1. Aim: How do we explain linear momentum and its conservation?

2. Linear Momentum
p=mv Momentum = Mass * Velocity px=mvx py=mvy pz=mvz Momentum is a vector and has components

3. Thought Question
Two objects have equal kinetic energies. Assume mass 1 is larger than mass 2. How do the magnitudes of their momenta compare?
p1 < p b) p1=p c) p1>p2
d) Can’t be Determined

4. Newton’s 2nd Law Restated
Fnet =dp/dt How can we use this along with Newton’s 3rd Law to prove that momentum is conserved?

5. Conservation of Linear Momentum
The total momentum of an isolated system remains constant ptot=constant Momentum is conserved for an isolated system regardless of the nature of internal forces, even if the forces are nonconservative

6. Thought Question 2
A baseball is projected into the air at an upward angle to the ground. As it moves through its trajectory, its velocity and therefore its momentum constantly change. Is this a violation of conservation of momentum? No, gravity is an external force acting on the baseball so the baseball by itself is not a closed system.

7. Problem 1 1. A 3kg particle has a velocity of (3.00i – 4.00j)m/s.
a) Find its x and y components of momentum.
Find the magnitude and direction of its momentum.
px = mvx = 3(3) = 9 kg m/s
py = mvy=3(-4) =-12 kg m/s
b) p = √(px 2 + py 2 ) = √( ) = 15 kg m/s
tanᶿ = py/px = 12/9 so ᶿ=53 degrees south of west or just 307 degrees

8. Problem 2
A baseball player wishes to maintain his physical condition during the winter. He uses a 50.0 kg pitching machine to help him, placing the machine on the pitcher’s mound. The ground is covered with a thin layer of ice, so that friction between the ground and the machine is negligible. The machine fires a 0.15 kg baseball horizontally with a speed of 36 m/s. What is the recoil speed of the machine?
Total momentum of system is 0.
m1v1+m2v2=0
50v1 +(0.15)(36)=0
V1= m/s

9. Conservation of Momentum in the Subatomic World
. One type of nuclear particle, called the neutral kaon (K0), decays into a pair of other particles called pions (∏+ and∏-) which are oppositely charged but equal in mass. Assuming the kaon is initially at rest, prove that the two pions must have momenta that are equal in magnitude and opposite in direction. (You can try this)

10. Problem 3
A 60 kg boy and a 40 kg girl, both wearing skates face each other at rest. The girl pushes the boy, sending him eastward with a speed of 4.0 m/s.
a) What is the final velocity of the girl after the collision?
b) What is the final kinetic energy of the system?
Total Momentum of System = 0 = m1v1 +m2 v2
0= 40v1 +60(4) so v1 = -6 m/s
b) Total KE = 1/2m1v12 + 1/2m2 v2 2 = ½(40)(-6)2 +1/2(60)(4)2
Total KE = 1200 J

11. Problem 4
Suppose you have a mass of 60 kg and that the earth has a mass of 5.98 x 1024kg. You jump up with a speed of 5 m/s.
a) What is the maximum recoil speed of the earth?
b) What is the final kinetic energy of the system?
c) Can we really ignore the kinetic energy of the earth?
Total Momentum = 0= m1v1 + m2v2
0=60(5)+(5.98 x 1024)(v2) v2 =5 x m/s
b) KE = ½ m1 v /2m2 v2 2 = ½(60)(5)2 + ½(5.98 x 1024)(5 x )2
KE = J
c) Yes, we can ignore the kinetic energy of the earth. It is negligible.