Spring Problems

1
Spring Problems
Examples of
Frequency and Period Problems
Pendulum Problems

• Equations for Equation sheet for Springs and
  Pendulum Problems

2
Examples of Period Frequency Problems
3
Frequency and Period Problem(Without Period or
Frequency given)

• Terry Jumps up and down on a trampoline 30 times
  in 55 seconds. What is the frequency with which
  he is jumping?

30 times
55 seconds
0.55 Hz
4
Frequency and Period Conversion problem

• Terry Jumps up and down on a trampoline with a
  frequency of 1.5 Hz. What is the period of
  Terrys jumping?

1.5 Hz
0.67 sec
5
Examples of Pendulum Problems
6
(No Transcript)
7
Problem

• At the California Academy of Sciences the length
  of the pendulum is 90m L
• The acceleration of gravity at this location
  is 9.8 m/s/s g
• What is the Period? T???? seconds

8
Solution
Solve Plug and Chug

• List
• L 90m
• g 9.8 m/s/s
• T???? seconds
• Choose equation

90 m
9.8 m/s/s
9.18 s2
(3.03 s)
(19.0 s)
9
A pendulum has a length of 3 m and executes 20
complete vibrations in 70 seconds. Find the
acceleration of gravity at the location of the
pendulum.
A problem where you Find the period or
frequency 1st
10
A pendulum has a length of 3 m and executes 20
complete vibrations in 70 seconds. Find g.

• 1.
• f cycles / seconds
• 20 cycles / 70 seconds
• 0.286 hz
• 0.286 / sec
•  
• 2.
• T 1 / f
• (1 / 0.286) seconds
• 3.5 seconds
• What short cut could I have used?

vibrations
seconds is the time for all the oscillations
11
L 3m and T 3.5 secondsFind the acceleration
of gravity at the location

• 3.5 s 2pv(3/g)
• 3.5 s 6.28 v(3/g)
• Square both sides
• 12.25 39.43 (3/g)
• 12.25 118.3/g
• 12.25(g) 118.3
• Divide by 12.25
• g 9.658 m/s/s

Heads up!! If you by 2p ? Use (2p ) !!
12
A problem Where "g" 9.8 m/s/s is
understoodKnow you use g9.8 m/s/s ifg
not given or asked for used 9.8 m/s/sPart 1 A
simple pendulum has a period of 2.400 seconds
where "g" 9.810 m/s/s. Find the length?Part
2 Find "g" where the period of the same pendulum
is 2.410 seconds at a different location.
13
Why are the items green on this
problem??Pendulum is not a variable, why is it
marked??

• A simple pendulum has a period of 2.400 seconds
  where "g" 9.810 m/s/s. Find the length?
• Find "g" where the period of the same pendulum is
  2.410 seconds at a different location.

14
1st find the LengthA simple pendulum has a
period of 2.400 seconds where "g" 9.810 m/s/s.

• T24p2 (L/g)
• 2.40024 p2 (L/9.810)
• 2.4002 39.44 (L/9.810)
• 2.4002(9.810) L
• 39.44
• L1.433 m

• Write equation
• Substitute s
• Square 4 p2
• 39.44
• And X 9.810
• Answer with label

15
Part 2 Use Length from 1st part of problemSame
Pendulum, same length NOWFind "g" where the
period of the pendulum is 2.410 seconds.

• T24p2 (L/g)
• 2.4102 4p2(1.433/g)
• 2.410239.44(1.433/g)
• g 2.410239.44 (1.433)
• g 39.44(1.433)/2.4102
• g 9.73 m/s/s

Equation Substitute s 4 p2 39.44 X by g
2.4102 Answer and label
16
Examples of Spring Problems Hookes
Lawgraphing
17
Examples of using the graph to find the Slope
and the value of k for springs
18
What is the spring constant for the data graphed
below?
?x(m)
19
(0,0)
y2 - y1 x2-x1
Slope
(6,147)
147N 49N 6 m 2m
k
(2,49)
98 N 4 m
k

?x(m)
k 24.5 N/m
How do I know the Label?? Labels on axes Rise
(N) Run (m) So rise/run is N/m !!
20
Examples of Spring Problems UsingEquations
21
Examples ofHookes Law problemsStretch or
compress at rest

• In anticipation of her first game, Alesia pulls
  back the handle of a pinball machine a distance
  of 5.0 cm. The force constant is 200 N/m. How
  much force must Alesia exert?

22
Examples of Hookes Law problems
In anticipation of her first game, Alesia pulls
back the handle of a pinball machine a distance
of 5.0 cm. The force constant is 200 N/m. How
much force must Alesia exert?

• List
• ?x 5.0 cm .05 m
• k 200 N/m
• Fsp???

Equation Substitute s Answer with label
Fsp k ?x
Fsp 200N/m(0.05 m)
Fsp 10N
23
Example of Oscillation spring ProblemsOscillatin
g or bouncing

• Bianca stands on a bathroom scale which has a
  spring constant of 220 N/m. The needle is
  bouncing from side to side. Biancas mass is 180
  kg. What is the period of the vibrating needle
  attached to the spring?

24
Example of Oscillation Spring Problem

• Bianca stands on a bathroom scale which has a
  spring constant of 220 N/m. The needle is
  bouncing from side to side. Biancas mass is 180
  kg. What is the period of the vibrating needle
  attached to the spring?

List k 220 N/m m 180 kg T ??
0.818 s2
180 kg
(0.904 s)
220N/m
5.7 sec
25
Spring Problems Use Both EquationsExample of
Combination of Hookes Law and Oscillation of
springFind k from Hookes Law and then use the
oscillation equation
Autumn, a young 20 kg girl, is playing on a
trampoline. The trampoline sinks down 9 cm when
she stands in the middle. What is the spring
constant? If the trampoline then begins to
bounce, what would the frequency of the bounces
be?
26
1st Find Force of Gravity on mass 2nd Find k
from Hookes Law 3rd use the oscillation
equation to find T4th convert to
Frequency
Autumn, a young 20 kg girl, is playing on a
trampoline. The trampoline sinks down 9 cm when
she stands in the middle. What is the spring
constant? If the trampoline then begins to
bounce, what would the frequency of the bounces
be?
The PLAN Using Hookes Law and Oscillation of
spring
Fg m ag
List m 20 kg ?x 9 cm 0.09 m f ??
Fsp k ?x
27
Autumn, a young 20 kg girl, is playing on a
trampoline. The trampoline sinks down 9 cm when
she stands in the middle. What is the spring
constant?
Using Hookes Law Oscillation of spring
1st Find Force of Gravity on mass
List m 20 kg ?x 9 cm 0.09 m f ??
Fg m ag
Fg 20kg(-9.8m/s/s)
Fg - 196 N
Recall From the FBD on the Lab
FS 196 N
SO. . .
28
Autumn, a young 20 kg girl, is playing on a
trampoline. The trampoline sinks down 9 cm when
she stands in the middle. What is the spring
constant?
Example of Combination of Hookes Law and
Oscillation of spring
2nd Find k from Hookes Law
List m 20 kg ?x 9 cm 0.09 m Fs 196 N
f ??
Fsp k ?x
196 N k(0.09m)
2180 N/m k
29
Autumn, a young 20 kg girl, is playing on a
trampoline. The trampoline sinks down 9 cm when
she stands in the middle. What is the spring
constant? If the trampoline then begins to
bounce, what would the frequency of the bounces
be?
Example of Combination of Hookes Law and
Oscillation of spring
3rd use the oscillation equation to find T
List m 20 kg ?x 9 cm 0.09 m Fs 196
N k 2180 N/m T f ??
20 kg
2180 N/m
(0.958 s)
.00917 s2
.602 sec
30
Autumn, a young 20 kg girl, is playing on a
trampoline. The trampoline sinks down 9 cm when
she stands in the middle. What is the spring
constant? If the trampoline then begins to
bounce, what would the frequency of the bounces
be?
Example of Combination of Hookes Law and
Oscillation of spring
4th convert to frequency
List m 20 kg ?x 9 cm 0.09 m Fs 196 N
k 2180 N/m T 0.602 sec f ??
.602 s
1.66 Hz
31
Spring Problems 4 part Spring problemUse Fg to
find the k value and then use same string with
same k to find 2nd mass.
If two Grumpy Old Men went ice fishing and
were comparing their fish with the extension of
the same spring, solve the following spring
problem Grumpy Sam caught the first fish and
magically realized the fish had a mass of 23 kg.
When this fish was suspended on the spring, like
the one we suspended masses on in lab, the spring
stretched so it was 3 cm longer than it was
without the fish. What is the spring constant
for the spring? Grumpy Joe then caught a fish
that caused the same spring to extend 5 cm from
the length of the empty spring,. What was the
mass of Grumpy Joes fish?
32
Example of 4 part Spring problem
If two Grumpy Old Men went ice fishing and
were comparing their fish with the extension of
the same spring, solve the following spring
problem Grumpy Sam caught the first fish and
magically realized the fish had a mass of 23 kg.
When this fish was suspended on the spring, like
the one we suspended masses on in lab, the spring
stretched so it was 3 cm longer than it was
without the fish. What is the spring constant
for the spring?
The Plan to solve
1st Use Fg to find the Force on the spring
2nd Use Hooke to find the k value 3rd
Same spring with same k to find 2nd Force
4th Convert weight to mass.
List m 23 kg Fg ?? ?x 3 cm 0.03
m Fsp ??
33
Examples of 4 part Spring problem
If two Grumpy Old Men went ice fishing and
were comparing their fish with the extension of
the same spring, solve the following spring
problem Grumpy Sam caught the first fish and
magically realized the fish had a mass of 23 kg.
When this fish was suspended on the spring, like
the one we suspended masses on in lab, the spring
stretched so it was 3 cm longer than it was
without the fish. What is the spring constant
for the spring?
List m 23 kg Fg ?x 3 cm 0.03 m Fsp
1st Use Fg to find the Force on the spring
Fg m ag
- 225 N - Fs
Fg 23kg(-9.8m/s/s)
Fg - 225 N
225 N Fs
34
Examples of 4 part Spring problem
If two Grumpy Old Men went ice fishing and
were comparing their fish with the extension of
the same spring, solve the following spring
problem Grumpy Sam caught the first fish and
magically realized the fish had a mass of 23 kg.
When this fish was suspended on the spring, like
the one we suspended masses on in lab, the spring
stretched so it was 3 cm longer than it was
without the fish. What is the spring constant
for the spring?
List m 23 kg Fg - 225 N ?x 3 cm
0.03 m Fsp 225 N
2nd use Hooke to find the k value
Fsp k ?x
225 N k(0.03m)
7500 N/m k
35
Examples of 4 part Spring problem
Grumpy Joes Fish NEW FORCE NEW MASSSAME
SPRING!! Grumpy Joe then caught a fish that
caused the same spring to extend 5 cm from the
length of the empty spring,. What was the mass
of Grumpy Joes fish?
List m ??? kg Fg ???? N ?x 5 cm
0.05 m Fsp ?? N k 7500 N/m
3rd same spring with same k to find other Force
Fsp k ?x
Fsp 7500N/m (0.05m)
Fsp 375 N
36
Examples of 4 part Spring problem
Grumpy Joes Fish NEW FORCE NEW MASSSAME
SPRING!! Grumpy Joe then caught a fish that
caused the same spring to extend 5 cm from the
length of the empty spring,. What was the mass
of Grumpy Joes fish?
List m ??? kg Fg -375 N ?x 5 cm
0.05 m Fsp 375 N k 7500 N/m
4th convert weight to mass
Fg m ag
- 375 N - Fs
-375 N m(-9.8m/s/s)
m 38.3 kg
375 N Fs
37
Equation SheetSlides

• for
• Springs
• and
• Pendulums

38
Period and Frequency-notes

• Hertz is unit that means 1/sec
• Abbreviated ------- Hz
• Mega Hertz FM radio
• Kilo Hertz AM radio

Page 3 Space 4
Period
repetitions cycles revolutions
Hz Sec-1 1/sec
f
Frequency
39
Period and Frequency

• Hertz is unit that means 1/sec
• Abbreviated ------- Hz
• Mega Hertz FM radio
• Kilo Hertz AM radio

Page 3 Space 5
Period
Hz Sec-1 1/sec
Use when you know either T or f
f
Frequency
40
Oscillations for Pendulums only-Notes

• Length of the pendulum and gravity determine how
  fast the pendulum oscillates back and forth.

Page 3 Space 6
Period
All 3 equations are the same, just re-arranged
m/s/s m/s2
Scalar-positive!!
Hz Sec -1 1/sec
41
Page 4 1
Page 4 2
42
page 4 Space 3
Springs only
43
Period and Frequency

• Hertz is unit that means 1/sec ( Hz)

44
Hookes Law for Springs only
45
Springs only