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Apr 3, 2024
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PHYSICS 1401 Lab 7 - Hooke's Law Objectives: ●
Validate Hooke’s Law ●
Use Hooke’s Law to determine unknown masses and an unknown value. ●
Analyze how different combinations of spring affect the stretching of a system. Background: Hooke's law states that extension of a spring is proportional to applied force. If a spring obeys Hooke's law, then a graph of applied force against extension will be a straight line, whose gradient (slope) is k: The equation of the straight line is: where: = stretching force applied to the spring = spring constant = extension of the spring Part 1: Validating Hooke’s Law Open the following simulator and click the lab
option: https://phet.color ado.edu/sims/html/masses-and-springs/latest/masses-and-springs_en.html a)
Place the 100g mass onto the spring. The spring will begin to oscillate up and down. Stop this by clicking on the mass several times or increasing the ‘Damping’ value to ‘Lots’.
b)
Click the ‘Displacement’ and ‘Movable Line’ options on the right. Adjust the movable red line to the tip of the green arrow.
c)
Use the ruler tool (the units are in mm) on the bottom right to measure the extension of the spring with the 100g mass. Convert this mass to a weight (use ) and add this data to table 1. Remember to convert g
to kg
. Table 1 Mass added (g)
Weight (N)
Extension (mm)
50 g 0.49 N
900 mm
100 g
0.98 N
170 mm
150 g
1.47 N
250 mm
200 g
1.96 N
340 mm
250 g
2.45 N
410 mm
300 g
2.94 N
500 mm
d)
Using the slider at the top, change the mass and record 5 more results of weight and extension. Add your results to table 1. e)
Plot a graph (either on paper or using Excel) for Force (y-axis) against extension (x-axis). Draw a line of best fit through your points. f)
Using your graph, determine the spring constant of your spring (in ) by finding the gradient. K = F / x = 2.94 / 500 = 5.9 x 10Nmm-3-1 g)
What evidence from your graph shows that the spring obeys Hooke’s Law? The line is moving at a constant slope or a straight line, which obeys Hooke's Law. Part 2: Determining Unknown Masses Using your value for the spring constant in part 1, determine the masses of the two unknown, red and blue masses in the simulation. Show your working and measurements taken for this part. To get a good average result, at least 3 measurements should be taken of each mass. red mass = ........
370
.....................
g blue mass = .........
230
.......................
g Red Mass: X= 610 mm K 5.9x10^-3 Nmm^-1 F= kx= 5.9x 10^ -3 Nmm^-1 (610mm) = 3.6 N (3.6 N/ 9.8 N mm) = 3.6 N
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Related Questions
Part A
You are asked to design spring bumpers for the walls of a parking garage. A freely rolling
1200 kg car moving at 0.63 m/s is to compress the spring no more than 0.078 m before
stopping.
What should be the force constant of the spring? Assume that the spring has negligible mass.
Express your answer in newtons per meter.
a
x•10"
k =
N/m
Submit
Previous Answers Request Answer
X Incorrect; Try Again; 3 attempts remaining
Provide Feedback
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The specific dynamic action (SDA) is measured for an animal is fed 300 g of food. This measurement is repeated a few days later, after the animal has been fed 100 g of food. According to the usual model of SDA, how will the magnitude of the second SDA compare with the first SDA measurement.
A) It will be about the same
B) It will be about three times as much
C) It will be more than three times as much
D) It will be about 1/3 as much
E) It is not possible to estimate
arrow_forward
A 2000 kg car traveling at a speed of 16 m/s skids to a halt on wet concrete where k
= 0.30.
For the steps and strategies involved in solving a similar problem, you may view a
Video Tutor Solution.
Part A
How long are the skid marks?
Express your answer in meters.
L =
Submit
15. ΑΣΦ
Review I Constants I Periodic Table
Provide Feedback
Request Answer
?
m
Next >
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Fs = kx
6000 N= 400 N/m
x = 15 cm
6.In a spring experiment the results were as follows:
Force (N)
1
4
5
7
Length (mm)
50
58
70
74
82
90
102
125
Extension (mm)
8
20
24
32
40
52
75
a.
What is the length of the spring when unstretched?
b.
Complete the 'Extension' row of the table
C.
Plot a graph of extension against force. Circle the anomalous point.
d.
Mark the limit of proportionality on your graph (elastic limit).
е.
What load would give an extension of 30mm?
f.
What would be the spring length for a load of 4.5N?
g.
Extension: Determine a value for the spring constant in this example.
DELL
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EXCEL Spring Problem:
An experiment is conducted to determine the value of a spring constant. Objects of varied mass are suspended from the spring and the spring deflections are measured. The results are as follows:
Mass, m (kg)
Deflection, x (mm)
5.3
15
7.1
22
10.2
31
12
38
15.4
45
Use EXCEL to determine the spring constant, k, in N/m.
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A 64 kg student is standing atop a spring in an
elevator that is accelerating upward at 3.2 m/s?.
The spring constant is 2400 N/m.
Part A
You may want to review (Pages 219 - 221) .
By how much is the spring compressed?
Express your answer to two significant figures and include the appropriate units.
Ay =
Value
Units
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A Hooke’s Law spring is compressed 15.0 cm by an applied force of 75 N. This compressed spring is then used to project a 23.0 g marble straight up into the air. To what maximum height does the marble rise? Draw a diagram of situation
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A mass is sliding on a frictionless surface with a speed v. It runs into a linear spring with a spring constant of k, which compresses from position xi to position xf.
1)Write a general expression for the force that the spring exerts on the mass, in term of k and x. Choose the initial position of the front of the spring to be xi=0.
2)Select the equation that correctly describes the work done by the spring to stop the mass.
3)Evaluate the relationship in part (b) to arrive at an expression for the work done in terms of known variables.
4) Solve for the numerical value of the work done in Joules given that xi = 0, xf = 42 cm, and k = 105 N/m.
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You push a 2.0 kg block against a horizontal spring, compressing the spring by 15 cm. Then you release the block, and the spring sends it sliding across a tabletop. It stops 75 cm from where you released it. The spring constant is 200 N/m. What is the block–table coefficient of kinetic friction? Draw free-body diagram.
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letter B)Determine the velocity of the block when it slides at a distance of 0.6m from point A.
and letter A)Determine the distance the block will slide until it stops measured from point A.
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Suppose that the speed that a fish can swim depends on the 3/2 power of the length of the fish. Also suppose that that a herring with the length of 0.30 meters swims at a speed of 1.67 m/s.
a)Find the particular equation showing the relationship between swimming speed and length for this herring
b)
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Considering the spring shown below with spring
coefficient = 2000 N/mm, mass = 400 kg and
original length = 300 mm. Calculate the actual
length of this spring after effecting the load.
= 2000 N/mm
Hibbeler, 2006
Select one:
O i. 302 mm
ii. 298 mm
iii. 200 mm
iv. 300 mm
www
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Hooke's law can be used to describe how much force is needed to stretch a spring a certain distance.
For a certain spring, this relationship can be modeled by y = 0.25x .The graph of this relationship is
and
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A spring gun shoots out a plastic ball at speed vo. The spring is then compressed
twice the distance it was on the first shot.
Part A
By what factor is the ball's speed increased?
v' /vo =
Submit
IVE ΑΣΦ
Request Answer
?
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Hooke’s Law Hooke’s Law states that the force needed tokeep a spring stretched x units beyond its natural length isdirectly proportional to x. Here the constant of proportionality is called the spring constant.(a) Write Hooke’s Law as an equation.(b) If a spring has a natural length of 5 cm and a force of30 N is required to maintain the spring stretched to alength of 9 cm, find the spring constant.(c) What force is needed to keep the spring stretched to alength of 11 cm?
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H
k
-0000-
-X--
Problem 9
A block of mass m = 3 kg is initially at a height H = 0.4 m above the
bottom of a frictionless ramp as in the diagram above. The block slides
down the ramp and eventually encounters a spring. The block
compresses the spring by an amount x = 0.02 m before momentarily
coming to rest. What is the spring constant, k, describing the stiffness of
the spring? Remember, g = 9.8 m/s². Don't forget units!
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Please give explanation on what's the right answer.A block of mass M is attached to the lower end of a vertical spring. The spring is hung from the ceiling and has force constant value k. The mass is released from rest with the spring initially unstretched. The maximum tension produced in the length of the spring will be _____.a. 2Mg/kb. 4Mg/k c. Mg/2k d. Mg/k
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q1
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A nonlinear spring is compressed horizontally. The spring exerts a force that obeys the equation F(x) = Ax^½, where x is the distance from equilibrium that the spring is compressed and A is a constant. A physics student records data on the force exerted by the spring as it is compressed and plots the two graphs below, which include the data and the student's best-fit curves.
a. From one or both of the given graphs, determine A. Be sure to show your work and specify the units.b.
i. Determine an expression for the work done in compressing the spring a distance x.ii. Explain in a few sentences how you could use one or both of the graphs to estimate a numerical answer to part (b)i for a given value of x.c. The spring is mounted horizontally on a countertop that is 1.3 m high so that its equilibrium position is just at the edge of the countertop. The spring is compressed so that it stores 0.2 J of energy and is then used to launch a ball of mass 0.10 kg horizontally from the countertop.…
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Learning Goal:
To understand the use of Hooke's law for a spring.
Hooke's law states that the restoring force F on a spring when
it has been stretched or compressed is proportional to the
displacement of the spring from its equilibrium position. The
equilibrium position is the position at which the spring is neither
stretched nor compressed.
Recall that Fx I means that F is equal to a constant times
2. For a spring, the proportionality constant is called the spring
constant and denoted by k. The spring constant is a property of
the spring and must be measured experimentally. The larger
the value of k, the stiffer the spring.
In equation form, Hooke's law can be written
F = -kz.
The minus sign indicates that the force is in the opposite
direction to that of the spring's displacement from its equilibrium
length and is "trying" to restore the spring to its equilibrium
position. The magnitude of the force is given by F = kx,
where z is the magnitude of the displacement.
▼
A 62 kg driver…
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4) Now the elevator is moving downward with a velocity of v = -2.1 m/s but accelerating upward with an acceleration of
a = 3.9 m/st. (Note: an upward acceleration when the elevator is moving down means the elevator is slowing down.)
What is the force the bottom spring exerts on the bottom mass?
N Submit
5) What is the distance the upper spring is extended from its unstretched length?
cm ( Submit
6) Finally, the elevator is moving downward with a velocity of v = -2.5 m/s and also accelerating downward at an
acceleration of a = -2.3 m/s?.
The elevator is:
Ospeeding up
Oslowing down
O moving at a constant speed
Şubmit
7) Rank the distances the springs are extended from their unstretched lengths:
Ox, = X2 = X3
Ox, > x2 > X3
Ox, < x2 < X3
Submit
+
8) What is the distance the MIDDLE spring is extended from its unstretched length?
cm ( Submit
...... ........-
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The ceiling of an arena is 22 m above the floor. What is the minimum speed that a thrown ball would need to just reach the ceiling
arrow_forward
. For a spring-powered candy dispenser, which of the statements correctly expresses the relationship of the candy’s speed to the compression of the spring?
The speed is proportional to the square root of the compression distance of the spring
The speed is directly proportional to the compression distance of the spring
The speed is inversely proportional to the compression distance of the spring
The speed is proportional to the square of the compression distance of the spring
None of these statements are correct
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1. A block of mass m = 10 Kg is at rest on the inclined plane seen at figure 1. The
coefficient of static friction between the block and the plane is µ, = 0.5 N/Kg. The
block of mass m is pulled by a force F =100 N through a spring of force constant k
= 0.3 as seen in figure 1. The block is pushed against a spring, compressing it.
Determine the speed of the block after the block is released (g = 10 m/s²).
k
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A crate with mass m is placed above a ramp with an angle 0, and a distance L from a spring with a spring
constant k. Suppose that the ramp and crate experience a coefficient of kinetic friction u, solve for the
following:
a. speed of crate before it compresses the spring
b. maximum compression of the spring
C.
How far does the crate get to its initial distance when it rebounds?
Wwwww
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Learning Goal:
To understand the use of Hooke's law for a spring.
Hooke's law states that the restoring force F on a
spring when it has been stretched or compressed is
proportional to the displacement of the spring
from its equilibrium position. The equilibrium position
is the position at which the spring is neither
stretched nor compressed.
Recall that Fx means that F is equal to a
constant times . For a spring, the proportionality
constant is called the spring constant and denoted
by k. The spring constant is a property of the spring
and must be measured experimentally. The larger
the value of k, the stiffer the spring.
In equation form, Hooke's law can be written
F = -kx.
The minus sign indicates that the force is in the
opposite direction to that of the spring's
displacement from its equilibrium length and is
"trying" to restore the spring to its equilibrium
position. The magnitude of the force is given by
F = kx, where x is the magnitude of the
displacement.
Part A
Part B
After…
arrow_forward
Learning Goal:
To understand the use of Hooke's law for a spring.
Hooke's law states that the restoring force F on a
spring when it has been stretched or compressed is
proportional to the displacement of the spring
from its equilibrium position. The equilibrium
position is the position at which the spring is neither
stretched nor compressed.
Recall that Fx means that F is equal to a
constant times . For a spring, the proportionality
constant is called the spring constant and denoted
by k. The spring constant is a property of the spring
and must be measured experimentally. The larger
the value of k, the stiffer the spring.
In equation form, Hooke's law can be written
F = -kz.
The minus sign indicates that the force is in the
opposite direction to that of the spring's
displacement from its equilibrium length and is
"trying" to restore the spring to its equilibrium
position. The magnitude of the force is given by
F = kx, where is the magnitude of the
displacement.
In Haiti, public…
arrow_forward
1. Calculate the work done on the suitcase by F→.
Express your answer with the appropriate units.
2. Calculate the work done on the suitcase by the gravitational force.
Express your answer with the appropriate units.
3.Calculate the work done on the suitcase by the normal force.
Express your answer with the appropriate units.
4. Calculate the work done on the suitcase by the friction force.
Express your answer with the appropriate units.
5. Calculate the total work done on the suitcase.
Express your answer with the appropriate units.
6. If the speed of the suitcase is zero at the bottom of the ramp, what is its speed after it has traveled 3.90 mm along the ramp?
Express your answer with the appropriate units.
arrow_forward
*Chapter 8, Problem 24
A block of mass m = 1.5 kg is dropped from height h = 78 cm onto a spring of spring constant k 2190 N/m (see the
figure). Find the maximum distance the spring is compressed.
Number
1 Units
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