Momentum and Impulse

1. v2=v1+at Kinematics equation mv2=mv1+mat mat=mv2-mv1 Ft=mv2-mv1 Momentum and Impulse 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

2. Miscellaneous Impulse-Momentum Notes • Is a Ns=kg m/s? Ns=(kgm/s2)s=kgm/s Plural of momentum: Momenta

3. Impulse is the Area Under a Force-Time Graph F F F t1 t2 t t I=Ft I= ½ Ft

4. The Impulse-Momentum Theorem mat=mv2-mv1 Ft=mv2-mv1=m(v2-v1)=m(Δv) I = p2 – p1 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) Ft=Δp A large force acting for a small time. 2) Ft=ΔpA small force for a long time.

5. 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.

6. Impulse Momentum-Theorem Example p1=mv1 • The original momentum plus and impulse gave the ball a new momentum • p1+I=p2 • Impulse-Momentum Theorem: • The impulse of the racket caused a change of • momentum of the ball of I = Δp=p2-p1. Impulse=Ft p2 = mv2

7. 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. • 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 1 2