Welcome back to Physics 215

Welcome back to Physics 215 Today’s agenda: Friction, drag Tension, pulleys Forces in circular motion Impulse

Current homework assignment • HW5: • Knight textbook Ch.6: 38, 42, 56, 58 • Ch.7: 46, 54 • due Friday, Oct. 3rd in recitation

Summary of friction • 2 laws of friction: static and kinetic • Static friction tends to oppose motion and is governed by inequality Fs ≤ msN • Kinetic friction is given by equality FK = mKN

What if  > tan-1ms ? The magnitude of the forceofkinetic friction between two objects • depends on the type of surfaces of the objects • depends on the normal force that the objects exert on each other • does not depend on the surface area where the two objects are touching • does not depend on the speed with which one object is moving relative to the other

What if  > tan-1ms ? • Block begins to slide • Resolve along plane: Wsinq- mKWcosq= ma • Or: a = g(sinq- mKcosq)

For an ideal string or rope connecting two objects: • does not stretch  inextensible • has zero mass Tension • Let’s look at an example of a cart connected to a falling mass by an ideal string...

Blocks A and C are initially held in place as shown. After the blocks are released, block A will accelerate up and block C will accelerate down. The magnitudes of their accelerations are the same. Will the tension in the string be 1. equal to 1.0 N (i.e. the weight of A), 2. between 1.0 N and 1.5 N, 3. equal to 1.5 N (i.e. the weight of C), or 4. equal to 2.5 N (i.e.the sum of their weights)?

Demo: Pulleys *2 pulleys 2T = W F = T = W/2 T F *N pulleys F = W/N! W

Motion around circular track, constant speed (for now): Forces in circular motion arad = v2/r

Two identical balls are connected by a string and whirled around in circles of radius r and 2r at angular speed. The acceleration of ball B is 1. four times as great 2. twice as great 3. equal to 4. one half as great as the acceleration of ball A.

The two identical balls are whirled around in a circle as before. Assume that the balls are moving very fast and that the two strings are massless. The tension in string P is 1. less than 2. equal to 3. greater than the tension in string R.

Motion around circular track, constant speed (for now): Car on circular track with friction arad = v2/r

Motion of car on banked circular track (no friction) car R N a = q W Speed v Horizontal forces: Vertical:

Motion on loop-the-loop What is normal force on car at top and bottom of loop? Neglect friction; assume moves with speed vB at bottom and vT at top car At bottom At top

Impulse • Constant force F12 acting on object 1 due to object 2 for a time Dt yields an impulse I12 = F12t • In general, for a time varying force need to use this for small Dt and add: I =  F(t)t =

Impulse for time varying forces F(t) * area under curve equals impulse t t2 t1

Impulse  change in momentum • Consider first constant forces ... • Constant acceleration equation: vf = vi + at mvf - mvi = mat = • If we call p = mv momentum we see that p =

Impulse demo • Cart equipped with force probe collides with rubber tube • Measure force vs. time and momentum vs. time • Find that integral of force curve is precisely the change in p!

Definitions of impulse and momentum Impulse imparted to object 1 by object 2: I12 = F12t Momentum of an object: p = mv

Impulse-momentum theorem Inet = p The net impulse imparted to an object is equal to its change in its momentum.

Consider the change in momentum in these three cases: A. A ball moving with speed v is brought to rest. B. The same ball is projected from rest so that it moves with speed v. C. The same ball moving with speed v is brought to rest and immediately projected backward with speed v. 1. Case A. 2. Case B. 3. Case C. 4. Cases A and B. In which case(s) does the ball undergo the largest change in momentum?

Reading assignment • Momentum, collisions • Chapter 9 in textbook

Welcome back to Physics 215