving v = √(2 g h). A student falling 2 m (from a wall) hits the ground at √(2 × 9.8 × 2) = 6.3 m/s, about 23 km/h, whatever their mass.
Efficiency: bouncing balls
In real collisions some energy is always transformed into heat and sound, which spread into the surroundings and are very hard to use again. We say this energy is "wasted" or "lost", although it still exists.
efficiency = useful energy out ÷ total energy in × 100%
When a ball bounces, its GPE becomes KE, then elastic PE as it squashes, then KE and GPE again. Since GPE is proportional to height, the efficiency of a bounce is simply rebound height ÷ drop height. A tennis ball dropped from 2.0 m that rebounds to 1.1 m has a bounce efficiency of 55%; the other 45% became heat and sound. Official rules for tennis balls and basketballs actually specify how high they must bounce.
- Drop the Tennis ball from 2 m. Check the first rebound is 1.1 m and the efficiency is 55%. Watch the energy bars as the ball squashes on the ground.
- Compare all five balls from the same height. Rank them from most to least efficient.
- Drop the Squash ball (cold), then the Squash ball (warm). Why do squash players hit the ball for a few minutes before a match?
- Does the drop height change the efficiency? Try the superball from 1 m and 2.5 m.
Energy in sport
Hitting or kicking a ball is a chain of transfers and transformations. The moving bat, racquet, club or foot has KE. On impact, the ball is squashed and stores EPE. As the ball springs back into shape, the EPE becomes the ball's KE. Some energy becomes sound (the "thwack" that Snicko detects) and heat (which Hot Spot's infrared camera sees, and which warms up a squash ball during a game).
Bodies collide too. In a tackle, players' KE is transformed into work that compresses tissues, and if the forces are big enough, into damage: torn ligaments, bruising or broken bones. Landing from a jump is a collision with the ground, and bending the knees spreads the stop over a longer distance, so the force is smaller.
Test yourself
A 2 kg ball moves at 3 m/s. Its kinetic energy is
KE = ½ × 2 × 3² = 9 J.
A car's speed increases from 50 km/h to 100 km/h. Its kinetic energy becomes
KE ∝ v²; doubling v multiplies KE by 2² = 4.
How much work is done when a 400 N force pushes a crate 5 m?
W = F × d = 400 × 5 = 2000 J.
A ball dropped from 2.0 m rebounds to 1.3 m. The bounce efficiency is
1.3 ÷ 2.0 × 100 = 65%. The other 35% became heat and sound.
At the top of its flight, a ball thrown straight up has
It momentarily stops, so all its KE has become GPE.
Label the bouncing ball diagram.
Put the energy changes during one bounce in order, starting with the ball held above the ground.
Kinetic energy depends on mass and the of the speed. Work equals force × and is measured in . Energy cannot be created or . In a collision, some energy is always transformed into and sound.
A ball is dropped and rebounds to 65% of its starting height. (a) Explain, using the law of conservation of energy, what has happened to the other 35% of the energy. (b) A golfer wants a ball that travels as far as possible. Explain why she would choose a ball that bounces efficiently. (c) Would you want a car to behave like an efficient or an inefficient ball in a crash? Justify your answer.
(a) Energy cannot be created or destroyed. The ball's GPE became KE as it fell, then elastic PE as it squashed against the floor. Not all of the elastic PE turned back into KE: about 35% was transformed into heat, warming the ball and floor slightly, and into sound. Only 65% was left to lift the ball again, so it rebounds to 65% of the height. (b) When a club hits a ball, the club's KE is transformed into elastic PE in the squashed ball and then into the ball's KE. An efficient ball wastes less of this as heat and sound, so it leaves the club with more KE and a higher speed, and travels further. (c) A car should behave like an inefficient ball. In a crash, the car's KE should be absorbed by doing work crumpling the front of the car, not stored and given back as a bounce. If the car bounced back, its velocity would change by even more (from forwards to backwards), so the occupants would experience a larger change in momentum and bigger forces.