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