Chapter 5 - Force and Motion II

• Friction– Static

– Kinetic

• Incline/Horizontal Plane with friction

• Drag Forces– Terminal Velocity

• Uniform Circular Motion– Banked and Flat Turns

– Cresting Hills

– Loop the Loops

– Conical Pendulums

– Ferris Wheels

– Aircraft Turns

Friction

fr s NF F

fr k NF F

Coefficients of Friction

To push or pull a sled?

Or

fr k NF F

Measuring coefficients of friction

s tan k tan

mgsin

mg cos

NF

mg

frF

Two boxes and a pulley

Incline plane (no friction)

• m2 = 7 kg• Which way do

blocks move?• What is

acceleration?• What is tension

in cord?

Incline plane (friction)

• What range of masses keep the blocks at rest?

• If m2 = 10 kg, determine the system acceleration

s 0.40 k 0.30

Uniform Circular Motion

2

R

va

r

2

R R

vF ma m

r

Banked Roads

v gr tan

No friction required:

Conical Pendulum

v gr tan gLsin tan

LcosT 2

g

Motion in a vertical circle with gravity

• m = .150 kg • r = 1.10 m• Find minimum speed

to continue moving in a circle

• If speed is twice this minimum, find tension in cord at top and bottom.

Demo

Non-uniform circular motion

Velocity Dependent ForcesTerminal Velocity

y

dvF bv mg m

dt

bt

mmg

v 1 eb