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Conservation of Momentum p mv
In the absence of an external force, the total linear momentum of a system remains constant.
Before Collision
After Collision
v1i v2i
v1fv2f
m1 m2
Impulse = change in momentum
F t m v m vf i1 1 1 1 1
F t m v m vf i2 2 2 2 2
F1 2F F
Newton’s 3rd: F t F t1 2
m v m v m v m vf i f i1 1 1 1 2 2 2 2 ( )
2F
m v m v m v m vf f i i1 1 2 2 1 1 2 2
final momentum = initial momentum Conserved!
Is momentum conserved if you jump up from the earth?
What about a Mexican jumping bean?
Problem: A canon of mass 100 kg is initially at rest and fires a 1 kg canonball with speed 75 m/s horizontally. What is the recoil velocity of the canon?
Mm
Demo of carts on track
Conservation of Angular Momentum
For point mass around circle,
L mvrIf there are no external torques, angular momentum is conserved.
mvR mVr Rr
Conservation of Energy
The total energy of an isolated system is always conserved.
Conservative forces: work done by conservative force is independent of path taken.
A BAllow you to define potential energy.
If you have only conservative forces, then the sum of potential and kinetic energy is conserved.
i i f fKE PE KE PE
For gravity near earth’s surface,
2 21 1
2 2i i f fmv mgy mv mgy
Other conservation laws:
Conservation of Baryon number (nucleon number):
Alpha decay: nucleus emits helium nucleus (alpha particle).
138 n
88 p
8 82 2 6Ra
136 n
86 p
8 62 2 2 Rn
+
24 He
parent daughter
ZA
ZAX Y H e
24
24
Baryons interact via strong nuclear force, e.g. protons and neutrons.
Conservation of electric charge