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Kinetic energy
Textbook: pp. 155–156
GoalKnow kinetic energy E_k = mυ²/2 and the work–energy theorem (A = ΔE_k).
New words
kinetic energy · kinetik energiyasquare of speed · tezlik kvadratiwork–energy theorem · kinetik energiya teoremasiwork · ish
Explanation
The energy of a moving body is called kinetic energy. For mass m and speed υ it is E_k = mυ²/2. It is proportional to the mass and to the square of the speed: doubling the speed makes the kinetic energy 4 times larger. This explains why speed is dangerous: stopping a fast car takes a very large amount of work. The work–energy theorem: the work done by the resultant of the forces on a body equals the change of its kinetic energy: A = E_k2 − E_k1 = mυ₂²/2 − mυ₁²/2. Kinetic energy is a scalar and never negative; its unit is the joule.
Worked examples
m = 2 kg, υ = 6 m/s: E_k = 2 · 36 : 2 = 36 J.
A 1000 kg car speeding up from 10 to 20 m/s: A = 1000 · 400 : 2 − 1000 · 100 : 2 = 200 000 − 50 000 = 150 000 J.
Class activity
“Double the speed”: fill a table — m = 1 kg, υ = 1, 2, 3, 4 m/s gives E_k = 0.5; 2; 4.5; 8 J. Safety: calculation only; do not play on roads.
Practice
1
What is the formula for kinetic energy?
E_k = mυ²/2.
2
m = 4 kg, υ = 5 m/s. E_k (J)?
50
3
If the speed triples, by what factor does E_k grow?
9
4
Why is a fast car hard to stop?
E_k depends on the square of speed, so the work needed to stop it rises sharply.