Impulse & Momentum Physics 11

Problem A baseball of mass 0.145kg is pitched toward a batter with an initial velocity of 35 m/s. If the batter hits the ball in the opposite direction at 45 m/s, determine the force that is applied by the bat on the ball if the contact time was 0.013s.

Impulse When an object is accelerated, typically the force will only be applied for a given time So instead of considering Newton’s Second Law as we have previously discussed it, we will rearrange the equation

Impulse Use Newton’s Second Law and substitute the definition for acceleration Rearrange the equation so there are no terms in the denominator This expression is known as impulse (J)

Example A tennis ball is struck by a racquet with a force of 750N; if the time of contact was 0.023s, what impulse was delivered to the ball?

Momentum Momentum can also be defined starting from Newton’s Second Law The rate of change of momentum can also be used to determine the force Momentum is defined as the product of an object’s mass and velocity  1st Law of Motion

Example A cyclist is travelling at 32km/h and the bike and rider have a mass of 85kg. What is their momentum?

Impulse-Momentum Impulse and momentum can be related in order to solve dynamics problems Substitute the definition for momentum into the impulse equation

Example – again… A baseball of mass 0.145kg is pitched toward a batter with an initial velocity of 35 m/s. If the batter hits the ball in the opposite direction at 45 m/s, determine the force that is applied by the bat on the ball if the contact time was 0.013 s.

Example

Collisions Physics 11

Conservation of Momentum The vector quantity momentum will be conserved in any collision That is, the sum of all momenta prior to the collision will be equal to the sum of all momenta following a collision Every object that has mass and velocity will have momentum and must be included in the total momentum of the system

Collisions With any collision, it is imperative that you diagram the system prior to and following the collision and identify all objects involved in the collision This allows you to ensure that you calculate the total momentum for the system to properly analyze the situation While this may seem onerous, generally we will be looking at a maximum of two particles

Recall Momentum Momentum Impulse

Momentum Conservation Momentum is conserved This is an expression of Newton’s first law: “An object at rest or in uniform motion will remain at rest or in uniform motion unless acted on by an external force.” External forces can change the momentum of a system (Impulse)

Momentum Conservation In interactions between two bodies, momentum of one object can change, but the total momentum of the system remains constant.

Types of Momentum Problems Elastic collisions Inelastic collisions Explosions Final Initial Final Initial Initial Final

Explosions: Recoil A Barrett M82 is a high calibre sniper rifle. Below are it’s specifications: Barrel length: 73.7 cm Weight: 14.0 kg Muzzle Velocity: 853 m/s Typical ammunition weight: 50.0g Calculate the magnitude force exerted on the riflemen.

Explosion: Recoil The plan is this Calculate the momentum of the rifle knowing the momentum of the bullet Calculate the impulse imparted to the riflemen to stop the gun. Impulse is change in momentum Impulse is force multiplied by time Need to know the time (how long) the explosion takes.

The Momentum Problem Barrel length: 73.7 cm Weapon mass: 14.0 kg Muzzle Velocity: 853 m/s Typical ammunition mass: 50.0g

Impulse We know the person stops the gun, so to find the force, we need to know the interaction time.

Explosions: Recoil Barrel length: 73.7 cm Weapon mass: 14.0 kg Muzzle Velocity: 853 m/s Typical ammunition mass: 50.0g

Bring it all together

For Comparison How many people would have to sit on your shoulder to get the same force?

Collision A billiard ball, mass 155g, is travelling at 3.5m/s across the table. It strikes another ball at rest, mass 150g and comes to rest. What is the velocity of the second ball after the collision?