PHYSICS 231 INTRODUCTORY PHYSICS I Lecture 6

PHYSICS 231
INTRODUCTORY PHYSICS I
Lecture 6
Last Lecture:
•
•
•
Gravity
Normal forces
Strings, ropes and Pulleys
Today:
•
Friction
•
Work and Kinetic Energy
• Potential Energy
• Conservation of Energy
Frictional Forces
• RESISTIVE force between object and neighbors
or the medium
• Examples:
• Sliding a box
• Air resistance
• Rolling resistance
Sliding Friction
• Parallel to surface,
opposing direction of motion
• ~ independent of
the area of contact
• Depends on the surfaces in contact
• Object at rest: Static friction
• Object in motion: Kinetic friction
Static Friction, ƒs
fs ! µ s N
• Just enough force to
keep object at rest.
• µs is coefficient of
static friction
• N is the normal force
f
F
Kinetic
Friction, ƒk
f k = µk N
µk < µs
! • µk is coefficient of
kinetic friction
!• Friction force opposes
direction of motion
• N is the normal force
f
F
Coefficients
of Friction
f ! µs N
f = µk N
µs > µk
Example 4.7
The man pushes/pulls with a force of 200 N. The
child and sled combo has a mass of 30 kg and the
coefficient of kinetic friction is 0.15. For each case:
What is the frictional force opposing his efforts?
What is the acceleration of the child?
f=59 N, a=3.80 m/s2
/
f=29.1 N, a=4.8 m/s2
Example 4.8
Given m1 = 10 kg and m2 = 5 kg:
a) What value of µs would stop the block from sliding?
b) If the box is sliding and µk = 0.2, what is the
acceleration?
c) What is the tension of the rope?
a) µs = 0.5
b) a=1.96 m/s2
c) 39.25 N
Example 4.9
What is the minimum µs required to
prevent a sled from slipping down a
hill of slope 30 degrees?
µs = 0.577
Chapter 5
Work and Energy
Forms of Energy
• Mechanical
• Kinetic, gravitational
• Thermal
• Microscopic mechanical
• Electromagnetic
• Nuclear
Energy is conserved!
Work
• Relates force to change in energy
r r
r
W = F ! ( x f " xi )
= F#x cos$
• Scalar quantity
• Independent of time
Units of Work and Energy
W = F!x
SI unit = Joule
1 J = 1 N⋅m = 1 kg⋅m2/s2
Example 5.0
A man holds a 50 lb box at waist level for 10
minutes. Has he done any work during this time?
120 m
Work can be positive or negative
• Man does positive work
lifting box
• Man does negative work
lowering box
• Gravity does positive
work when box lowers
• Gravity does negative
work when box is raised
Work and friction
A block is pulled a distance Δx
by constant force F.
N
fk
F
mg
•
•
•
•
Work
Work
Work
Work
of
of
of
of
F> 0
N = 0
mg = 0
fk < 0
Work of (kinetic) frictional force is always < 0.
-> It removes mechanical energy from system.
Kinetic Energy
1 2
KE = mv
2
Same units as work
Remember the Eq. of motion
v 2f
vi2
!
= a"x
2
2
Multiply both sides by m,
1
2
mv 2f " 12 mv i2 = ma#x
KE f " KE i = Fnet #x
!
!
KE f " KE i = W net
Work-Energy Theorem
Example 5.1
A skater of mass 60 kg has an initial velocity of 12
m/s. He slides on ice where the frictional force is 36
N. How far will the skater slide before he stops?
120 m
Potential Energy
If force depends on distance, we can define
Potential Energy
This must be independent of Path
-> “Conservative Force”
!PE = "F!x
For gravity (near Earth’s surface)
!PE = mgh
Conservation of Energy
PE f + KE f = PEi + KEi
!KE = "!PE
Conservative forces:
• Gravity, electrical, …
Non-conservative forces:
• Friction, air resistance…
Non-conservative forces still conserve energy!
Energy just transfers to thermal energy (heat)
Example 5.2
A diver of mass m drops from
a board 10.0 m above the
water surface, as in the
Figure. Find his speed 5.00 m
above the water surface.
Neglect air resistance.
9.9 m/s
Example 5.3
A skier slides down the frictionless slope as shown.
What is the skier’s speed at the bottom?
start
H=40 m
finish
L=250 m
28.0 m/s
Example 5.4
Three identical balls are
thrown from the top of a
building with the same initial
speed. Initially,
Ball 1 moves horizontally.
Ball 2 moves upward.
Ball 3 moves downward.
Neglecting air resistance,
which ball has the fastest
speed when it hits the ground?
A)
B)
C)
D)
Ball 1
Ball 2
Ball 3
All have the same speed.
Example 5.5
Two blocks, A and B (mA=50 kg and mB=100 kg), are
connected by a string as shown. If the blocks begin
at rest, what will their speeds be after A has slid
a distance s = 0.25 m? Assume the pulley and
incline are frictionless.
1.51 m/s
s
Example 5.6
Tarzan swings from a vine whose
length is 12 m. If Tarzan starts at an
angle of 30 degrees with respect to
the vertical and has no initial speed,
what is his speed at the bottom of
the arc?
5.61 m/s