Conservation of Momentum

In a collision or an explosion where there is no external force, the total momentum is conserved. “The total momentum before equals the total momentum after” Σp before = Σp after

“Before” Collision (Collision) “After” Collision A A A B B B

Σp before (Total momentum “before”) Σp before = Momentum of ball A “before” + Momentum of ball B “before” Σp before = p Ai + p Bi = m A v Ai + m B v Bi “Before” Collision A B

Σp after (Total momentum “after”) Σp after = Momentum of ball A “after” + Momentum of ball B “after” Σp after = p Af + p Bf = m A v Af + m B v Bf “After” Collision AB

Conservation of Momentum Principle says: “Total momentum before = Total momentum after” Σp before = Σp after which means: p Ai + p Bi = p Af + p Bf m A v Ai + m B v Bi = m A v Af + m B v Bf *Sometimes this is written as: m A u A + m B u B = m A v A + m B v B

Total momentum before = Total momentum after p A(before) + p B(before) = p A(after) + p B(after) m A u A + m B u B = m A v A + m B v B Before After

Example: Two balls, A and B, are rolling towards each other and are about to collide. Ball A has a mass of 400 g and is travelling at 0.8 ms -1. Ball B has a mass of 300 g and is travelling at 0.7 ms -1. Calculate the total momentum “Before”

The two balls have collided and now are moving away from each other. What is the total momentum now? If the momentum of ball A immediately after the collision is kgms -1, calculate: the momentum of ball B the velocity of ball B “After”

Example (Page 125, example H) A shunting locomotive (m = 5000 kg) travelling at 3 ms -1 bumps into and locks onto a stationary carriage of mass 3000 kg. What combined speed do the locomotive and carriage have after the collision?

Example A Morris Minor car (mass 750 kg) is travelling at 30 ms -1 and collides head-on with a Mercedes Benz car (mass 1600 kg) travelling at 20 ms -1 in the opposite direction. The two cars lock together in the crash. a)Calculate the total momentum b)Calculate the velocity of the combined wreckage after the collision c)Would the wreckage keep moving at this velocity? Why or why not?

Example (Page 126, example I) A rifle (m 4 kg) fires a bullet (m = 20 g) which travels at a speed of 400 ms -1. What is the recoil speed of the rifle?

Worksheets 10 & 11 Activity 10B Questions 1 ~ 6

Conservation of Momentum and Impulse (Δp) Two balls, A and B, are rolling towards each other. Ball A (m = 500 g) is moving at 1.0 ms -1 and ball B (m = 1.5 kg) is moving at 0.50 ms -1. After they collide, Ball A moves in the opposite direction at 1.25 ms -1. Calculate: the change in momentum of ball A (Δp A ) the change in momentum of ball B (Δp B )

Conservation of Momentum and Impulse (Δp) In a collision between two objects, the change in momentum (impulse) of one object is equal to the change in momentum of the other object, only in the opposite direction. (Δp A = -Δp B ) This is because when the two objects collide, they apply the same force on each other, in the opposite direction. (Newton’s 3 rd Law!! )

Example An over-speeding boy racer travelling at 25 ms -1, crashes into the back of another car which is only travelling at a speed of 12.5 ms -1 in the same direction. Boy racer’s car = 1200 kg The other car = 2000 kg a)Find the total momentum. b)The speed of the boy racer’s car immediately after the crash is 9.37 ms -1. Calculate the speed of the other car immediately after the crash. c)Calculate the change in momentum of each car.

Think about this: Conservation of momentum principle says: “In a collision or an explosion where there is no external force, the total momentum is always conserved” How about kinetic energy? Would total kinetic energy be conserved in a collision as well? (ΣK E(before) = ΣK E(after) ?)

Collisions – elastic vs. inelastic One may ask – “Couldn’t we just use the conservation of energy principle, by calculating the total kinetic energy?” The answer is NO – because often kinetic energy is lost due to friction, meaning that the “total kinetic energy” is not conserved. However, there are collisions where “total kinetic energy” IS conserved. These collisions are called “elastic collisions”.

An elastic collision is a collision which: the total kinetic energy before equals the total kinetic energy after. (The total kinetic energy is conserved.) Total E k(before) = Total E k(after) *If the total kinetic energy is NOT conserved, the collision is inelastic.

Example Two objects of equal mass, A and B, are travelling towards each other. Object A (2 kg) is moving at 0.6 ms -1 and object B is moving at 0.5 ms -1. After they collide, the two objects travel in the opposite direction. Object A travels at 0.39 ms -1 and object B travels at 0.49 ms -1. Is the total momentum conserved? Is the total kinetic energy conserved? Is this collision elastic or inelastic?

Worksheets 10 & 11 Activity 10B Questions 1 ~ 6 Homework Booklet: “Momentum”