Momentum and collisions

What is momentum?  Momentum is the mass and velocity of a moving object. We find it mathematically using the formula: p = mv  Momentum has units of kgms -1

Conservation of momentum  In a closed system (one where no external forces are acting), momentum is conserved  That means the total momentum doesn’t change in that system  A pool table has collisions where momentum is conserved between balls  Two balls that collide will have the same total momentum before and after  One ball moving transfers all its momentum to a stationary ball  Balls share momentum between them

Worked example one  A car of mass 1000kg moving at 5ms -1 hits a stationary car of mass 1200kg. After the collision, the two cars are joined together and move off with a new combined velocity. Find the new velocity.  Explain why, in reality, momentum would not be conserved in this system

Worked example one Write down what you know: m 1 = 1000kg m 2 = 1200kg v 1 = 5ms-1 Momentum before the collision: p 1 = m 1 v 1 = 1000 x 5 = 5000 kgms -1

Worked example one Momentum after the collision = 5000kgms -1 Combined mass = = 2200kg p 2 = (m 1 + m 2 )v = 2200 x v 2 v 2 = 2.27ms -1 Check your answer: units? reasonable?

Worked example one This answer assumed that momentum is conserved. In real life, momentum would not be conserved because there would be external forces like friction in a collision like this.

Momentum and impulse  Impulse is change in momentum  When an object hits another and changes its velocity, mass or direction, it changes its momentum  A force is required for this to happen Δp = F/t  We see this happening in situations where things bounce or come to a complete stop over a period of time

Worked example two  A gymnast practices on a balance beam and jumps off onto a spongy mat. Explain why the gymnast would practice on a mat instead of on a hard floor

Worked example two  Impulse is the change in momentum. When the gymnast hits the floor, they come to rest, so the change in momentum is always the same.  However, the spongy floor absorbs the impact and moves with them, so it takes longer to come to rest than it does on a hard floor  Because the time is longer on the spongy floor, while the change in momentum is the same, the force of the floor on the gymnast is less  Because the force is less, the effect on the gymnast will not be as severe and they are less likely to be injured

Worked example three  A student of mass 55kg running at a constant speed of 2.1ms -1 through an obstacle course has a 8kg load dropped onto her back.  After the load is dropped, she accelerates back up to her constant speed over a time of 0.8s. Find the unbalanced force acting on her over this time.

Worked example three This is an impulse problem First, find the change in momentum: m 1 = 55kg m 2 = 8kg v = 2.1ms -1 Initial momentum: p = m 1 v = 55 x 2.1 = 115.5kgms -1

Worked example four Momentum is not conserved Final momentum: p = (m 1 + m 2 )v = (55 + 8) x 2.1 = 132.3kgms -1 Change in momentum: – = 16.8kgms-1 Impulse equation to find unbalanced force: Δp = F/t 16.8 = F/0.8 F = 13.44N