Topic 2.2

 When have you heard this term? Some examples:  The Maple Leafs have won 5 straight games and they are building momentum towards the playoffs  The momentum to use technology has been huge in the past few years  Keeping your momentum is the key to reaching yearly resolutions

 What makes an object hard to stop?  Is it harder to stop a bullet, or a truck travelling along the highway?  What makes each object hard to stop?

 The bullet is hard to stop because it is travelling very fast, whereas the truck is hard to stop because it has a very large mass.

 It makes sense to assume that a bullet travelling twice as fast would be twice as hard to stop, and a truck twice the mass would also be twice as hard to stop.

 Momentum is a useful quantity to consider when thinking about "unstoppability". It is also useful when considering collisions and explosions. It is defined as Momentum (kg.m.s -1 ) = Mass (kg) x Velocity (m.s -1 ) p = mv

 A truck has a mass of kg and a velocity of 3 m.s-1. What is its momentum? Momentum = Mass x velocity = x 3 = kg.m.s -1.

 The momentum p of a body of constant mass m moving with velocity v is, by definition mv  p = mv  It is a vector quantity  Its units are kg m s -1 or Ns  It is the property of a moving body.

1. In a collision between two objects, momentum is conserved (total momentum stays the same) 2. In an isolated system (no outside forces), momentum remains constant isolated system = translational equilibrium We can use this to calculate what happens after a collision (and in fact during an “explosion”). Momentum is not energy!

 To derive this law we apply Newton´s 2 nd law to each body and Newton´s 3 rd law to the system  i.e. Imagine 2 bodies A and B interacting  mass of m A and m B  A has a velocity change of u A to v A and B has a velocity change of u B to v B during the time of the interaction t

 Then the force on A given by Newton 2 is  F A = m A v A – m A u A t  And the force on B is  F B = m B v B – m B u B t  But Newton 3 says that these 2 forces are equal in magnitude and opposite in direction

 Therefore m A v A – m A u A = - (m B v B – m B u B ) t t m A v A – m A u A = m B u B – m B v B  Rearranging gives: m A u A + m B u B = m A v A + m B v B  Total Momentum before = Total Momentum after

 A car of mass 1000 kg travelling at 5 m.s -1 hits a stationary truck of mass 2000 kg. After the collision they stick together. What is their joint velocity after the collision?  What does ‘joint velocity’ mean?  What ELSE does it mean?

5 m.s kg 2000kg Before After V m.s -1 Combined mass = 3000 kg Momentum before = 1000x x0 = 5000 kg.m.s -1 Momentum after = 3000v

The law of conservation of momentum tells us that momentum before equals momentum after, so p 1total = p 2total 5000 = 3000v V = 5000/3000 = 1.67 m.s -1

 Momentum is a vector, so if velocities are in opposite directions we must take this into account in our calculations

Snoopy (mass 10kg) running at 4.5 m.s -1 jumps onto a skateboard of mass 4 kg travelling in the opposite direction at 7 m.s -1 What is the velocity of Snoopy and skateboard after Snoopy has jumped on? I love physics

10kg 4kg-4.5 m.s -1 7 m.s -1 Because they are in opposite directions, we make one velocity negative 14kg v m.s -1 Momentum before = 10 x x 7 = = -17 Momentum after = 14v

Momentum before = Momentum after -17 = 14v V = -17/14 = m.s -1 The negative sign tells us that the velocity is from left to right (we choose this as our “negative direction”)

 F = maF = m v - m u t t  F = mv – mu F =  p t t  The rate of change of momentum of a body is proportional to the resultant force and occurs in the direction of the force.

 Where have you heard this term? Some Examples:  I bought that from the internet on impulse after seeing the commercial on TV  I got into a fight on impulse after being called a name

 F =  pF = mv – mu t t  Ft = mv – mu =  p  This quantity Ft is called the impulse of the force on the body  It is a vector quantity  Its units are kg m s -1 or Ns

 Ft = mv – mu =  p  The quantity Ft is called the impulse, and mv – mu is the change in momentum  (v = final velocity and u = initial velocity)  Impulse = Change in momentum

Impulse is measured in N.s (Ft) or [kg.m.s -2 ]x[s] = [kg.m.s -1 ] (mv – mu)

 Note: For a ball (mass m) bouncing off a wall, don’t forget the initial and final velocity are in different directions, so you will have to make one of them negative.  In this case mv – mu = 5m – (-3m) = 8m 5 m/s -3 m/s

 Dylan punches Joseph in the face. If Joseph’s head (mass 10.0 kg) was initially at rest and moves away from Dylan’s fist at 3.0 m/s, and the fist was in contact with the face for 0.20 seconds, what was the force of the punch?  m = 10.0kg, t = 0.20s, u = 0, v = 3.0 m/s  Ft = mv – mu  0.2F = 10x3 – 10x0  0.2F = 30  F = 30/0.2 = 150N

 A tennis ball (0.3 kg) hits a racquet at 3 m/s and rebounds in the opposite direction at 6 m/s. What impulse is given to the ball?

3 m/s -6 m/s

 A tennis ball (0.3 kg) hits a racquet at 3 m/s and rebounds in the opposite direction at 6 m/s. What impulse is given to the ball?  Impulse = mv – mu = = 0.3x-6 – 0.3x3 = -2.7kg.m.s -1 3 m/s -6 m/s