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 rolling 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 = pfinal - pinitial = 2p

Newton’s 2nd Law:F = ma = mv/t

p

Impulse-Momentum Theorem

Ft = 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?

Ft = mv F = mv/tF = (0.2 kg)(20 m/s)/0.05 sF = 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 = mv/t = (2500 kg)(10 m/s – 25m/s)/6sF = -6250 N

How far will it go in that time?x = ½(vi + vf)t = ½(25m/s + 10m/s) 6s

x = 105 m

Conservation of Momentum

The total momentum before equals the total momentum after, if there are no external forces.

m1v1i + m2v2i = m1v1f + m2v2f

80 kg Schoettle steps out of his 100 kg boat with a velocity of 2 m/s. What is the boat’s velocity?

m1v1i + m2v2i = m1v1f + m2v2f

0 0

v2f = -m1v1f/m2

v2f = -(80 kg)(2 m/s)/100 kg

v2f = 1.6 m/s

Types of collisions (two things hitting each other)

Perfectly Inelastic: the two things stick together m1v1i + m2v2i = (m1 + m2)vf

10 kg 5 kg

v1i = 3 m/s What is the velocity after they stick?

m1v1i + m2v2i = (m1 + m2)vf

m1v1i = (m1 + m2)vf vf = 2 m/s

Kinetic Energy is lost in inelastic collisions

from the previous problem: m1 = 10 kg, v1i = 3 m/s, m2 = 5 kg, v2 = 0How much of the KE got changed into other types of energy (sound, heat)?KEi = ½m1v1i

2 = ½(10kg)(3 m/s)2 = 45 J

KEf = ½(m1 + m2)vf2 = ½(10kg + 5kg)(2 m/s)2

= 30 J

KEi – KEf = 15 J

Elastic CollisionsTwo objects hit and bounce off with no damage or loss of KE or momentum

momentum: m1v1i + m2v2i = m1v1f + m2v2f

KE: ½m1v1i2 + ½m2v2i

2 = ½m1v1f2 + ½m2v2f

2

Most collisions are neither elastic or perfectly inelastic.