You’re Quite Impulsive An Introduction to Impulse and Momentum
A Review of What We Know About Motion Chapters 2 & 3 introduced us to vectors such as displacement, velocity, and acceleraton No mass was included Chapter 4 introduced forces and mass into the mix Chapter 5 has brought the concept of energy to motion. It includes mass and motion but not as vectors Chapter 6 will combine the vectors of motion with mass quantities
Where (and why) We Start Vector Motion Energy Analysis A ball is thrown up at 25m/s at 53o above horizontal. Find final velocity. How we solve: Strengths: Weaknesses: A ball is thrown up at 25m/s at 53o above horizontal. Find final velocity. How we solve: Strengths: Weaknesses:
How we can combine both strengths We need a quantity that expresses motion with a mass component and a directional component. Welcome to the world of impulse and momentum! Impulse: force times time- force is a vector; time is not. It expresses an effort and duration. Units are Ns or kgm/s Momentum: mass times velocity- mass is scalar; velocity is vector. It includes direction and size. Units are kgm/s or Ns.
As an object moves with a velocity it has a “quantity” of motion that relates to its size and motion. This is momentum (m x v) • Newton’s 2nd law tells us that an outside force will create a proportional velocity change. • The longer the force acts the more the change in velocity. • So, the force acting for a time creates a m-v (momentum) change. How Momentum and Impulse relate Momentum= mass x velocity Velocity changes are expressed as accelerations: acc = Dv/Dt Accelerations are created by forces acting on masses The “longer” the force acts the more the object accelerates Force = mass x (Dv / Dt) After a little algebra Force x Dt = mass x Dv Impulses create momentum changes
A Few Examples If a 25.0 kg cart rolls at 15 m/s east and a 200. N force (west) acts on it for 30.0 seconds, (a) what is its initial momentum and kinetic energy? (b) what is its final momentum, velocity and kinetic energy? A 50.0 kg object travels at 30.0 m/s east. A 100.0 N (south) force acts on the object for 15.0 seconds. (a) What is its final momentum? What is its final velocity? What is its final kinetic energy?