Phys1_05-Springs_152e618a-cf17-4e8b-8ac4-57b0bc38c36d
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Georgia Institute Of Technology *
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2111
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Physics
Date
Apr 3, 2024
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Slide 1
Hooke's Law and Spring Potential Energy
Objectives
Use Hooke's law to find the spring constant of both springs that came in your kit.
Determine the spring potential energy of the smaller spring.
Determine if energy is conserved after a collision.
Physics Overview
Hooke’s Law is defined as a restoring force in which the force needed to stretch or compress
a spring is proportional to the amount the spring is stretched (or compressed). The distance
that the spring is stretched (or compressed) is always measured from the equilibrium position
and the constant of proportionality between the force and distance is known as the spring
constant. This spring constant is a property of the spring and in effect measures the stiffness
of the spring. A restoring force means that the direction of the force is always oriented so that the object is
directed back towards the equilibrium position. This means that depending on the position of
the object in relation to the equilibrium position, the spring force may be pointing in different
directions. This is depicted in the picture below. The equation for Hooke's Law is shown below. The negative sign indicates the fact that this
is a restoring force.
In this lab, the spring constant of two different springs will be discovered. In addition, we
will use the spring constant to explore the potential energy of a spring. This energy can be
found using the following equation:
If you would like to further review Spring Potential Energy, you can watch this video:
ConservationOfEnergy
Slide 2
Let's try it out!
Slide 3
Accelerometer (200 Hz)
Remote 1
Ax Ay Az
Time (s)
0
1
2
3
4
5
6
7
8
9
10
a (m/s²)
-20
-15
-10
-5
0
5
10
15
20
∆t: 3.90161 s
μ: 0.046 m/s² — σ: 0.062 m/s²
a: 0.179 m/s
s: -0.02 m/s³ (r²: 0.08)
μ: -9.806 m/s² — σ: 0.13 m/s²
a: -38.260 m/s
s: -0.01 m/s³ (r²: 0.00)
μ: 0.155 m/s² — σ: 0.045 m/s²
a: 0.603 m/s
s: -0.00 m/s³ (r²: 0.01)
Force (200 Hz)
Remote 1
Time (s)
0
1
2
3
4
5
6
7
8
9
10
Fᵧ (N)
-5
-4
-3
-2
-1
0
1
2
3
4
5
∆t: 3.90065 s
μ: -1.981 N — σ: 0.073 N
a: -7.726 Ns
s: 0.05 N/s (r²: 0.69)
Rezero sensor
Finding the "Known" Value of the Mass
Watch the video below to find out how to find the mass of the device. Please note that the
iOLab mass will be needed in many future labs and you should remember the procedure
you've done here in order to repeat it for those labs.
01 Finding the Mass of the Device
Here are some instructions in words:
Take off the plate and attach the screw instead.
Turn the device so that the y-axis is pointing downwards.
Press record and let it sit there for 1 second. Then use the screw to lift the device. Hold
it steady.
Find the average force and acceleration (in the direction) once you have picked up the
device. This will give you the force due to gravity and the acceleration due to gravity,
respectively. Again, since the force of gravity is in the direction, you can uncheck the and the boxes.)
Using the gravitational force equation, you can find the mass.
Be certain that you include a sceenshot of your own data in your lab report in the "Analysis
Mode", while highlighting the region over which you wish to average the data. Be certain to
extract meaningful numbers into a clear table and explain in detail how you use the
measurements to calculate the mass of your iOLab.
Your preview ends here
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Related Questions
ACTIVITY 3
Problem Solving
Gravitational Potential Energy and Elastic Potential Energy
Energy is the ability to produce changes in matter. It has two states, the kinetic energy and potential energy.
Kinetics energy has 3 forms, vibrational, rotational, and translational, While potential energy has 3 types, gravitational,
chemical, and elastic potential energy. Gravitational PE is the energy stored because of its height and elastic PE is
the energy stored in elastic materials as the result of their stretching or compressing.
nga Read, analyze, and solve the following problems using the GUFSA template. Show your complete
solution. Round off your final answer to the nearest hundredths.
A. GPE
woH
1. How much G.P.E. does a 100 kg boulder that is 75m above the ground has?
arrow_forward
A 20kg block starts from rest and slides 6m down an incline as shown below. The
block then hits a spring that has a force constant of 200 N/m. The angle of the
incline is 30° and there is a coefficient of kinetic friction equal to 0.2 between the
block and the incline.
HK = 0.2
6m
K = 200N/m
www
300
Answer the following questions on your own paper and staple it to this sheet.
1. What is the speed of the block as it hits the spring?
2. At what distance from the top does the maximum speed occur?
3. What is the maximum speed of the block?
4. What is the total distance that the spring gets compressed?
The spring recoils to push the block back up the incline.
5. What will be the speed of the block when it leaves the spring?
6. How far up the incline will the block travel? (above the spring)
arrow_forward
Fill in the chart
arrow_forward
Please answer the question correctly
arrow_forward
YOU MUST ONLY USE ENERGY CONCEPTS TO COMPLETE THE PROBLEMS BELOW.
3. A 55 kg man is standing on a 2.5 m tall block. The man drops off the block from rest, and falls towards a spring whose length is 1.7 m at equilibrium. A. Determine the max speed. B. Calculate the speed of the person when the spring is compressed 58 cm, assuming a spring constant of 2780 N/m.
arrow_forward
What are the units of the constant k? please show work and explain.
algebra based physics
arrow_forward
Automatic Zoom
9. Students are given a pendulum. The teacher also provides students with a
pictorial model labeled A, 0, and B. Each letter signifies the position of the
pendulum.
Part A.
Which of the following explanations describes the potential and kinetic energy
at each position?
A. The potential energy is greatest at O and the kinetic energy is equal at A and B.
B. The potential energy is greatest at A, followed by B, and then O.
C. The kinetic energy is greatest at O, followed by B. and then A
D. The potential energy is equal at A and B and the kinetic energy is greatest at O.
Part B.
What factors could students adjust to explain the transformation between
potential and kinetic energy?
A. Students could push the pendulum instead of releasing it from position A to
increase the kinetic energy at position O.
B. Students could move position A higher which would increase the kinetic energy
at position O.
C. Students could increase the length of the string which would increase the…
arrow_forward
Problem 1:
A) Energy Methods Look at the below system. Using the conservation of energy method, solve for the governing equation of motion for the system. Put a box around your final answer. Also, put a box around your equations for the potential and kinetic energy of the system. Assume the system’s springs are initially unstretched (i.e., assume that there is no gravity until t = 0 [s]).
B) Numerical Methods Using ode45, your answer to problem 1, and the following initial conditions and system parameters, plot the response of the above system in MATLAB for at least 5 complete oscillations, and no more than 20 oscillations. m = 72 (if your last 2 digits are 00, than assume m = 1) [kg] k1 = 673 [N/m] k2 = 880 digits of your student ID [N/m] g = 9.81 [m/s2] x0 = 0 [m] v0 = 0 [m/s]
arrow_forward
For spring in series:
a. Draw the figure of spring in series.
b. Derive the equivalent spring constant of spring in series
c. Derive the potential energy for the spring combination in series
arrow_forward
Student
A block attached to a horizontal spring is displaced along the x axis from an initial
position of x = -4.00 cm to a final position of xf = -2.00 cm. The origin (x = 0) is
placed at the unstretched length of the spring. Determine if the change in potential
energy of the spring-block system is positive, negative, or zero.
arrow_forward
its is possible to vary the diameter of the wire ande the diameter of the spring coil to produce a sprinf for which F=ax3
A) write the expression for an infinitestimal amount of work dWk done to stretch this spring an infinitesimal distance dx.
B) integrate your expression from part a to get an expression for the work done to stretch the spring from elongation x1 to elongation x2
c) if your spring has a= 1,200 N/m3 find the work done to stretch the spring 8.00 cm from its unloaded length
arrow_forward
Needed to be solved correctly in 30 minutes and get the thumbs up please show neat and clean work for it
Please complete all requirements for questions
arrow_forward
huma
The mass of the block depicted in the image is 1.08 kg. The spring has a spring
constant of 78.1 N/m. The coefficient of static friction between the block and the
floor is 0.594. Assume that the spring makes no contact with the floor and
therefore friction only acts on the block.
How far must the block and spring assembly be compressed to just barely
overcome the force of static friction acting on the block?
Report your result in meters.
arrow_forward
A block with mass 0.50 kg is forced against a horizontal spring of
negligible mass, compressing the spring a distance of 0.20 m
(Figure 1). When released, the block moves on a horizontal tabletop
for 1.00 m before coming to rest. The spring constant k is 100 N/m.
Part A
What is the coefficient of kinetic friction between the block and the tabletop?
Hk =
Submit
Request Answer
Provide Feedback
Figure
k = 100 N/m
m = 0.50 kg
0.20 m
1.00 m
arrow_forward
A certain spring which obeys Hooke’s law has a force constant k 0f
60 Nm-1. a. Draw a graph of the stretching force F against extension x for this spring for a range of x from 0 to 25 mm. show all calculations used to determine the plotting points.
b. Use your graph to determine the work required to stretch the spring from an initial extension of 5 mm to final extension of 25 mm.
arrow_forward
Please help me to answer this question and explain the answer why
arrow_forward
10
arrow_forward
Kindly solve this question correctly in 30 minutes and get the thumbs up please show me neat and clean work for
Kindly provide correct solution
arrow_forward
Two identical springs are connected in parallel as shown, each spring has a spring constant of 30 N/m. What is the spring constant of the overall two-spring system, in
N/m?
needed. Do not include the positive sign if the answer is positive. No unit is
Your answer needs to have 2 significant figures, including the negative sign in your answer
needed in your answer, it is already given in the question statement.
arrow_forward
Task 1: Elastic potential energy
1. State Hooke's Law both in words and equation form.
2. Consider the concepts related to springs. Choose one of the following to answer:
i. Compare and contrast restoring force and applied force.
ii. Compare and contrast a real spring and an ideal spring.
3. Spring A is harder to stretch than Spring B. Explain how the spring force constants
of each spring would compare in this situation.
4. Using the following image as an aid, describe the energy conversions a spring
undergoes during simple harmonic motion as it moves from the point of maximum
compression to maximum stretch in a frictionless environment. Be sure to indicate
the points at which there will be:
i) Maximum speed.
ii) Minimum speed.
iii) Minimum acceleration.
Lwwwwwwwww
Ax = A
equilibrium
Ax = A
at max
at max
compression
stretch
5. A mass of 4.0 kg is in motion along a horizontal, frictionless surface with a speed of
2.5 m/s when it makes contact with a horizontal spring anchored to a wall.…
arrow_forward
A student is investigating potential and kinetic energy by stretching a spring across a table. When the student lets go, the spring recoils.At which time is potential energy in the spring being converted into kinetic energy in this system?
A.
when the spring is fully stretched
B.
when the spring is recoiling
C.
when the spring is fully recoiled
D.
when the spring is stretching
arrow_forward
Practice
1. A block slides down a ramp from a fixed height and collides with a spring, compressing the
spring until the block comes to rest. Compare the amount of compression in the case that the
ramp is frictionless to the case where the ramp is not frictionless Explain your answer.
arrow_forward
In the diagram below, the spring is stretched a distance x from its equilibrium position.
PEpring = 0
www
A unstretched
Force
PEspring
kx²
wwW.
B Stretched
PEspring0
C unstretched
www
What is the spring's potential energy at the equilibrium position?
What is the spring's potential energy at the maximum stretched position, x?
Suppose the spring is pulled 0.40 meters away from the equilibrium position and then released from
rest. How much work is done in pulling the spring away from its equilibrium position. Assume the spring
constant is .10 N/m
arrow_forward
Please help me I need it today.
Please see the attached image
arrow_forward
***IMAGE IS ATTACHED***
First two parts only please.
A spring with a force constant of 1100 N/m has been compressed by 5 cm.What is the strength of the force that the spring is exerting? N
Be careful about units. The Force Constant was given in N/m, so the displacement must be in meters!
Incorrect.
Tries 1/2
Previous Tries
How much potential energy is stored by the spring? J
Tries 0/2
If the compression of the spring is doubled, by what factor does the spring force change?Correct: Two times largerIncorrect Four times largerIncorrect SameIncorrect One half as large
Computer's answer now shown above. You are correct.Your receipt no. is 156-9250
Previous Tries
If the compression of the spring is doubled, by what factor does the Potential Energy of the Springchange?Correct: Four times largerIncorrect Two times largerIncorrect SameIncorrect One half as large
Computer's answer now shown above. You are correct.Your receipt no. is 156-152
Previous…
arrow_forward
A and c please
arrow_forward
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- Please answer the question correctlyarrow_forwardYOU MUST ONLY USE ENERGY CONCEPTS TO COMPLETE THE PROBLEMS BELOW. 3. A 55 kg man is standing on a 2.5 m tall block. The man drops off the block from rest, and falls towards a spring whose length is 1.7 m at equilibrium. A. Determine the max speed. B. Calculate the speed of the person when the spring is compressed 58 cm, assuming a spring constant of 2780 N/m.arrow_forwardWhat are the units of the constant k? please show work and explain. algebra based physicsarrow_forward
- Automatic Zoom 9. Students are given a pendulum. The teacher also provides students with a pictorial model labeled A, 0, and B. Each letter signifies the position of the pendulum. Part A. Which of the following explanations describes the potential and kinetic energy at each position? A. The potential energy is greatest at O and the kinetic energy is equal at A and B. B. The potential energy is greatest at A, followed by B, and then O. C. The kinetic energy is greatest at O, followed by B. and then A D. The potential energy is equal at A and B and the kinetic energy is greatest at O. Part B. What factors could students adjust to explain the transformation between potential and kinetic energy? A. Students could push the pendulum instead of releasing it from position A to increase the kinetic energy at position O. B. Students could move position A higher which would increase the kinetic energy at position O. C. Students could increase the length of the string which would increase the…arrow_forwardProblem 1: A) Energy Methods Look at the below system. Using the conservation of energy method, solve for the governing equation of motion for the system. Put a box around your final answer. Also, put a box around your equations for the potential and kinetic energy of the system. Assume the system’s springs are initially unstretched (i.e., assume that there is no gravity until t = 0 [s]). B) Numerical Methods Using ode45, your answer to problem 1, and the following initial conditions and system parameters, plot the response of the above system in MATLAB for at least 5 complete oscillations, and no more than 20 oscillations. m = 72 (if your last 2 digits are 00, than assume m = 1) [kg] k1 = 673 [N/m] k2 = 880 digits of your student ID [N/m] g = 9.81 [m/s2] x0 = 0 [m] v0 = 0 [m/s]arrow_forwardFor spring in series: a. Draw the figure of spring in series. b. Derive the equivalent spring constant of spring in series c. Derive the potential energy for the spring combination in seriesarrow_forward
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