Transcript Chapter 6

Announcements:
- Midterm 1 in less than a week, Sept. 19 (Chapter 1-6)
- Can use a 3x5 inch cheat card with 10 formulas
- I will post practice test on the Web
- HW 10 is due on Friday, Sept. 23, 10 pm
- Extended office hours this Friday 1-3
Chapter 6: Force and Motion - II
Reading assignment: Chapter 7.1-7.5
Homework : Due Friday Sept 23, 2005 (an extra week to do it!
Chapter 7: Q13, 4, 9, 18, 22, 29
•
In this chapter we will learn about
• static friction
• kinetic friction
• centripetal force
• kinetic drag force
Black board example 5.6
Two objects of mass m1 and m2 are attached by a string over a pulley
as shown in the Figure. m2 lies on an incline with angle q.
(a) Determine the magnitude of the acceleration of the two objects
and the tension in the cord.
(b) m1 = 10.0 kg, m2 = 5.00 kg, q = 45º
Forces of Friction
• Static friction, fs
• Kinetic friction, fk
The following
laws hold true about friction:
- Friction force, f, is ________________ to normal force, n.
fs  msn
f k  mk n
- ms and mk: coefficients of ___________ and ____________
friction, respectively
- Direction of frictional force is ______________ to direction of
relative motion
- Values of ms and mk depend on nature of surface.
- ms and mk don’t depend on the ________ of contact
- ms and mk don’t depend on ____________.
- Friction is due to the surfaces interacting with each other on the
microscopic level (sliding over bumps, chemical bonds)
Black board example 6.1
Measuring the coefficient of static
friction
A brick is placed on an inclined
board as shown in the figure.
The angle of incline is
increased until the block starts
to move.
(a) Determine the static friction coefficient from the critical angle,
qc, at which the block starts to move.
(b) What is ms if the block starts sliding at qC = 31°
Black board example 6.2
Measuring the coefficient of
kinetic friction
A hockey puck is given an
initial speed of 20.0 m/s.
It slides 115 m before
coming to rest.
(a) Determine the coefficient of kinetic friction between the puck
and the ice.
(b) Could the coefficient of friction be larger than 1?
Thus far we have applied Newton’s law, F = m*a to linear motion.
Now we’ll apply it to rotational motion
Particle moving with __________ speed v in a circular path with
radius r has an acceleration ar:
2
v
ar 
r
(Derivation: see Chapter 4.7)
- The acceleration points
towards the _________
of the circle!
- Centripetal acceleration
Newton’s law along the radial direction (along r):
2
v
 F r  m  ar  m  r
Uniform Circular motion:
• The velocity of the particle is along the __________
• The centripetal acceleration is towards the __________
• The centripetal force acting on the particle is towards the ________
• Centripetal force causes a change
in the ________________ but no
change in ________________.
The magnitude of the centripetal
acceleration is: a =______________
Newton’s law: The force on the
particle is (centripetal force)
F= m·a = ______________
A particle is moving in a circular path.
If the force on the particle would suddenly vanish (string cut)
in which direction would the ball fly off?
Black board example 6.3
Franz rotates a stone (m = 0.50
kg) that is attached to the end
of a 1.5 m cord above his head
in a horizontal circle.
If the cord can hold 50 N of
tension, at what maximum
speed will it rupture.
Which force “provides” the
centripetal force?
Black board example 6.4
Jeff Gordon leads his race and must drive into a curve at top speed
to win it all.
The radius of the curve is 1000.0 m and the coefficient of static
friction between his tires and the dry pavement is 0.500. Find the
maximum speed he can have and still make the turn.
Which force “provides” the centipetal force?
Motion in the presence of drag (or ________) forces
Motion in ________ media.
Objects interact with the
medium through which they
are moving.
- Air
- Water, oil, liquids.
The drag forces depend on
the ________ of the object.
F ~ v: Objects falling in __________, tiny objects falling in air.
F ~ v2: ________________ objects moving in air.
Terminal velocity.
When the ___________ force of
the falling object is equal to the
_________________ force on the
object.
Examples:
- skydivers
- soap bubbles falling in air
- small spheres dropping in liquid.
Air drag at high speeds.
For objects moving at high speeds through air:
Drag force:
1
2
D  __  __  A  v
2
Where:
___… Drag coefficient of object (depends on shape)
___…density of air
A… cross-sectional area of object
v… velocity of object
Black board example 6.5
A careless person drives a pick-up truck with a mattress tied to
the roof. The mattress is 50 cm high and 150 cm wide.
(a) Calculate the resistive force acting on the mattress if the truck
drives with a speed of 30 m/s (67 mi/hr).
(b) Should the driver worry about his load if it is tied down with
a rope capable of holding 250 N?
Drag coefficient = 0.5
density of air = 1.29 kg/m3
Air drag at high speeds.
For objects moving at high speeds through air:
Drag force:
1
2
D  C    Av
2
Where:
C… Drag coefficient of object (depends on shape)
…density of air
A… cross-sectional area of object
v… velocity of object
Black board example 6.5
A careless person drives a pick-up truck with a mattress tied to
the roof. The mattress is 50 cm high and 150 cm wide.
(a) Calculate the resistive force acting on the mattress if the truck
drives with a speed of 30 m/s (67 mi/hr).
(b) Should the driver worry about his load if it is tied down with
a rope capable of holding 250 N?
Drag coefficient = 0.5
density of air = 1.29 kg/m3