Linear Momentum

5-1 Linear Momentum

Linear Momentum, p – defined as mass x velocity The unit is kgm/s A quantity used in collisions So a small object with a large velocity could have the same momentum as a large object with a small velocity 9-1 Linear Momentum

5.2 Momentum and Newton’s Second Law

Newton’s Second Law is This is only true for objects with a constant mass The original form of the equation was This statement is true even if the mass varies 5.2 Momentum and Newton’s Second Law

5.3 Impulse

A baseball player hits a pitch Bat delivers an impulse We actually on consider average force Impulse is define as 5.3 Impulse Impulse Sim

An increase in time produces a decreases in force A decrease in time produces an increase in force 5.3 Impulse Airbag

5.4 Conservation of Linear Momentum

If no net external force is applied to a system Then momentum is conserved 5.4 Conservation of Linear Momentum Explode Sim

External Forces will result in a change in momentum, so no conservation 1.Force added in 2.Force removed 5.4 Conservation of Linear Momentum Shuttle Launch

5.5 Inelastic Collisions

Inelastic collision – two objects collide and stick together Momentum is conserved Energy is not conserved 5.5 Inelastic Collisions

Example: On a touchdown attempt, a 95 kg running back runs toward the end zone at 3.75 m/s. A 111kg linebacker moving at 4.10 m/s meets the runner in a head on collision. If the two players stick together what is their velocity immediately after the collision? 5.5 Inelastic Collisions

Example: In a ballistic pendulum, a 100g bullet is fired at a velocity of 200 m/s at the bob of a pendulum. The bob has a mass of 10 kg. After the collision, the object and the bob stick together and swing through an arc. How high does it get? This is first a conservation of momentum problem (how fast does the combination of bullet and bob go after the collision) Then it is a conservation of energy problem. 5.5 Inelastic Collisions

Example: In a ballistic pendulum, a 100g bullet is fired at a velocity of 200 m/s at the bob of a pendulum. The bob has a mass of 10 kg. After the collision, the object and the bob stick together and swing through an arc. How high does it get? 5.5 Inelastic Collisions

If the collision occurs in two dimensions We need to consider the x and y axis separately 5.5 Inelastic Collisions

The we use vector addition to calculate the magnitude and velocity. 5.5 Inelastic Collisions

Example: A 950kg car traveling east at 16m/s collides with a 1300 kg car traveling north at 21 m/s. If the collision is inelastic, what is the magnitude and direction of the cars after the collision? 5.5 Inelastic Collisions

5.6 Elastic Collisions

Elastic collision – two objects collide and bounce apart Momentum is conserved In a perfect elastic collision, energy is conserved too 5.5 Inelastic Collisions

A 10 kg car moving at 2 m/s runs into a 5 kg car that is parked. What is the velocity of each car after the collision? 5.5 Inelastic Collisions

A 10 kg car moving at 2 m/s runs into a 5 kg car that is parked. What is the velocity of each car after the collision? 5.5 Inelastic Collisions

A 10 kg car moving at 2 m/s runs into a 5 kg car that is parked. What is the velocity of each car after the collision? 5.5 Inelastic Collisions

A 10 kg car moving at 2 m/s runs into a 5 kg car that is parked. What is the velocity of each car after the collision? Confirm 5.5 Inelastic Collisions

5.7 Center of Mass

The point where the system can be balanced in a uniform gravitational field Uniform objects center of mass is in the center 5.7 Center of Mass Motion of CMCM Center of mass of Triangle

Center of mass is not always in the object Objects balance if supported at their center of mass 5.7 Center of Mass

5.8 Systems with Changing Mass: Rockets

When a rocket is launched (or a plane takes off). Fuel is used as the rocket launches This causes the mass to decrease 5.8 Systems with Changing Mass: Rockets

So The force due to the ejected fuel is called thrust 5.8 Systems with Changing Mass: Rockets

In a Saturn V rocket, fuel is ejected at 13,800 kg/s and at a speed of 2440 m/s Since the initial weight of the rocket is 28,500,000N (or mass of 2,850,000 kg) 5.8 Systems with Changing Mass: Rockets

As the rocket travels its mass drops, so the acceleration will actually increase 5.8 Systems with Changing Mass: Rockets