Momentum and Impulse v 2 =v 1 +at Kinematics equation mv 2 =mv 1 +mat mat=mv 2 -mv 1 Ft=mv 2 -mv 1 Impulse = I = Ft Impulse: The product of Force and time. Vector quantity Causes a change in momentum Measured in Ns 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

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

Impulse is the Area Under a Force-Time Graph F t F t F t1t1 t2t2 I=FtI= ½ Ft

The Impulse-Momentum Theorem mat=mv 2 -mv 1 Ft=mv 2 -mv 1 =m(v 2 -v 1 )=m(Δv) I = p 2 – 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) F t=Δp A large force acting for a small time. 2) F t = Δp A small force for a long time.

Alternate Impulse-Momentum Theorem Derivation F=ma F=ma F=m(Δv/t) F=m(Δv/t) Ft=m(Δv)=m(v 2 -v 1 )=p 2 -p 1 =Δp Ft=m(Δv)=m(v 2 -v 1 )=p 2 -p 1 =Δp I=Δp I=Δp The impulse-momentum theorem is another way to interpret Newton’s 2 nd Law. The impulse-momentum theorem is another way to interpret Newton’s 2 nd Law.

Impulse Momentum-Theorem Example p 1 =mv 1 Impulse=Ft p 2 = mv 2 The original momentum plus and impulse gave the ball a new momentum p 1 +I=p 2 Impulse-Momentum Theorem: The impulse of the racket caused a change of momentum of the ball of I = Δp=p 2 -p 1.

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)p rock = mv = (1.0 kg)(1.0 m/s) =1.0 kg m/s 2) p bullet = mv = (.001kg)(1000m/s)= 1.0 kg m/s 1 2