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### Chapter 9

Momentum and Its Conservation

What’s the relationship between force and velocity?

- What happens when the baseball is struck by the bat?
- _______________tells us that the forces on the bat and ball are equal.
- _______________tells us that both bat and ball will experience an acceleration proportional to their masses.
- But what is the relationship between the velocities of the ball and the bat and the forces they experience?

“The Big Mo”: Momentum

- The ________________ of an object of mass m moving with a velocity is defined as the __________ of the ______ and the __________.
- SI Units are kg m/s (Dimensions = ML/T)
- Vector quantity, the direction of the momentum is the same as the velocity’s.

More About Mo

- Momentum components:
- px = m vx and py = m vy
- Applies to two-dimensional motion.
- Again the direction of momentum and velocity are the same.

- px = m vx and py = m vy
- Momentum is related to ________________.
- We can derive an equation that relates KE and momentum.
- More on kinetic energy in chapter 10.

Changing the big mo

- How does an object change its acceleration?
- How would an object change its momentum?
- In order to change the momentum of an object, a _______________ must be applied.

Impulse

- The _________of change of momentum of an object is equal to the __________acting on it.
- Just like with acceleration, when the __________is zero, no change occurs to momentum.
- Gives an alternative statement of Newton’s second law.

Impulse

- When a single, constant force acts on the object, there is an ____________ delivered to the object.
- is defined as the impulse.
- ____________________, the direction is the same as the direction of the __________.
- The impulse is also described using the letter J.
- Impulse is useful for describing ______________ that do not last a long time. (More on this later.)

Impulse-Momentum Theorem

- The theorem states that the ___________ acting on the object is equal to the ___________________ of the object.
- This theorem holds for _________ and ____________ forces.
- If the force is not constant, use the average forceapplied.

Sample Problem

Rico strikes a 0.058 kg golf ball with a force of 272 N and gives it a velocity of 62.0 m/s. How long was Rico’s club in contact with the ball?

Average Force in Impulse

- The ______________can be thought of as the constant force that would give the same impulse to the object in the time interval as the actual time-varying force gives in the interval.

Average Force and collisions

Impulse and collisions

- Impulse is most useful in describing _________ of _______________.
- The impulse-momentum theorem allows us to study the effects that the ________________of a collision has on the _________ felt by the ____________.
- For example, why is it important for boxers to wear boxing gloves?

Changing Impulse and Collisions

- _____________ the contact time increases the ___________ but reduces the _________ during the collision.
- Increasing force increases the impulse as well.

Impulse Applied to Auto Collisions

- The most important factor is the ___________or the time it takes the person to come to a rest.
- Increasing the collision time is the key factor.
- This will reduce the chance of dying in a car crash.

Typical Collision Values

- For a 75 kg person traveling at 27 m/s and coming to stop in 0.010 s.
- F = -2.0 x 105 N
- a = 280 g

- Almost certainly fatal:
- F = 90 kN fractures bone.
- a = 150 g for 4 ms causes spinal cord damage (causes the nerves to enter the base of the brain)

Collisions

- ______________ is conserved in any _________.
- ______________is not always conserved.
- Some KE is converted to other forms of energy (i.e. internal energy, sound energy, etc.) or is used to do the work needed to deform an object.

- Two broad categories of collisions:
- Elastic collisions
- Inelastic collisions: Perfectly inelastic and inelastic
- Elastic and perfectly inelastic collisions represent ideal cases of collisions.
- Most real world cases fit somewhere between these two extremes.

Conservation of Momentum

- Momentum in an isolated system in which a collision occurs is conserved.
- A collision may be the result of _______________ between two objects.
- “Contact” may also arise from the ______________ interactions of the electrons in the surface atoms of the bodies.
- An isolated system will have no external forces acting on the objects.

Conservation of Momentum

- 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.

F

Forces in a Collision

- The force with which object 1 acts on object 2 is equal and opposite to the force with which object 2 acts on object 1.
- Impulses are also equal and opposite.

Conservation of Momentum formula

- Mathematically:
- Momentum is conserved for the system of objects.
- The system includes _____________________ interacting with each other.
- Assumes only internal forces are acting during the collision.
- Can be generalized to any number of objects.

Sample Problem

A 1875 kg car going 23 m/s rear-ends a 1025 kg compact car going 17 m/s on ice in the same direction. The two cars stick together. How fast do the two cars move together immediately after the collision?

Recoil and Propulsion in Space

- Xe atoms are expelled from the ion engine.
- vatoms = 30km/h; Fatoms = 0.092 N
- Advantage: runs for a very long time

Glancing Collisions

- 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.
- Use subscripts for identifying the object, initial and final velocities, and components.
- We will examine collisions in two-dimensions.

Glancing Collisions

- The “after” velocities have x and y components.
- Momentum is conserved in the x direction and in the y direction.
- Apply conservation of momentum separately to each direction.

Sample problem

A 1,500 kg car traveling east with a speed of 25.0 m/s collides at an intersection with a 2,500 kg van traveling north at a speed of 20.0 m/s as shown in the figure. Find the direction and magnitude of the velocity of the wreckage after the collision, assuming that the vehicles undergo a perfectly inelastic collision and assuming that friction between the vehicles and the road can be neglected.

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