Download Lecture 8: Forces & The Laws of Motion

Lecture 10:
Work & Energy
Questions of Yesterday
1) A student pushes her physics book across a flat table.
Another student pushes his physics book up a 30o inclined
plane. Assuming the coefficient of kinetic friction is the same
in both cases, in which case is the force of friction acting on
the book greater?
a) the book on the flat table
b) the book on the inclined plane
c) the force of friction is the same in both cases
2) If you hold your physics book up against the chalkboard, in
what direction is the force of friction directed?
a) upwards
b) downwards
c) away from the chalkboard
d) into the chalkboard
Work
We often apply FORCE to an object because we want to
move it from one point to another
WORK is done on an object when…
a FORCE is applied to the object while
moving that object through a certain DISPLACEMENT
F
Dx
W = FDx
Work
ONLY valid if F and Dx are in the SAME DIRECTION!!
W = FDx
Units =
N*m = Joule
Magnitude of F * Magnitude of Dx
Work is a SCALAR - NO direction!
F
Dx
What about the directions of F and Dx ??
Work
F
q
F
Dx
Will the same work be done if F is applied in different directions?
Only the component of force in the same direction as the
displacement does work on the object!!
W = (Fcosq)Dx
Work
W = (Fcosq)Dx
What force is needed to raise
the box to the table at a constant
velocity?
How much work do you
do when you lift it
to the table?
10 kg
F
2m
10 kg
Work
W = (Fcosq)Dx
What force is needed to lower
the box from the table
to the ground
at a constant velocity?
How much work do you
do when you lower it
to the ground?
10 kg
2m
10 kg
Work
W = (Fcosq)Dx
Negative work
is done on an object
when the force is in
the opposite direction
to the displacement
10 kg
2m
10 kg
Work
W = (Fcosq)Dx
10 kg
10 kg
10 m
What force is needed to carry
the box horizontally to the table
at constant velocity?
How much work do you
carrying it to the table?
Work
W = (Fcosq)Dx
10 kg
10 kg
10 m
NO WORK
is done on the object if the
applied force is perpendicular to
the displacement!
NO component of force is in
direction of displacement
Work-Energy Theorem
Newton’s 2nd Law (∑F = ma) can be difficult to solve when
many forces are acting on an object in many different
directions….
The scalar quantity WORK can tell us information about the
net force acting on an object and its induced motion
Wnet = FnetDx = (ma)Dx
v2 = v02 + 2aDx
Wnet = (1/2)mv2 - (1/2)mv02
Work-Energy Theorem
Wnet = (1/2)mv2 - (1/2)mv02
KINETIC ENERGY
the energy of an object
associated with its motion
Units = kg*m2/s2 = Joules (J)
KE = (1/2)mv2
Kinetic Energy KE
of an object with mass m
moving with a speed v
Wnet = KEf - KEi = DKE
WORK-ENERGY
THEOREM
The total work done on an object is equal to
the change in the object’s kinetic energy
Conservative Forces
Wnet = KEf - KEi = DKE
2
h
What work does gravity do on
the ball (mass = m)
from 1-2?
From 2-3?
v0
1
3
From 1-3?
Gravity caused NO change in energy over entire trip!
The energy lost from 1-2 is regained in 2-3
The work done against gravity from 1-2 is recovered in 2-3
Conservative Forces
Wnet = KEf - KEi = DKE
Gravity is a
Conservative Force
2
v0
1
h
3
Gravity caused NO change in energy over entire trip!
The energy lost from 1-2 is regained in 2-3
The work done against gravity from 1-2 is recovered in 2-3
Conservative Forces
Wnet = KEf - KEi = DKE
h
2
v0
1
Would the work done from 1-3 be
different in this case?
What about 1-2? 2-3?
3
A force is conservative if the work it does moving an object
between two points is the same no matter what path taken
Nonconservative Forces
The coefficient of
kinetic friction between
the box and table is mk
Wnet = KEf - KEi = DKE
What work does friction
do on the box from 1-4?
4
What about
over the
path 1-2-3-4?
1
m
3
m
x
2
m
What about 1-2-3-4-1?
Friction is a Nonconservative Force
Energy lost from friction is NOT recovered
m
Work done by Friction
Friction always acts in a
direction opposite an object’s
motion.
Wnet = KEf - KEi = DKE
Work done by friction is
always Negative
4
1
Friction causes an object
to lose energy in the
form of heat and noise
m
3
m
x
2
m
m
Work done by Friction
A block slides down the inclined plane at a constant velocity.
What forces are acting on the block along the incline?
What is the work done by each of the forces?
What is the net work Wnet done on the block
over the distance d?
M
d
M
q
Wnc + Wc = KEf - KEi = DKE
Practice Problem
A 70-kg runner begins his slide into second base when he is
moving at a speed of 4.0 m/s. The coefficient of friction between
his clothes and Earth is 0.70. He slides so that his speed is zero
just as he reaches the base.
How much kinetic energy is lost due to friction acting on the
runner?
How far does he slide?
Questions of the Day
1) You slam on your brakes in a panic and skid a certain distance d
down a straight and level road before coming to a stop.
If you had been traveling twice as fast, what would the skidding
distance be?
a) 2d
b) d/2
c) 4d
d) d/4
2) As a pendulum swings back and forth, the forces acting on the
pendulum are the force of gravity and tension in the supporting
cord. Which of these forces does no work on the pendulum?
a) Gravity
b) Tension
c) neither one does work on the pendulum
d) they both do work on the pendulum