Phys. 121: Tuesday, 09 Sep.● Reading: finish ch. 6 by Thursday.● Written HW 3: Due Thursday.● Mastering Phys.: Second assignment is due tonight. Third assignment due in one week.● Office hours (tentative): Mon. 10-11:45, Tues. 11-12, or by appointment.● Clicker update: The Academic Center for Technology (Distance Ed.) has agreed to share their supply with us. If you still need a clicker, please bring your I.D. to Speare 14 between 3-5 pm today or from 8-10 am tomorrow. (Return these to ME at the end of the semester, and not the library - thanks!)

Newton's First Law of Motion

An object in uniform straight-line motionat constant velocity will remain in that stateof motion unless acted upon by a non-zerototal outside force.

In particular, an object at rest will remainat rest unless acted upon by a net force.

(At some level, this is just the DEFINITIONof what a “force” is. But we'll see inNewton's 2nd law that there's more to it.)

•This equation is exactly true, always!p = m v for objects moving slowly compared with the speed of light.

v⃗¿

p⃗=m ¿

¿

is called the momentum of the object. SoNewton's 2nd law says: forces change momentum.p⃗

SI unit of force: “Newtons” (N)

This is the “usual” case: does not applyto anything whose mass is changing,however.

If mass is changing, Newton's secondlaw becomes:

a⃗+ v⃗ (dm /dt )

F⃗ =m

... which shows that a force can benecessary even to move at constantvelocity! (Example: train car in therain, gaining mass from the rainwater.)

As a vector formula, this gives 2 equationsin 1 (or 3-in-1 in 3 dimensions). We willuse it over and over again!

Strategy: draw a force diagram forthe relevant object(s). Construct acoordinate system which simplifiesthings as much as possible.

The x and y components of the motion behaveindependently! We can look at each vectorcomponent of the motion separately from the other(s).

Example: Find the tension in the elevator cable if its acceleration is known (to be 0,or to be 1.0 m/s² downward, or 1.0 m/s² upward).

CLICKERS: the net (total) horizontal force on the 3 kg block is....

a) Less than 2 N b) Exactly equal to 2N c) Greater than 2 N

Example: Normal force perpendicular to surface: netforce does NOT vanish here, so skier accelerates!

Clickers: Diego wants to shoot a tranquilizer dart at a rabid smart monkey, who lets go when he sees the dart fire. Where should

Diego aim the dart?• a) A fixed bit above the target• b) Above the target; farther above

if the target is farther away• c) Right at the target• d) A fixed bit below the target• e) Below the target; farther below

if the target is farther away

This is the magnitude of a for purelycircular motion. The direction is towardthe center of the circle!

Again, this is merely a description of a type ofmotion. We'll see why something might movein circular motion beginning with chapter 5.

The inward force for an object in circularmotion is called the centripetal force. Here,it is provided by the ground pushing on thecar's tires sideways.

Clickers: Space stationoccupants feel weightless

because... a) they are outside the pull of Earth's gravity

b) the atmosphere acts like a big pillow, cushioning their

weight

c) their weight on the station is balanced by the station's weight on them, by Newton's 3rd law

d) their weight is opposed by Earth's normal force

e) their weight is just enough to move them in the

circle made by their orbit

Roller coaster occupants don't fall out(even with seat belts off!) for the samereason orbiting satellites don't hit theground: because they're moving.

The inward force for an object in circularmotion is called the centripetal force. Here,it is provided by the ground pushing on thecar's tires sideways.

Wait: then what is centrifugal force?That term is only used when acting as if the car is in an inertial reference frame (it is NOT);then a force must be invented to “push” theoccupants outward (their natural motion wouldbe a straight line). (We won't use it in this class.)

Clickers: A ball is whirled around on a stringin a vertical circle (gravity points down), atconstant speed. If the string breaks, where

will the ball most likely be at that moment? a) Top of the circle b) Bottom of the circle c) On the circle's side d) All positions are

equally likely e) That's impossible;

the string will

NEVER break.

F

X X

Tension in Massless Cables or Strings

Once things have stopped stretching, tension pulls BOTH directions on the interior bits of the string or cable. Upward tension and downward tension at each point are equal but opposite (Newton's Third Law).

Tension for a massless (meaning much less mass than the load placed on it) vertical cable or string is CONSTANT with varying height.

Clickers: how should tension in a heavy rope or chain vertically suspended behave?

a) It should be equal upward and downward at each point, but should decrease with altitude

b) It should be equal upward and downward at each point, but should increase with altitude

c) It should be equal upward and downward at each point and constant with altitude

d) It should be stronger downward than upward at each point

e) It should be stronger upward than downward at each point

Clickers: A given force F pulls straight down.What value for the angle minimizes the force on

each anchor point (R and L)? a) 0 degrees b) Between 0 and 45

degrees c) Between 45 and 90

degrees d) Exactly 90 degrees e) Need more

information to tell.F

X X

RL

(This angle) (equal to this)