☰ Contents · Physics

Conservation of momentum. Jet motion

Lessons 37–38 · 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
37

The law of conservation of momentum

Textbook: pp. 135–139
GoalState the law of conservation of momentum and apply it to collisions and recoil.
New words
closed system · yopiq sistemaconservation of momentum · impulsning saqlanishiinelastic collision · noelastik urilishrecoil · orqaga tepish
Explanation

A system made up only of interacting bodies, with no external forces acting (or with them balanced), is a closed system. The law of conservation of momentum: the total momentum of the bodies of a closed system is the same before and after their interaction: m₁υ₁ + m₂υ₂ = m₁υ₁′ + m₂υ₂′. It follows from Newton’s second and third laws: whatever one body’s momentum gains, the other’s loses. In an inelastic collision the bodies move together: m₁υ₁ + m₂υ₂ = (m₁ + m₂)υ. In a push-apart (a shot) the total momentum stays zero, which is why a gun recoils opposite to the bullet. Since momentum is a vector, direction (sign) must be taken into account.

Worked examples
A 2 kg cart at 3 m/s hits a stationary 1 kg cart and they stick: υ = (2 · 3 + 0) : (2 + 1) = 2 m/s.
A 4 kg rifle fires a 0.01 kg bullet at 400 m/s: 0 = 0.01 · 400 + 4 · υ, so υ = −1 m/s (recoil of 1 m/s backward).
Class activity

“Carts”: collide two toy carts gently with a soft bumper and discuss the motion afterwards. Safety: only light toys, keep fingers clear.

Practice
1
State the law of conservation of momentum.
2
A 3 kg body at 4 m/s hits a stationary 1 kg body and they stick. Common velocity (m/s)?
3
A 40 kg child standing still on roller skates throws a 0.4 kg ball forward at 10 m/s. At what speed does the child recoil (m/s)?
4
Why does a boat move back when you jump from it to the shore?