Physics · Grades 8–12
Energy Lab
Energy changes jobs. A skater trades height for speed. A spring trades a squeeze for a launch. Two lifts can do the same work and still differ in power. The bars keep the books: what leaves one store shows up in another, or as warmth from friction. The joule is named for James Joule, whose paddle-wheel result was published in A.D. 1850.
The start is 2.2 m high and the far hill is 1.35 m. Height is measured from the valley. Space plays and pauses. R resets. g = 9.8 m/s². Friction takes μmg|cos θ| along the track.
The spring launches the ball straight up. Gravity is left out while the spring is still pushing, because that push is short. After release, kinetic energy and gravitational energy trade. The green line is a shelf at 0.40 m.
Useful work is the gravitational energy the load gains. Power is that work divided by the time. Efficiency is useful work divided by the energy the motor takes in. James Watt compared engines with horses in the A.D. 1780s; a watt is one joule each second.
What to watch
Height is stored energy. Speed is moving energy. A rough track turns some of both into warmth, so the skater cannot climb as high as it started.
A squeezed spring holds energy. Let go, and that energy becomes speed, then height. The mass changes the height: a heavier ball does not fly as high from the same spring.
Both lifts do the same work when they raise the same load the same distance. The quicker one is more powerful. A wasteful motor takes in more energy than the load gains.
Kinetic energy is ½mv². Gravitational potential energy is mgy, measured here from the valley floor. Elastic energy is ½kx². Friction’s work is −μmg|cos θ| along the track, and that work is the thermal bar. The three bars add to the energy the skater had at the start.
Work is W = Fd cos θ. A force perpendicular to the motion does none. Power is P = W/t, and also Fv when the force and speed stay steady. Efficiency is useful work divided by energy in.
On the smooth ramp the mass cancels: v = √(2gh). It does not cancel for the spring, because the stored energy does not grow with the ball’s mass.
Practice
Try these before you look. The worked answers are on a separate answer page, not beside the problems. Use g = 9.8 m/s².
- A 3 kg wagon rolls at 4 m/s. What is its kinetic energy?
- A 2.5 kg bag of flour is lifted from the floor onto a shelf 1.6 m higher. How much gravitational potential energy does it gain?
- A spring with k = 120 N/m is squeezed by 0.20 m. How much elastic potential energy is stored?
- A student pushes a crate with 50 N in the direction it moves, through 2.5 m. How much work does that push do?
- A student carries a 6 kg box across a level room, holding it at the same height the whole way. How much work does the upward force do on the box?
- A lift does 1,800 J of useful work in 12 s. What is its useful power?
- A motor takes in 800 J and gives 600 J of useful work. What is its efficiency?
- A 1 kg cart starts from rest and drops 0.45 m on a smooth ramp. How fast is it at the bottom?
- That same cart drops 0.45 m, but 2.0 J becomes thermal energy from friction. How fast is it now?
- Two lifts raise the same 25 kg crate by 2.0 m. Lift A takes 5 s. Lift B takes 20 s. Compare the useful work and the useful power.
Original School Launch model. Straight track pieces, g = 9.8 m/s², and no outside data. Nothing you do here is saved or sent. The ramp is a sketch, not a measured coaster.