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Oscillations!
(Today: Springs)
Extra Practice: 5.34, 5.35, C13.1, C13.3, C13.11, 13.1, 13.3, 13.5,
13.9, 13.11, 13.17, 13.19, 13.21, 13.23, 13.25, 13.27, 13.31
Test #3 is this Wednesday!
• April 12, 7-10pm, Eiesland G24 as usual.
MAKE-UP EXAMS: If you haven’t gotten a
confirmation email, you’re not scheduled for a
make-up.
• Practice test, practice key, and equation sheet
are on my website.
• Today’s homework due Thursday.
No homework due Sunday (no class Friday!).
http://sarahspolaor.faculty.wvu.edu/home/physics-101
The rest of this semester.
wave concepts
sound
springs
ultrasonic waves
string vibrations/
music
pendula
Familiar concepts…
• Forces/free body diagrams!
Fspring
• Newton’s laws!
Fg
ΣF = ma = 0
• Work and energy conservation!
PEg = mgh
All converted to
spring potential
Let’s think about springs.
Fs = -k x
spring constant [Units: N/m]
Fpull
Fspring
“Hooke’s Law!”
Fs = -k x
spring constant [Units: N/m]
Low k
(soft spring)
High k
(stiff spring)
Familiar problem #1:
Newton’s second (and third) laws
A 2.5 kg object is hanging vertically on a spring, which is
stretched by the weight by a distance d. What is the magnitude
of the force the spring is applying to the object?
d
A.
B.
C.
D.
6.3 N
16 N
25 N
Not enough information
Q107
Familiar problem #1:
Newton’s second (and third) laws
A 2.5 kg object is hanging vertically on a spring, which is
stretched by the weight by a distance d. What is the magnitude
of the force the spring is applying to the object?
b) If the string stretches by 2.76 cm due to this
mass, what is the spring constant?
d
A.
B.
C.
D.
0.55 N/m
77 N/m
888 N/m
5 x 105 N/m
Q108
c) What is the spring force if you stretch the
spring to 8 cm?
Springs as harmonic oscillators.
Spring (Elastic) Potential Energy
When stretched or
compressed, a spring
gains potential energy!
Recall: Work and
Gravitational Potential Energy.
Work:
Energy associated with a force and its action.
W = F||Δx
Wg = -ΔPEg
PEg = mgh
PEg = 0 J
If an object is
released from height
h, gravity has the
potential to do an
amount of work
equal to mgh.
How Do We Find Spring
Potential Energy?
F0 = 0 N
(PEs = 0 N)
Fs = -kx (Hooke’s Law)
W = F||Δx (Work done by spring)
Ws = -ΔPEs (Work done by spring)
Conservation of energy applies to springs, too!
PEs = ½ kx2
(KE + PEg + PEs)f = (KE + PEg + PEs)i
(if no friction)
Wnc = (KE + PEg + PEs)f - (KE + PEg + PEs)i
(if friction or other non-conservative
forces are present)
Energy lost to non-conservative forces
Where does an oscillating spring
provide a maximum kinetic energy?
A.
B.
C.
D.
E. Both B and D
Q109
Kinetic and Potential
A weight is suspended by a spring. The spring is then
stretched until the weight is just above some eggs, and then it
is released. The weight springs upward and then comes back
down due to gravity. Ignoring air resistance, what happens?
A. the weight bounces back well
above the eggs
B. the weight bounces back just
before it reaches the eggs
C. it smashes the eggs!
Q110
Total energy in an oscillator
Total energy = KE + PE
x=A
Total energy in
oscillator
= ½ kA2
At max
displacement,
energy is all
in PEs!
= ½ kx2
at x = A
Velocity as a Function of Position
v=0
max -v
1
2
KE
PEs
Total E
mv 2 + 12 kx 2 = 12 kA2
• We can derive the velocity of the
object at any position
v=0
max +v
– Speed is a maximum at x = 0
– Speed is zero at x = ±A
– The ± indicates the object can
be traveling in either direction
A block whose mass is 0.5 kg is retracted against a
release spring with spring constant 75 N/m. If the
spring is initially stretched A=0.25 m, what is the
velocity of the block when the spring returns to its
equilibrium position? (assume a flat, frictionless
release surface)