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? Dp = pfinal - pinitial = 2p
Newton’s 2nd Law: F = ma = mDv/Dt p Impulse-Momentum Theorem FDt = 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? FDt = mDv F = mDv/Dt 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 = mDv/Dt = (2500 kg)(10 m/s – 25m/s)/6s F = -6250 N How far will it go in that time? Dx = ½(vi + vf)Dt = ½(25m/s + 10m/s) 6s Dx = 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 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
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
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
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
Most collisions are neither elastic or perfectly inelastic.