Download Momentum

Momentum and Impulse
v2=v1+at
mv2=mv1+mat
mat=mv2-mv1
Ft=mv2-mv1
Kinematics equation
Dynamics equation
p= momentum
p = mv
• momentum: quantity of motion (mass in motion)
•Product of mass and velocity
•Vector quantity
•Momentum can be transferred between objects
•Measured in kg m/s in the SI system
Impulse = I = Ft
Impulse: The product of Force and time.
• Vector quantity
•Causes a change in momentum
•Measured in Ns
Miscellaneous Impulse-Momentum Notes
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Is a Ns=kg m/s?
Ns=(kgm/s2)s=kgm/s
Plural of momentum: Momenta
Impulse is the Area Under a Force-Time Graph
F
F
F
t
I=Ft
t
I= ½ Ft
t1
t2
t2
I   F(t) dt
t1
The Impulse-Momentum Theorem
mat=mv2-mv1
Ft=mv2-mv1=m(v2-v1)=m(Δv)
I = p2 – p 1
I = Δp
Impulse-momentum
Theorem
•The impulse-momentum theorem is a cause and effect relationship
•An impulse of a certain quantity causes the same change in momentum
The same change in momentum can be achieved in two ways:
1)
2)
Ft=Δp
Ft=Δp
A large force acting for a small time.
A small force for a long time.
Alternate Impulse-Momentum
Theorem Derivation





F=ma
F=m(Δv/t)
Ft=m(Δv)=m(v2-v1)=p2-p1=Δp
I=Δp
The impulse-momentum theorem is another
way to interpret Newton’s 2nd Law.
Impulse Momentum-Theorem Example
p1=mv1
• The original momentum plus and
impulse gave the ball a new momentum
p1+I=p2
Impulse=Ft
• Impulse-Momentum Theorem:
The impulse of the racket caused a change of
momentum of the ball of I = Δp=p2-p1.
p2 = mv2
Momentum Comparison
A 1.0 kg rock traveling at 1.0 m/s can have the same momentum
as a 1.0 g bullet traveling at 1000 m/s.
1) prock = mv = (1.0 kg)(1.0 m/s) =1.0 kg m/s
2) pbullet= mv = (.001kg)(1000m/s)= 1.0 kg m/s
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