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Chapter 7
Impulse, J
𝐹̅ average force
∆𝑡 change in time
Unit for impulse:_________
Linear Momentum, p
m mass
v velocity
Unit for momentum:_________
Impulse-Momentum Theorem
∑ 𝐹̅ net force
Final Velocity of 2 objects in a
head-on collision where one
object is initially at rest
1: moving object
2: object at rest
Conservation of Linear
Momentum (in 1D)
Elastic Collision
Conservation of Linear
Momentum (in 1D)
Inelastic Collision
Conservation of Linear
Momentum (in 2D)
𝐽 = 𝐹̅ ∆𝑡
Eq.
7.1
p=mv
7.2
(∑ 𝐹̅ ) ∆𝑡 = 𝑚𝑣𝑓 − 𝑚𝑣0 = 𝑚∆𝑣
7.4
𝑣𝑓1
Or J=Δp
𝑚1 − 𝑚2
=(
)𝑣
𝑚1 + 𝑚2 01
𝑣𝑓2 = (
7.8a
2𝑚1
)𝑣
𝑚1 + 𝑚2 01
7.8b
Final total linear momentum =initial total linear
momentum
𝑚1 𝑣01 + 𝑚2 𝑣02 = 𝑚1 𝑣𝑓1 + 𝑚2 𝑣𝑓2
7.7b
𝑚1 𝑣01 + 𝑚2 𝑣02 = _________________________
𝑚1 𝑣01𝑥 + 𝑚2 𝑣02𝑥 = 𝑚1 𝑣𝑓1𝑥 + 𝑚2 𝑣𝑓2𝑥
𝑚1 𝑣01𝑦 + 𝑚2 𝑣02𝑦 = 𝑚1 𝑣𝑓1𝑦 + 𝑚2 𝑣𝑓2𝑦
Center of mass location
x refers to position relative to
the coordinate origin (distance)
unit for center of mass:_______
Center of mass velocity
Unit for center of mass
velocity:_______
7.9
𝑥𝑐𝑚 =
𝑚1 𝑥1 + 𝑚2 𝑥2
𝑚1 + 𝑚2
7.10
𝑣𝑐𝑚 =
𝑚1 𝑣1 + 𝑚2 𝑣2
𝑚1 + 𝑚2
7.11
When there is only one force then ∑ 𝐹̅ = 𝐹̅
An elastic collision is one in which the total kinetic energy of the system after the collision is
equal to the total kinetic energy of the system before the collision.
An inelastic collision is one in which the total kinetic energy of the system is not the same
before and after the collision. If the objects stick together after the collision, the collision is said
to be completely inelastic.
Impulse: something that changes the momentum of an object
Momentum: amount of motion occurring in something that is moving; a measure of motion
Mary Stangler Center for Academic Success
Revised 11/13