Phys. 121: Thursday, 16 Oct.● Reading: Finish ch. 12.• Written HW 8: due Tuesday. ● Mastering Phys.: Sixth assign. due by midnight. Assign. 7 now up and due in one week. Extra credit problems now available.● Exam 1: I will add 1 pt. (curve) to score shown.

Written problems (9 and 10) may be re-worked for

half the credit back if you missed more than 0.1 on

them; go to an OSL tutor by next Monday, then

bring the corrected problems AND exam back to me.● Exam 2: will cover chapters 7, 8, 10, and 11, and

will most likely be the week after next.

Clickers: The total momentum of a system is conserved...

Reading Question 9.4

A. Always.

B. If the system is isolated.

C. If the forces are conservative.

D. Never; it’s just an approximation.

Law of Conservation of Momentum

An isolated system is a system for which the net external force is zero:

Or, written mathematically:

For an isolated system:

Clickers:

The two boxes are on a frictionless surface. They had been sitting together at rest, but an explosion between them has just pushed them apart. How fast is the 2 kg box going?

A. 1 m/s.

B. 2 m/s.

C. 4 m/s.

D. 8 m/s.

E. There’s not enough information to tell.

A 2.0 kg object moving to the right with speed 0.50 m/s experiences the force shown. What are the object’s speed and direction after the force ends?

A. 0.50 m/s left.

B. At rest.

C. 0.50 m/s right.

D. 1.0 m/s right.

E. 2.0 m/s right.

Clickers: 9.3

A force pushes the cart for 1 s, starting from rest. To achieve the same speed with a force half as big, the force would need to push for

Clickers:

A. s.

B. s.

C. 1 s.

D. 2 s.

E. 4 s.

1

2

1

4

Clickers: Which of the following statementsis true for an inelastic collision?

• a) Total momentum is not conserved.

• b) Total energy is not conserved.

• c) Kinetic energy is gained.

• d) Kinetic energy is lost.

• e) The Socorro Warm Springs are famous for having a unique species of trilobite living in them.

Collisions: Elastic vs. Inelastic• Energy is always conserved in collisions! But sometimes

it takes other forms (heat, sound) besides kinetic or potential energy.

• In an Elastic Collision, the kinetic energy of the objects is conserved also. (Example: drop a ball onto the floor

which bounces ALL the way back up.)

• In a Totally Inelastic Collision, the objects stick together after colliding. (Example: drop a lump of clay onto the

floor which sticks without bouncing at all.)

• Most collisions are neither perfectly elastic nor inelastic (most dropped balls will bounce back to only part of their

original height).

Strategy for collision problems:

• Always conserve total momentum of colliding objects! Special case: if one object is VERY much more massive than the other (a brick wall or the Earth versus a ping-pong ball, for example), then treat the massive object as fixed in place instead.

• If perfectly elastic, use conservation of kinetic energy to solve for the final velocities. If perfectly inelastic, assume that the objects stick together and only use momentum conservation to solve for final velocities (or masses or other unknowns).

Let's work this out again, CAREFULLY...

Example: find the final velocity ofeach block after all (elastic) collisions areover.

m m2 m

Example: find the final velocity ofeach block after all (elastic) collisions areover.

m m2 m

[Clickers: While moving inventory at the gym,you drop several balls toward the floor. Can anyof these ever bounce back to higher than theiroriginal height, if they were dropped from rest?]

a) Yes; physics will allow it. b) No: that's magic and only works for Harry Potter. c) Ask again when it's not 49ers week, and maybe I will care then.

Example (Astro-Blaster): Two balls are droppedfrom a height h, and bounce elastically off eachother and the floor. Find the maximum heightthat the top ball rebounds to if it has much lessmass than the bottom ball.

(Chapter 12:) Definition of the center of mass:

The center of mass is used a lot in physics! Forinstance, the weight of an object acts like it pointsdownward from the center of mass (for instance,remember the front-wheel-drive problem: 70 percentof the normal force was on the front tires, because thecenter of mass was close to the front tires).

The center of mass is where you can balance anextended object. In force diagrams, it's as if theentire object's weight acts “at” the center of mass.

Total momentum P is total mass times velocityof the center of mass... this gives:

Ptotal

= pi= m

ivi=M

totalv

CM

Only external forces, which come from thingsyou're not keeping track of in the total momentum,can change the total momentum.

Example with no external force: Ptotal = 0!But things can still happen anyway...

External force (gravity): CM moves in a parabola