Momentum P = m • v Definition: Formula: Momentum= mass • velocity Momentum is Inertia in motion Formula: Momentum= mass • velocity P = m • v the units of momentum is kgm/s

Example A truck of mass 1200 kg is moving with a speed of 40 m/s, calculate its momentum.

Changing momentum Δp =m•Δv When velocity of an object changes, the momentum of that object changes. Therefore; Change in momentum= mass • change in velocity Δp =m•Δv

Problem An average force of 20 N is exerted on a 2 kg cart to change its speed by 30 m/s for about 3 seconds. Calculate the Cart’s change of momentum.

Force and change of Momentum Changing momentum requires Force Since ‘Rate of change in velocity’ is called acceleration ----------------1, And, acceleration according to Newton's 2nd law is; -------------------2

Then, Which translates to; Where; F—is the force of impact/force applied t---is the time during which force is applied. Also known as time of impact.

Impulse mΔv is change in momentum ∑F·t is Impulse From the formula Impulse = change in momentum

impulse http://glencoe.com/sec/science/physics/ppp_09/animation/Chapter%209/Impulse.swf

Example An average force of 20 N is exerted on a 2 kg cart to change its speed from 0 m/s to 30 m/s for about 3 seconds. Calculate the Cart’s: a). Impulse. b). Change in momentum

Class work & Homework Textbook page 188 # 1-7

Lesson 2: Increasing momentum How can the momentum of an object be increased or decreased? From F • t = m • Δυ, If the largest force is applied for the longest time, the change in momentum is large. Examples: Impact on a Golf ball(Increasing) Baseball(increasing) Stop a moving vehicle (decreasing)

Time of impact vs. Force of impact How does a short time of impact affect the force of impact? ( give example) The force of impact is large, when the time is short. Example: Hitting a brick wall with a moving car. How does a long time of impact affect the force of impact? (give example) It reduces the force of impact. Example: Hitting a haystack with a moving car

Question You can’t throw a raw egg against a wall without breaking it, but you can throw it at the same speed into a sagging sheet without breaking it. Explain.

Bouncing Why is impulse greater when objects bounce than when they don’t? Answer: Since Impulse = F•t = m•Δv; when an object bounces the object’s velocity changes from positive initial velocity (υi) to a negative final velocity (-υf).

answer Therefore, ∆υ = |-υf - υi| This is a large change in velocity that causes the impulse to be large. If the time for bouncing is small, then the Impact force is large.

Example ∆υ = |(-υf) – (υi)| A ball thrown to the floor with a velocity of 25 m/s and bounces off the floor with a velocity of 20 m/s would have its velocity changed by: ∆υ = |(-υf) – (υi)| = |(-20) – (25)| = 45 m/s

Problem 1 Tiger Woods hits a 0.06 kg golf ball, giving it a velocity of 75 m/s. How much momentum does the ball gain? What impulse does he impart on the ball? If the impact lasts 0.5 sec, how much force does he exert on the ball?

Problem 2 A ball of mass 0.5 kg is coming towards you with a speed of 25 m/s; you hit it back with a force of 25 N so that it acquires a speed of 35 m/s. Calculate the change in momentum of the ball. How much time does the ball take to bounce off your foot?

Class work Text pg 187, # 1-10