Impulse and Momentum Momentum is defined as Inertia

Impulse and Momentum

Momentum is defined as “Inertia in Motion” Refers to “how difficult” it is to stop an object p = momentum m = mass v = velocity Unit: kg x m/s Momentum is a vector: NEEDS direction (due to velocity)

Impulse = ∆Momentum If an object changes its velocity, then momentum changes If velocity changes, then there is an acceleration In order to change an objects velocity, a net force must act on the object. Newton’s 2 nd Law Impulse is a change in momentum Impulse = = =

Impulse – Momentum Theorem IMPULSE CHANGE IN MOMENTUM This theorem reveals some interesting relationships such as the INVERSE relationship between FORCE and TIME

Impulse – Momentum Relationships

Impulse – Momentum Relationships Constant Since TIME is directly related to the VELOCITY when the force and mass are constant, the LONGER the cannonball is in the barrel the greater the velocity. Also, you could say that the force acts over a larger displacement, thus there is more WORK. The work done on the cannonball turns into kinetic energy.

Example A 2. 5 kg ball strikes a wall with a velocity of 8. 5 m/s to the left. The ball rebounds with a velocity of 7. 5 m/s to the right. The ball is in contact with the wall for 0. 25 sec. What is the momentum of the ball before the collision? What is the momentum of the ball after the collision? What is the change in momentum of the ball? What is the impulse experience by the ball? How much force does the ball experience?

How about a collision? Consider 2 objects speeding toward each other. When they collide. . . What do we know about the force that each object experiences? Due to Newton’s 3 rd Law the FORCE they exert on each other are EQUAL and OPPOSITE. The TIMES that the force acts over are also equal. Therefore, the IMPULSES of the 2 objects colliding are also EQUAL

How about a collision? If the Impulses are equal then…

Momentum is conserved! The Law of Conservation of Momentum: “In the absence of an external force (gravity, friction), the total momentum before the collision is equal to the total momentum after the collision. ”

Collision Summary Sometimes objects stick together or blow apart. In this case, momentum is ALWAYS conserved. When 2 objects collide a DON’T stick Elastic Collision When 2 objects collide an stick together; vf 1 = vf 2 ; v Inelastic Collision When 1 object breaks into 2 objects Elastic Collision = Kinetic Energy is Conserved Inelastic Collision = Kinetic Energy is NOT Conserve

Relative Velocity Eq. (1 D-Head-on. Collision)

Example Vf 1 = Vf 2 =