AP Physics: Pearson Chapter 9 - Momentum

9.1 Impulse

• collision: a short-duration interaction between two objects

• the duration of a collision depends on the materials of the objects

  • the harder the objects the shorter the contact time

• a harder force or a longer duration causes a larger “effect”

  • the effect of an impulsive force is proportional to the area under the force-versus-time curve.

• impulse is a vector

• Formula for Area/Impulse : A=Favg over delta t

• preferred unit is kg*m/s (joules)

• A positive impulse - avg f in a positive x- direction

• a negative impulse - avg f in a negative x-direction

STOP TO THINK

• The two graphs show smoothed force vs. time data for two collisions. Which force delivers the greater impulse?

  • a.) force a

  • b.) force b

  • c.) both forces deliver the same impulse

9.2 Momentum and the Impulse-Momentum Theorem

MOMENTUM

• effect of impulsive depends on impulse delivered and mass of the object

• momentum of an object of mass and velocity

• momentum is a vector that points in the same direction as velocity

  

• MOST COMMON ERROR: failure to use the correct signs

  • positive - right or up

  • negative - left or down

• momentum formula: p=mv

• impulse-momentum theorem

  • j=pf-pi=delta p

  • impulse equals the change in momentum

  • states an impulse delivered to an object causes object’s momentum to change

STOP TO THINK

• A puck, seen from above, was moving with an initial momentum when it received an impulse J from a hockey stick, giving it the final momentum shown. Which arrow best represents the puck’s initial momentum?

EXAMPLE: CALCULATING THE CHANGE IN MOMENTUM

• Q: A ball of mass m= 0.25 kg rolling to the right at 1.3 m/s strikes a wall and rebounds to the left at 1.1 m/s. What is the impulse delivered to it by the wall?

• How to solve:

  • looking at the information given, we can see that this fits the impulse-momentum theorem

  • create a diagram of what is happening

  

• Solving

  • px:

    • (px)i = m*(vx)i= (0.25kg)(1.3m/s)=0.325 kg*m/s

    • (px)f = m*(vx)f = (0.25 kg)*(1.1 m/s) =-0.275

  • py:

    • py is zero before and after the bounce

  • Delta px:

    • px = (px)f-(px)i = (-0.275 kg m/s) - (0.325 kg m/s) = -0.6 kg * m/s

SYENTHESIZING

• If the duration of the collision can be increased, the force of the impact will be decreased

  • Used for issues like car safety

TOTAL MOMENTUM

• If we have more than one object moving — a system of objects— then the whole system has an overall momentum

• the total momentum (P) of a system of objects is the vector sum of the momentum of each object

STOP TO THINK

• The cart’s change of momentum is

  • a.) -30 kg * m/s

  • b.) -20 kg * m/s

  • c.) -10 kg * m/s

  • d.) 10 kg * m/s

  • e.) 20 kg * m/s

  • f.) 30 kg * m/s

9.3 Solving Impulse and Momentum Problems

Drawing a before-and-after visual overview

1. Sketch the situation.

2. Establish a coordinate system.

3. Define symbols.

4. List known information

5. Identify the desired unknowns

The Impulse Approximation

• when two objects interact during a collision the forces between them are generally large

• we use the impulse approximation are the values of the momentum (+velocity) immediately before and after

STOP TO THINK

• A 10 g rubber ball and a 10 g clay ball are each thrown at a wall with equal speeds. The rubber ball bounces; the clay ball sticks. Which ball receives the greater impulse from the wall?

  • a.The clay ball receives a greater impulse because it sticks

  • b.The rubber ball receives a greater impulse because it bounces

  • c. they receive equal impulses because they have equal values of momentum

  • d. neither receives an impulse because the wall doesn’t move

9.4 Conservation Of Momentum

• like energy, momentum is conserved

  • every action will have an equal and opposite reaction

Laws of Conservation of Momentum

• example of a system (tree)

  • if a tree is a system, then the rest of the world is the environment

  • tree’s natural processes can be divided into two different types:

    • interactions that happen with the system (between different elements of the system

    • interactions between the system and the environment

  • note: the boundaries of what a system are change depending on the question asked

• internal forces - forces that act only between objects within the system

• external forces - forces that come from agents outside the system

• the total momentum of a system subject to only internal forces is conserved

• if the f net = 0 the total momentum p of the system does not change (isolated system)

  • the total momentum remains constant regardless of whatever interactions are going on inside the system

Explosions

• an explosion ( particles move apart after a brief interaction) are the opposite of a collision

STOP TO THINK

• An explosion in a rigid pipe shoots three balls out of its ends. A 6 g ball comes out the right end. A 4 g ball comes out the left end with twice the speed of the 6 g ball. From which end, left or right, does the third ball emerge

9.5 Inelastic Collisions

• example of elastic collision:

  • a rubber ball dropped on the floor bounces

  • a golf club hitting a golf club causes the ball to rebound away from the club

• example of inelastic collision:

  • a ball of clay sticks to the floor without bouncing

  • a bullet striking a block of wood becomes embedded in the block

• perfectly in elastic collision: a collision in which the two objects stick together and move with a common final velocity

  

STOP TO THINK

• the two objects shown collide and stick together. After the collision, the combined objects

  • a.) Move to the right as shown

  • b) move to the left

  • c.) are at rest