Today: Notes and Practice problems!  Impulse and Momentum Get your Journals out. We have notes Today!!! Have a seat!! Today: Notes and Practice problems! 

Definition of Momentum Momentum: is the quantity of motion an object has. p = mv Momentum mass velocity * Measured in kg*m/s * Momentum is a Vector (direction matters) * Momentum is inertia in motion * Momentum depends on the mass and velocity 1 = (1)(1)

What Factors Affect Momentum? Since, p=mv Mass and Velocity will affect momentum Example, what is the momentum of a 4 kg object moving at 6 m/s? p=mv : 4kg*6m/s = 24 kgm/s What if the mass were cut in half? What is the new momentum? p=mv : 2kg*6m/s = 12 kgm/s

Momentum of Systems The total momentum of a system is the vector sum of the momentum of each particle in the system. Because momentum is a vector, you must assign  direction to be positive and negative. The total kinetic energy of a system is the simple sum of the  KE of each particle in the system.

Do not confuse momentum and kinetic energy

Momentum changes due to an Impulse Since IMPULSE CHANGES MOMENTUM… If there is a change in an object’s momentum there must be a change in its mass or its velocity (Usually it is the velocity that changes) A change in velocity (acceleration) is caused by a net force (F=ma). How long the force acts is important: The longer the force acts the greater the change in momentum

Impulse is also referred to as the change in momentum Definition of Impulse Impulse : is a Force acting over an interval of time. Impulse is also referred to as the change in momentum Force time Change in momentum J = Ft J = Δp Impulse Impulse * Measured in N*s * Impulse is a Vector (direction matters) * An object does not “have” Impulse, it is affected by a force resulting in an impulse.

Impulse is the Area under a F vs t Since, we don’t use calculus, we use an average force to determine the impulse. 5 2 4 6 T (s) What is the impulse? Area of Triangle + Area of Rectangle 5 + 20 = 25 Impulse = 25 N*s

Impulse – Momentum Theorem The impulse of a force F equals the change in momentum of the particle. J = FΔt = Δp This is another way of saying that a net force must be applied to change an objects state of motion.

What Factors Affect Impulse? Since, J=Ft Force and Time will affect Impulse Example, what is the impulse produced by a 30 N force applied for a time of 5s? J=Ft : 30N*5s = 150 N*s A ball hits a mallet with a force of 200 N, resulting in a 4 N*s impulse. How long was this force applied? J=Ft t= J/F : 4Ns / 200 N = 0.02s

p = mv Δp = mvf - mvi j = FΔt Δp = j FΔt = mvf - mvi Helpful hint: Directions Matter! Make sure forces and velocities have the appropriate sign.

A. 5kg baseball moves to the left at 20 m/s striking a bat A .5kg baseball moves to the left at 20 m/s striking a bat. The bat is in contact with the ball for 0.002 s, and it leaves in the opposite direction at 40 m/s. What was average force on ball? + 40 m/s 20 m/s m = 0.5 kg + - Dt F

+ - Dt F 20 m/s m = 0.5 kg 40 m/s F Dt = mvf - mvo vo = -20 m/s; vf = 40 m/s F(0.002 s) = (0.5 kg)(40 m/s) - (0.5 kg)(-20 m/s) F(0.002 s) = (20 kg m/s) + (10 kg m/s) F(0.002 s) = 30 kg m/s F = 15,000 N

Impulse in Two Dimensions + vfy A baseball with an initial velocity vo hits a bat and leaves with vf at an angle. vf + vfx Fy F vo Horizontal and vertical impulse are independent. Fx F = Fx + Fy vo = vox + voy vf = vx + vy Fx Dt = mvfx - mvox Fy Dt = mvfy - mvoy