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Spring Problems

Examples of

Frequency and Period Problems

Pendulum Problems

- Equations for Equation sheet for Springs and

Pendulum Problems

Examples of Period Frequency Problems

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

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

Examples of Pendulum Problems

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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

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)

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

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

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 ) !!

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.

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.

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

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

Examples of Spring Problems Hookes

Lawgraphing

Examples of using the graph to find the Slope

and the value of k for springs

What is the spring constant for the data graphed

below?

?x(m)

(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 !!

Examples of Spring Problems UsingEquations

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?

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

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?

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

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?

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

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. . .

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

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

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

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?

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 ??

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

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

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

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

Equation SheetSlides

- for
- Springs
- and
- Pendulums

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

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

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

Page 4 1

Page 4 2

page 4 Space 3

Springs only

Period and Frequency

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

Hookes Law for Springs only

Springs only