1. Impulse, Momentum and Collisions

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

3. 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

4. Momentum is a vector, it has a direction
The ball bounces off the wall. What is the change in momentum?
Dp = pfinal - pinitial
= 2p

5. Newton’s 2nd Law:
F = ma
= mDv/Dt p
Impulse-Momentum Theorem
FDt = p

6. 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?
FDt = mDv
F = mDv/Dt
F = (0.2 kg)(20 m/s)/0.05 s
F = 80 N

7. 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 = mDv/Dt
= (2500 kg)(10 m/s – 25m/s)/6s
F = N
How far will it go in that time?
Dx = ½(vi + vf)Dt
= ½(25m/s + 10m/s) 6s
Dx = 105 m

8. Conservation of Momentum
The total momentum before equals the total momentum after, if there are no external forces.
m1v1i + m2v2i = m1v1f + m2v2f

9. 80 kg Schoettle steps out of his 100 kg boat with a velocity of 2 m/s
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
v2f = -m1v1f/m2
v2f = -(80 kg)(2 m/s)/100 kg
v2f = 1.6 m/s

10. Types of collisions (two things hitting each other)
Perfectly Inelastic: the two things stick together
m1v1i + m2v2i = (m1 + m2)vf
5 kg
10 kg
What is the velocity after they stick?
v1i = 3 m/s
m1v1i + m2v2i = (m1 + m2)vf
m1v1i = (m1 + m2)vf
vf = 2 m/s

11. Kinetic Energy is lost in inelastic collisions
from the previous problem: m1 = 10 kg, v1i = 3 m/s, m2 = 5 kg, v2 = 0
How much of the KE got changed into other types of energy (sound, heat)?
KEi = ½m1v1i2 = 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

12. Elastic Collisions
Two objects hit and bounce off with no damage or loss of KE or momentum
momentum: m1v1i + m2v2i = m1v1f + m2v2f
KE: ½m1v1i2 + ½m2v2i2 = ½m1v1f2 + ½m2v2f2

13. Most collisions are neither elastic or perfectly inelastic.