Momentum and Impulse: Principles and Applications, Exercises of Physics

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Chapter 6

Momentum and Collisions

Momentum

Momentum  a property of moving things  means inertia in motion  more specifically, mass of an object multiplied by its velocity  in equation form: mass  velocity (momentum = mv )

Momentum components

  Applies to two-dimensional motion

p (^) x  mvx and py  mvy

Problem 6.

 A 0.10-kg ball is thrown straight up into the air with an initial speed of 15 m/s. Find the momentum of the ball (a) at its maximum height and (b) halfway to its maximum height.

Impulse

 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

I  F  t I

Impulse-Momentum

Theorem

 The theorem states that the impulse acting on the object is equal to the change in momentum of the object   If the force is not constant, use the average force applied

F  t   p  m v (^) f  m v i

Problem 6.

 A 0.500-kg football is thrown toward the east with a speed of 15.0 m/s. A stationary receiver catches the ball and brings it to rest in 0.020 0 s. (a) What is the impulse delivered to the ball as it’s caught? (b) What is the average force exerted on the receiver?

Problem 6.

 A car of mass 1.6 × 10^3 kg is traveling east at a speed of 25 m/s along a horizontal roadway. When its brakes are applied, the car stops in 6.0 s. What is the average horizontal force exerted on the car while it is braking?

Impulse Changes

Momentum

The greater the impulse exerted on something, the greater the change in momentum.

• in equation form: Ft = ( mv )

Newtons 2nd^ Law -

Restated

 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



 Gives an alternative statement of Newton’s second law

( (^) f i ) net

m v v t t

 (^)     

p (^) F

Impulse Changes

Momentum

examples: when a car is out of control, it is better to hit a haystack than a concrete wall physics reason: same impulse either way, but extension of hitting time reduces the force

Impulse Applied to Auto

Collisions

 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

Impulse Changes

Momentum

example (continued): in jumping, bend your knees when your feet make contact with the ground because the extension of time during your momentum decrease reduces the force on you in boxing, ride with the punch

Impulse Changes

Momentum

 Case 3: decreasing momentum over a short time  short time interval produces large force

example: Karate expert splits a stack of bricks by bringing her arm and hand swiftly against the bricks with considerable momentum. Time of contact is brief and force of impact is huge.