Review of three problems
PHY 303K: (Spring 2017) Lecture Notes unique # 56235, 56240, 56245, 56250
Instructor: Professor Shih Chapter 6: Further Applications of Newton’s Laws
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6.1 Friction
6.2 Restoring Force of a Spring; Hooke’s Law
6.3 Force for Uniform Circular Motion
6.4 The Four Fundamental Forces
Friction
Leonardo da Vinci’s empirical law
The magnitude of the friction force between unlubricated, dry surfaces sliding one over the other is proportional to the magnitude of the normal force acting on the surfaces and is independent of the area of contact and of the relative speed.
Force of kinetic friction (Direction opposes motion) Force of static friction (Direction opposes force which tries to move body; magnitude varies in response to applied force.)
k  coefficient of kinetic friction
s  coefficient of static friction
kinetic friction Example 1
Ship slipping
Free body Diagram
Example 2
kinetic friction Y‐component
N = P sin30o + mg
X‐component
Fx = P cos30o – fk,x
Static friction Example
The coefficient of static friction of the rubber of an automobile tire on a street surface is s=0.90.What is the steepest slope of a street on which an automobile with such tires (and locked wheels) can rest without slipping?
At maximum angle
=0
 = 42o for s=0.90
(force of friction)
48
Restoring Force of a Spring; Hooke’s Law
F
Negative slope = ‐k
x
k spring constant
FORCE FOR UNIFORM CIRCULAR MOTION
Example:
m = 7.3 kg
r = 1.9 m
v = 27 m /s
F = ?
What is the maximum speed with which an automobile can round a curve of radius 100 m without skidding sideways? Assume that the road is flat and that the coefficient of static friction between the tires and road surface is s = 0.80.
The friction is static because, by assumption, there is no lateral slippage.
fs,max = s N= smg
At a speedway in Texas, a curve of radius 500 m is banked at an angle of 22o . If the driver of a racing car does not wish to rely on lateral friction, at what speed should he take this curve?
F =