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Conservation of mechanical energy

Lessons 43–44 · 2 lessons · P.Q. Habibullayev, A. Boydedayev, A.D. Bahromov, S.O. Burxonov. Physics Grade 7, revised and enlarged 4th edition. “O‘zbekiston milliy ensiklopediyasi” State Scientific Publishing House, Tashkent, 2017
43

The law of conservation of mechanical energy

Textbook: pp. 157–161
GoalKnow the law of conservation of mechanical energy and use it to solve problems.
New words
total mechanical energy · to‘liq mexanik energiyaconservation law · saqlanish qonunienergy conversion · energiya aylanishiclosed system · yopiq sistema
Explanation

The sum of a body’s kinetic and potential energies is its total mechanical energy: E = E_k + E_p. The law of conservation of mechanical energy: with no friction or resistance, the total mechanical energy of a closed system stays constant: mυ₁²/2 + mgh₁ = mυ₂²/2 + mgh₂. When a body falls, potential energy decreases and kinetic energy increases by the same amount; when it rises, the reverse. For example, for a body falling from rest from height h, at the ground mgh = mυ²/2, so υ² = 2gh; note that the result does not depend on the mass. With friction, part of the mechanical energy turns into heat, yet the total energy is conserved.

Worked examples
A body falling from rest from h = 20 m hits the ground with υ² = 2 · 10 · 20 = 400, so υ = 20 m/s (20 · 20 = 400) (g = 10).
A body thrown vertically upward at υ₀ = 10 m/s: at the top υ = 0, mgh = mυ₀²/2, h = 100 : 20 = 5 m.
Class activity

“Pendulum”: raise a light weight on a string to one side and release it (with an adult). Watch E_p and E_k swap. Safety: light weight, away from the head, nobody nearby.

Practice
1
State the law of conservation of mechanical energy.
2
A body falls from rest from h = 45 m. Speed at the ground (g = 10), m/s?
3
A body thrown up at υ₀ = 20 m/s: what height does it reach (g = 10), m?
4
Why is mechanical energy not conserved with friction, but total energy is?