Download Lecture 11 (Feb 17) - West Virginia University

Announcements
There will be NO extra help session tomorrow. No one has
attended for the last 4 sessions, so PLEASE take advantage of
these sessions. They will resume next week, and are Tuesdays
and Thursdays, 3:30 PM - 5 PM in White 343.
WEST VIRGINIA UNIVERSITY
Physics
Weighing a fish in the elevator
A woman weighs a fish with a spring
scale attached to the ceiling of an
elevator. While the elevator is at rest,
she measures a weight of 40 N.
A. What weight does the scale read if
the elevator accelerates upwards
at 2 m/s2?
B. What does the scale read if the
elevator accelerates downwards at
2 m/s2?
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Physics
Example problem: Friction
A hockey puck struck by a hockey stick
is given an initial speed v0 in the positive
x-direction. The coefficient of kinetic
friction between the ice and the puck is µk.
A. Obtain an expression for the acceleration
of the puck as a function of µk and g.
B. Use the result of part (a) to obtain an
expression for the distance, d, the puck
slides. The answer should be in terms of
v0, µk, and g only.
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Physics
The Work-Energy Theorem
This theorem relates the net work done on an object to the change in its speed:
From chapter 2 (motion with uniform acceleration) we know:
This yields:
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Physics
Kinetic Energy
The net work done on an object can result
in a change of a quantity of the form 1/2mv2.
This scalar quantity has the unit of an
energy and is called kinetic energy:
Unit: J = kg · m2/s2
Work-Energy Theorem:
This will only be valid, if the work is completely transferred to kinetic energy.
Positive net work means that the object’s speed increases.
Negative net work means that the object’s speed decreases.
WEST VIRGINIA UNIVERSITY
Physics
A system of multiple objects
v1
m3
m1
v3
v2
2
m2
2
KEsystem = m1v1 + m2v2 + m3v3
1
2
1
2
1
2
2
In a system of multiple objects, the total kinetic energy is the sum of the
objects’ individual kinetic energies.
Energy is never lost: It can be transferred from one object to the other or transformed from
one kind of energy, e.g. kinetic energy, to another type of energy, e.g. potential energy.
WEST VIRGINIA UNIVERSITY
Physics
Clicker question
2v
v
2m
m
What is the total kinetic energy of the system of
vehicles?
A. 0 J
B. 1/2 mv2
C. mv2
D. 2 mv2
E. 3 mv2
WEST VIRGINIA UNIVERSITY
Physics
Conservative and non-conservative forces
There are 2 fundamentally different types of forces
in nature:
1. A force is called conservative, if the work it does
moving an object between two points is the same
independent of the path taken.
Example: Gravity
2. A force is called non-conservative, if this work
depends on the path taken.
Example: Friction
The Work-Energy Theorem can be written as the
sum of conservative, Wc, and non-conservative
parts, Wnc:
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Physics
Work-Energy Theorem II
The total work done is the sum of the work done by
conservative and non-conservative forces.
Let’s look at the work done by conservative forces,
e.g. gravitation: How much work will be done, if a
book falls down from yi to yf?
Definition of gravitational potential energy:
Substitute this into the Work-Energy Theorem:
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Physics
The meaning of potential energy
y ≙ height above reference level
An object has potential energy, because due to its
location it can potentially do work.
The choice of the reference level is arbitrary, since
only differences of potential energies matter in the
work-energy theorem:
Once chosen the reference level must remain the same.
Every conservative force can be associated with a
potential energy, since the work done by this force
depends only on the displacement and not on the path
length.
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Physics
Example: The reference height is arbitrary
A 60 kg skier is at the top of a slope. At
position A she is 10 m above point B.
A. Setting the zero level for the potential
energy at B, find the gravitational
potential energy, when the skier is at A.
B. Repeat this problem with the zero level at
point A.
WEST VIRGINIA UNIVERSITY
Physics
Clicker question
A piece of fruit falls straight down. As it falls,
A. the gravitational force does positive work on it and the gravitational potential energy
increases.
B. the gravitational force does positive work on it and the gravitational potential energy
decreases.
C. the gravitational force does negative work on it and the gravitational potential energy
increases.
D. the gravitational force does negative work on it and the gravitational potential energy
decreases.
WEST VIRGINIA UNIVERSITY
Physics
Conservation of energy
Work-Energy Theorem:
Let’s look at a situation, where non-conservative
forces, e.g. friction, can be neglected:
This equation means that the total energy (sum of
KE and PE) is conserved.
Substitution of the equations for the kinetic and
potential energy yield:
WEST VIRGINIA UNIVERSITY
Physics
Example problem: Conservation of energy
A diver of mass m drops from a board 10 m above
the water’s surface. Neglect air resistance.
A. What is his speed 5 m above the water surface?
B. Find his speed as he hits the water.
Conservation of energy:
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Physics