Energy & Its Transformations — Science

  1. Grade 6 — Forms of Energy
  2. Grade 6 — Energy Transformations & Conservation
  3. Grade 6 — Heat vs Temperature
  4. Grade 6 — Heat Transfer: Conduction, Convection & Radiation
  5. Grade 8 — Kinetic & Potential Energy

    ↑ Deepens: energy becomes kinetic + potential you can quantify.

  6. Grade 8 — Energy Transfer & Transformation
  7. Grade 8 — Thermal Energy & Heat Transfer
  8. Grade 8 — Conservation of Energy
  9. Grade 12 — Work & Power

    ↑ Deepens: energy tied to work, and conserved in collisions.

  10. Grade 12 — Kinetic & Potential Energy
  11. Grade 12 — Conservation of Energy
  12. Grade 12 — Momentum & Collisions

Apply it in a new setting

Problem 1

A 1500 kg car slows from 20 m/s to 10 m/s as the driver brakes. How much kinetic energy does the car lose? Use KE = ½mv^2.
Hints

Find the kinetic energy at both speeds separately, then subtract.

KE depends on v^2, so doubling the speed quadruples the energy — the two states are not close.

KE lost = ½m(v_0^2 − v^2) = ½ · 1500 · (400 − 100).

Answer and explanation

225000 J

Start: KE = ½ · 1500 · 20^2 = 750 · 400 = 300000 J.

End: KE = ½ · 1500 · 10^2 = 750 · 100 = 75000 J.

Energy lost = 300000 − 75000 = 225000 J.

Problem 2

A crane lifts a 200 kg steel beam straight up 15 m at a slow, steady speed. How much work does the crane do against gravity? Use g = 9.8 m/s^2 and W = Fd.
Hints

At steady speed the lifting force just balances the beam's weight.

Weight = mg, and work = force × distance lifted.

W = (200 · 9.8) · 15.

Answer and explanation

29400 J

Weight of the beam = mg = 200 · 9.8 = 1960 N.

The crane must pull up with 1960 N over 15 m.

W = Fd = 1960 · 15 = 29400 J.

Problem 3

An electric motor lifts a 50 kg load 12 m in 8 s at constant speed. What is the motor's average power output? Use g = 9.8 m/s^2 and P = W/t.
Hints

Power is the work done divided by the time taken.

The work here is the energy given to the load: W = mgh.

P = (50 · 9.8 · 12) ÷ 8.

Answer and explanation

735 W

Work done lifting the load = mgh = 50 · 9.8 · 12 = 5880 J.

Power = work ÷ time = 5880 ÷ 8.

P = 735 W.

Problem 4

A ball is dropped from rest and falls 8 m to the ground. Ignoring air resistance, how fast is it moving just before it lands? Use g = 9.8 m/s^2 and conservation of energy.
Hints

All the gravitational potential energy at the top becomes kinetic energy at the bottom.

Set mgh = ½mv^2 — the mass cancels out, so you don't even need it.

v = √(2gh) = √(2 · 9.8 · 8).

Answer and explanation

12.5 m/s

Conservation of energy: mgh = ½mv^2, so the mass cancels.

v = √(2gh) = √(2 · 9.8 · 8) = √156.8.

v ≈ 12.5 m/s.

Problem 5

How much heat energy is needed to raise the temperature of 2 kg of water from 20°C to 80°C? Use q = mcΔT with c = 4184 J/(kg·°C) for water.
Hints

ΔT is the temperature change, not the final temperature.

ΔT = 80 − 20 = 60°C.

q = 2 · 4184 · 60.

Answer and explanation

502080 J

Temperature change ΔT = 80 − 20 = 60°C.

q = mcΔT = 2 · 4184 · 60.

q = 502080 J (about 502 kJ).

Problem 6

A 2 kg cart rolls at 3 m/s and collides with a stationary 1 kg cart. The two carts stick together. Using conservation of momentum (p = mv), what is their common speed just after the collision?
Hints

Total momentum before the collision equals total momentum after.

Momentum before = (2 · 3) + (1 · 0); after, the moving mass is 2 + 1 = 3 kg.

v = total momentum ÷ combined mass = 6 ÷ 3.

Answer and explanation

2 m/s

Momentum before = 2 · 3 + 1 · 0 = 6 kg·m/s.

After sticking, combined mass = 2 + 1 = 3 kg, so 3 · v = 6.

v = 6 ÷ 3 = 2 m/s.

Problem 7

A student pulls back the elastic band of a slingshot and releases it, launching a stone straight up into the air. Which sequence best describes the main energy transformations from the moment of release until the stone reaches its highest point?
  1. Elastic potential energy → kinetic energy → gravitational potential energy
  2. Kinetic energy → elastic potential energy → gravitational potential energy
  3. Gravitational potential energy → kinetic energy → elastic potential energy
  4. Thermal energy → kinetic energy → elastic potential energy
Hints

Think about where the energy is stored at the very start, while the band is stretched.

At the highest point the stone is momentarily slow but high up — which store is full there?

Stretched band (elastic) → moving stone (kinetic) → high stone (gravitational).

Answer and explanation

Elastic potential energy → kinetic energy → gravitational potential energy

The stretched elastic band stores elastic potential energy at release.

As it snaps back, the stone speeds up — that is kinetic energy.

Rising to the top, the stone slows while gaining height, storing gravitational potential energy, so the order is A.

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