Impulse, Momentum and Collisions

momentum = mass x velocity p = mv units: kgm/s or Ns

What is the value of the momentum of a 10 kg ball running down a bowling alley at a speed of 5 m/s? p = mv p = (10 kg)(5 m/s) p = 50 kgm/s

Momentum is a vector, it has a direction The ball bounces off the wall. What is the change in momentum?  p = p final - p initial = 2p

Newton’s 2 nd Law: F = ma = m  v/  t p Impulse-Momentum Theorem F  t = p

If this girl throws a 0.2 kg snowball at 20 m/s…at you, and it impacts your skull for 0.05 s, what is the force of the impact? F  t = m  vF = m  v/  t F = (0.2 kg)(20 m/s)/0.05 s F = 80 N

Stopping Distance A 2500 kg car brakes to slow from 25 m/s to 10 m/s in 6 s. What was the force of braking? F = m  v/  t = (2500 kg)(10 m/s – 25m/s)/6s F = N How far will it go in that time?  x = ½(v i – v f )  t = ½(25m/s – 10m/s) 6s  x = 45 m

Conservation of Momentum The total momentum before equals the total momentum after, if there are no external forces. m 1 v 1i + m 2 v 2i = m 1 v 1f + m 2 v 2f

80 kg Schoettle steps out of his 100 kg boat with a velocity of 2 m/s. What is the boat’s velocity? m 1 v 1i + m 2 v 2i = m 1 v 1f + m 2 v 2f 0 0 v 2f = -m 1 v 1f /m 2 v 2f = -(80 kg)(2 m/s)/100 kg v 2f = 1.6 m/s

Types of collisions (two things hitting each other) Perfectly Inelastic: the two things stick together m 1 v 1i + m 2 v 2i = (m 1 + m 2 )v f 10 kg 5 kg v 1i = 3 m/s What is the velocity after they stick?

Kinetic Energy is lost in inelastic collisions from the previous problem: m 1 = 10 kg, v 1i = 3 m/s, m 2 = 5 kg, v 2 = 0 How much of the KE got changed into other types of energy (sound, heat)? KE i = ½m 1 v 1i 2 = ½(10kg)(3 m/s) 2 = 45 J KE f = ½(m 1 + m 2 )v f 2 = ½(10kg + 5kg)(2 m/s) 2 = 30 J KE i – KE f = 15 J

Elastic Collisions Two objects hit and bounce off with no damage or loss of KE or momentum momentum: m 1 v 1i + m 2 v 2i = m 1 v 1f + m 2 v 2f KE: ½m 1 v 1i 2 + ½m 2 v 2i 2 = ½m 1 v 1f 2 + ½m 2 v 2f 2

Most collisions are neither elastic or perfectly inelastic.