Download PHYS 1020 Lecture 18 Work Energy

PHYS 1020
Lecture 18 Work Energy
Work done by a constant force
Since -1 ≤ cosθ ≤ 1, W can be positive or negative.
See lecture posted online for corrected version.
You can calculate the work done on an object by
individual forces and by the net force.
ex: A person pulls a block (mass 10 kg) up an
inclined plane at constant speed. The block moves 1
m along the plane and the tension force acting on the
block is parallel to the plane. Find the work done on
the block by
(a) the tension force
(b) gravity
(c) the normal force
(d) the kinetic friction force
(e) the net force
Use µk = 0.20.
The Work-energy theorem and kinetic energy
An external force acts on an object. The object is
displaced a distance s, in the same direction as the net
force:
∑F
s
€
€
W = (€
∑ F ) s = ( ma) s
Constant forces: use kinematics equations for constant
a in 1-d.
1 2
2
as
=
v
−
v
( )
0
2
(
2
2
v = v0 + 2a ( x − x0 )
↓
s
W = m(as€) = 12 mv 2 − 12 mv0 2
Kinetic energy
€
€
KE = 12 mv 2
)
The Work-Energy Theorem
•  When a net external force does work on an object,
the KE of the object changes according to
Wnet = KE f − KE0 = 12 mv f 2 − 12 mv0 2
€
Image reprinted with permission of John Wiley and Sons, Inc.
i>clicker
C&J conceptual question 5
A 3.00-kg model airplane has velocity components of
5.00 m/s due east and 8.00 m/s due north. What is the
plane’s kinetic energy?
a)  134 J
b)  96 J
c) 
38 J
d)  254 J
C&J 6.20 A 16-kg sled is being pulled along the
horizontal snow-covered ground by a horizontal force of
24 N. Starting from rest, the sled attains a speed of 2.0
m/s in 8.0 m. Find the coefficient of kinetic friction
between the runners of the sled and the snow.
i>clicker
Conservative forces and potential energy
Conservative force: work
done by the force when
an object moves from
point A to point B doesn’t
depend on the path.
Examples of conservative
forces: gravity, electric,
spring force.
Friction is a non-conservative force!
Gravity is a conservative force.
Move block
from A to B by:
(a) Lift to height
2h then move
horizontally x,
or (b) carrying
the block up the
stairs to point
B. Calculate
the work done
by gravity.
Gravitational potential energy (PE)
W = (F cosθ)s
Wg = −mg(h f − h0 )
Wg =
mghf
( mgh0 )
Wg = mgh0
mghf
Wg = PE0 − PE f = −ΔPE
PE = mgh
Image reprinted with permission of John Wiley and Sons, Inc.
Gravitational PE is the energy that an object of mass m
has due to its position relative to the surface of the
earth, measured by the height h of the object relative to
an arbitrary zero level:
PE = mgh
€
Also Example: Gymnast on Trampoline in C+J (P. 152-3 10th
edition)
Potential energy
•  Potential energy is stored in the configuration of
(Consider the situation when W_g is balanced by W_T.)
a system.
– 
e.g. Earth and object, not just the object.
•  Only defined for conservative forces
e.g. Work done by gravity
Wc = −ΔPE
•  Examples of conservative forces: gravity,
springs, electromagnetic forces
€m
m
mg
W = −mgh
m
mg
W = mgh
m
mg
W = mg cos 90º = 0
mg
W = −mgh + 0 + mgh + 0 = 0
More on conservative and nonconservative forces
Conservative force
does no work on an
object moving around
a closed path,
starting and ending at
the same point.
Image reprinted with permission of John Wiley and Sons, Inc.
Friction always points in direction opposite to motion.
W = (F cosθ)s = f k cos180°s = − f k s
Work done by friction is always negative ⇒ friction is
a non-conservative force and no PE defined for it.
€
Another example of a dissipative force is air resistance.
i>clicker
C&J conceptual question 12 Air resistance is a
nonconservative force. It always opposes the motion of
an object. An airplane flies from New York to Atlanta
and then returns to its point of departure. The net work
done by air resistance during this round trip
___________.
a) 
b) 
c) 
d) 
is zero
is positive
is negative
is negative for slow speeds and positive for high
speeds.
e)  is positive for slow speeds and negative for high
speeds.
Work-energy theorem
•  New statement of theorem when both conservative
and nonconservative forces are present.
Wnet = ΔKE
Wc + Wnc = ΔKE
−ΔPE + Wnc = ΔKE
€
Wnc = ΔKE + ΔPE
Work-energy theorem
Two statements of the work-energy theorem
1)  Work done by the net force
Wnet = ΔKE
2)  Work done by nonconservative forces
€
Wnc = ΔKE + ΔPE
The change in both the KE and PE is always
the final value minus the intial value.
€
Conservation of mechanical energy
Total mechanical energy
Work-energy theorem
€
€
E = KE + PE
Wnc = ΔPE + ΔKE
= ΔE
If the work done on an object by nonconservative
forces is zero then the total mechanical energy
is constant (conserved). Ef = E0
THE PRINCIPLE OF
CONSERVATION OF
MECHANICAL ENERGY
The total mechanical energy (E = KE + PE) of an
object remains constant as the object moves, provided
that the net work done by external nonconservative
forces is zero.
C+J 6.37A gymnast is swinging on a high bar. The distance
between his waist and the bar is 1.1 m, as the drawing
shows. At the top of the swing his speed is momentarily
zero. Ignoring friction and treating the gymnast as if all of
his mass is located at his waist, find his speed at the
bottom of the swing.
(Where is the max and min KE?
The max and min PE?)
Work and energy so far
W = Fs cosθ
Constant force, straight path
Wnet = ΔKE
= 12 m v f 2 − v0 2
(
Wcons = −ΔPE
PE = mgh
Wnc = ΔPE + ΔKE
)
Work done by net force
Work done by conservative force
Gravitational potential energy
Work done by nonconservative forces
Homework
•  Read All of Chapter 6.
•  Last section is Power.
Office Hours: Allen 514 Tuesday 2:30-4:30 pm
Midterm:
Preparation session with Dr. Basnet
Tuesday, October 25, 12:00 – 2:00 in room 224
Education Building
(next page)
Midterm:
•  Please continually check the course website
http://www.physics.umanitoba.ca/undergraduate/
phys1020/exams.htm
•  There will be a formula sheet
http://www.physics.umanitoba.ca/undergraduate/
phys1020/wa_files/
Phys1020_20formula_20sheet_20midterm_202016.pdf
•  Prohibited calculators are described at
http://www.act.org/content/act/en/products-and-services/
the-act/help.html
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