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Chapter 8 - PowerPoint PPT Presentation

Chapter 8. Momentum and Momentum Conservation. Momentum. The linear momentum of an object of mass m moving with a velocity is defined as the product of the mass and the velocity SI Units are kg m / s Vector quantity, the direction of the momentum is the same as the velocity’s.

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Chapter 8

Momentum and Momentum Conservation

• The linear momentum of an object of mass m moving with a velocity is defined as the product of the mass and the velocity

• SI Units are kg m / s

• Vector quantity, the direction of the momentum is the same as the velocity’s

• Applies to two-dimensional motion

• In order to change the momentum of an object, a force must be applied

• The time rate of change of momentum of an object is equal to the net force acting on it, e.g.

• Gives an alternative statement of Newton’s second law

• When a single, constant force acts on the object, there is an impulse delivered to the object

• is defined as the impulse

• Vector quantity, the direction is the same as the direction of the force

• Unit N·s=kg·m/s

• The theorem states that the impulse acting on the object is equal to the change in momentum of the object

• Impulse=change in momentum (vector!)

• If the force is not constant, use the average force applied

• The most important factor is the collision time or the time it takes the person to come to a rest

• This will reduce the chance of dying in a car crash

• Ways to increase the time

• Seat belts

• Air bags

• The air bag increases the time of the collision

• It will also absorb some of the energy from the body

• It will spread out the area of contact

• decreases the pressure

• helps prevent penetration wounds

• Total momentum of a system equals to the vector sum of the momenta

• When no resultant external force acts on a system, the total momentum of the system remains constant in magnitude and direction.

• Momentum in an isolated system in which a collision occurs is conserved

• A collision may be the result of physical contact between two objects

• “Contact” may also arise from the electrostatic interactions of the electrons in the surface atoms of the bodies

• An isolated system will have not external forces

• The principle of conservation of momentum states when no external forces act on a system consisting of two objects that collide with each other, the total momentum of the system remains constant in time

• Specifically, the total momentum before the collision will equal the total momentum after the collision

• Mathematically:

• Momentum is conserved for the system of objects

• The system includes all the objects interacting with each other

• Assumes only internal forces are acting during the collision

• Can be generalized to any number of objects

A 60 grams tennis ball traveling at 40m/s is returned with the same speed. If the contact time between racket and the ball is 0.03s, what is the force on the ball?

A 5kg ball moving at 2 m/s collides head on with another 3kg ball moving at 2m/s in the opposite direction. If the 3kg ball rebounds with the same speed. What is the velocity of the 5 kg ball after collision?

• System is released from rest

• Momentum of the system is zero before and after

4 kg rifle shoots a 50 grams bullet. If the velocity of the bullet is 280 m/s, what is the recoil velocity of the rifle?

• Momentum is conserved in any collision

• Perfect elastic collision

• both momentum and kinetic energy are conserved

• Collision of billiard balls, steel balls

• Inelastic collisions

• Kinetic energy is not conserved

• Some of the kinetic energy is converted into other types of energy such as heat, sound, work to permanently deform an object

• completely inelastic collisions occur when the objects stick together

• Not all of the KE is necessarily lost

• Actual collisions

• Most collisions fall between elastic and completely inelastic collisions

• When two objects stick together after the collision, they have undergone a perfectly inelastic collision

• Conservation of momentum becomes

Railroad car (10,000kg) travels at 10m/s and strikes another railroad car (15,000kg) at rest. They couple after collision. Find the final velocity of the two cars. What is the energy loss in the collision?

• Momentum is a vector quantity

• Direction is important

• Be sure to have the correct signs

• Both momentum and kinetic energy are conserved

• Typically have two unknowns

• Solve the equations simultaneously

Head on elastic collision with object B at rest before collision.

One can show

• In an elastic collision, both momentum and kinetic energy are conserved

• In an inelastic collision, momentum is conserved but kinetic energy is not

• In a perfectly inelastic collision, momentum is conserved, kinetic energy is not, and the two objects stick together after the collision, so their final velocities are the same

• For a general collision of two objects in three-dimensional space, the conservation of momentum principle implies that the total momentum of the system in each direction is conserved

• Measure speed of bullet

• Momentum conservation of the collision

• Energy conservation during the swing of the pendulum