Understanding Momentum and Collision Physics

Topic 2.2

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?

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

A truck has a mass of 10 000 kg and a velocity of 3 m.s-1. What is its momentum? Momentum = Mass x velocity = 10 000 x 3 = 30 000 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-1or 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! Momentum is not energy!

To derive this law we apply Newtons 2nd law to each body and Newton s 3rdlaw to the system i.e. Imagine 2 bodies A and B interacting mass of mAand mB A has a velocity change of uAto vAand B has a velocity change of uBto vBduring the time of the interaction t

Then the force on A given by Newton 2 is FA= mAvA mAuA t And the force on B is FB= mBvB mBuB t But Newton 3 says that these 2 forces are equal in magnitude and opposite in direction

Therefore mAvA mAuA= - (mBvB mBuB) t mAvA mAuA= mBuB mBvB t Rearranging gives: mAuA+ mBuB= mAvA+ mBvB Total Momentum before = Total Momentum after

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

F = ma F = 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 a name on impulse on impulse after being called

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

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

Impulse is measured in N.s (Ft) or [kg.m.s-2]x[s] = [kg.m.s-1] (mv mu) Tiger%2520Woods%2520PGA%2520TOUR%25202006%2520-%2520Pebble%2520Beach%252018%2520-%2520Xbox%2520360

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

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?

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