Lab Hooke’s Law
PHY 105 Name____________________
Hookes Law 1
LAB: Hookes Law
Objective
To determine the direct relationship between force and displacement for ideal springs, the
spring constant, and the work done to stretch the springs. You will compare data for two
different springs
Materials
? Computer
? PhET website
? Google Sheets or MS Excel
Theory
If a mass on an ideal massless spring is displaced from the equilibrium position
(x0 = 0) to a new position x, Hookes law states that the spring will exert a restoring force
on the mass as follows.
Eq. 1
The - sign indicates that the direction of the spring force is in the direction opposite to
the direction of the displacement, or a restoring force. The value k (called the spring
constant, with units of N/m) is a constant for a given spring, but different springs have
different k-values. Thus, the force exerted by a spring is variable, specifically the
greater distance it is stretched from equilibrium, the greater is the spring force attempting
to restore the spring to its equilibrium position. This relationship holds up to a point
called the elastic limit. Each spring has its own value of this limit. If you stretch a spring
beyond its limit, then the spring will not return to its original shape, but will remain
stretched out.
Not all springy things obey Hookes Law. When a rubber band is stretched, the
rubber will exert a restoring force. The amount of this force depends on the amount that
the rubber is stretched, but it is not a simple proportional relationship.
Work is a measure of energy input to or energy output from a system. When the
force exerted on a system is constant, the quantity of work done by the force is easy to
determine,
Eq. 2
Work can have a negative value or a positive value. The value is negative when F points
in the direction opposite to the displacement, and the value of work is positive when F
points in the same direction as the displacement.
When, as in the case of a spring, the force is variable, the total work done by a
force cannot be simply calculated using this formula, but must instead be calculated by an
integral.
Eq. 3
Hookes Law 2
For an ideal spring, this becomes as follows
Eq. 4
If your force is always in the same direction as the displacement, the dot product may be
treated as simple multiplication. In addition, for sufficiently closely-spaced data points,
the integral can be treated as a summation and the total work can be calculated piece
wise. If you measure the force at many positions, xn, between x0 = 0 and xf, you can
estimate the amount of work done during any interval. The total work done in moving
the system from x0 to xf is then the sum of work done in the little intervals. The estimate
of the work done in a small interval is the average force in that interval times the distance
in that interval.
Eq. 5
Eq. 6
In general, the area of a trapezoid is given by the formula:
?????????????????????????? = 1
2 (????????1 + ????????2) ? ?????????? Eq. 7
Procedure
1. Go to the following website: https://phet.colorado.edu/sims/html/masses-and- springs/latest/masses-and-springs_en.html
2. Pick Intro. 3. Play around with this version for a bit. Please try the following:
a. Put a large mass on one spring, and a small mass on the other spring. Which spring bounces faster (high frequency)? You can use the
stopwatch (in the box on the right) if you want to time 10 bounces to
compare.
b. Hit the stop button for both springs without removing the masses to stop the bouncing. Which mass has stretched the spring down farther (large
displacement, x)? You can use the ruler (in the box on the right), or you
can turn on the Natural Length and Equilibrium Position lines, but you
dont have to do this.
c. Hit the reset button in the bottom right (orange with a circle arrow). Use the slider to change one the spring constant of one spring to large, and the
other to small. Put the two 100g masses, one on each spring. Now which
spring bounces faster?
https://phet.colorado.edu/sims/html/masses-and-springs/latest/masses-and-springs_en.html
https://phet.colorado.edu/sims/html/masses-and-springs/latest/masses-and-springs_en.html
Hookes Law 3
d. Hit the stop button again. Which spring is stretched further?
e. If you had an unknown weight, what are two ways you could determine its weight using the springs?
f. Make a guess at the mass of the blue unknown weight. Explain your reasoning.
4. Now switch to the Lab setup — look at the bottom edge, you should see four tabs, Intro, Vectors, Energy, and Lab. Pick Lab.
5. In this version of the setup, youll see that you can change the orange mass using the slider at the top, or can type in different masses.
6. Pick a value for the spring constant, and write down the position of the spring constant slider (you can number the tickmarks 1 at the left and 10 at the right).
Your spring constant slider value is: __________
7. In the upper right, click to turn on the Displacement and Natural Length checkbox. It may be useful to also turn on the Movable Line checkbox.
8. Drag the ruler from the right to next to the spring.
9. Select 8 different masses that you will investigate for your spring, within the range of masses available.
10. For each mass, record the mass, and the displacement in Table 1.
11. Calculate the force, making sure to use the mass in kg to do so.
12. In MS Excel or Google Sheets, create a graph of F (vertical axis) vs. x (horizontal axis).
13. As in the Graphing lab, fit a trendline to your graph, and display the equation and the R^2.
14. Determine the slope of your trendline. This slope is the spring constant k in N/m.
15. Using your trendline and either Equation 3 or Equation 4, determine a formula for the work. From this formula calculate the total work done to stretch the spring.
Hookes Law 4
16. Using your data and Equations 5 and 6 (that is, area under the curve using trapezoids), calculate the total work done to stretch the spring.
17. Determine the percent difference between this value and the one from Step 15.
18. If your percent difference is over 20%, you probably have an error.
19. Share data for steps 6-16 with a classmate who picked a different value for the slider. Make sure to use their name in your lab report.
Questions
In your lab report, include the questions from Step 3 with letters A-F.
1. Did you or your classmate (Step 19) have a stiffer spring (larger spring constant)?
2. Which spring stretched farther, the stiffer spring or the less stiff spring?
3. Which spring had a graph with a steeper slope?
4. Why do Steps 15 and 16 give different values? Which do you think is closer to the actual value, and why?
5. In the real world, what do you think would happen to the graphs for the springs if you continued to add mass until the metal started bending?
6. In the real world, what do you think would happen to the graphs for the springs if you continued to add mass until the metal broke?
7. Rubber bands do not quite follow the pattern established by your springs. If you had a rubber band, at first when you add just a small amount of mass, it would lengthen a
lot as it straightens out. Then it would behave similarly to a spring. And lastly it
would break. Sketch what you think this force vs. displacement graph would look
like.
Hookes Law 5
Data Table 1: Spring #1
Spring Constant slider value: __________
# Added mass ( ) Force applied to the
spring ( )
Displacement of spring
from equilibrium
( )
0 0 0 0
1
2
3
4
5
6
7
8
Spring Constant #1 from slope of trendline = _______________(______)
Work done according to Trendline and
integration (Step 15)
_________________(_____)
Work done according to data and
summation (Step 16)
_________________(_____)
Percent difference between the two values
_________________(_____)
Hookes Law 6
Data Table 2: Spring #2
Copy this data from a classmate.
Spring Constant slider value: __________
# Added mass ( ) Force applied to the
spring ( )
Displacement of spring
from equilibrium
( )
0 0 0 0
1
2
3
4
5
6
7
8
Spring Constant #2 from slope of trendline = _______________(______)
Work done according to Trendline and
integration (Step 15)
_________________(_____)
Work done according to data and
summation (Step 16)
_________________(_____)
Percent difference between the two values
_________________(_____)
Lab developed by Andria Schwortz from a lab by Ray Johnson (Quinsigamond Community College,
Worcester, MA).
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Home>Physics homework help>Lab Hooke’s Law
PHY 105 Name____________________
Hookes Law 1
LAB: Hookes Law
Objective
To determine the direct relationship between force and displacement for ideal springs, the
spring constant, and the work done to stretch the springs. You will compare data for two
different springs
Materials
? Computer
? PhET website
? Google Sheets or MS Excel
Theory
If a mass on an ideal massless spring is displaced from the equilibrium position
(x0 = 0) to a new position x, Hookes law states that the spring will exert a restoring force
on the mass as follows.
Eq. 1
The - sign indicates that the direction of the spring force is in the direction opposite to
the direction of the displacement, or a restoring force. The value k (called the spring
constant, with units of N/m) is a constant for a given spring, but different springs have
different k-values. Thus, the force exerted by a spring is variable, specifically the
greater distance it is stretched from equilibrium, the greater is the spring force attempting
to restore the spring to its equilibrium position. This relationship holds up to a point
called the elastic limit. Each spring has its own value of this limit. If you stretch a spring
beyond its limit, then the spring will not return to its original shape, but will remain
stretched out.
Not all springy things obey Hookes Law. When a rubber band is stretched, the
rubber will exert a restoring force. The amount of this force depends on the amount that
the rubber is stretched, but it is not a simple proportional relationship.
Work is a measure of energy input to or energy output from a system. When the
force exerted on a system is constant, the quantity of work done by the force is easy to
determine,
Eq. 2
Work can have a negative value or a positive value. The value is negative when F points
in the direction opposite to the displacement, and the value of work is positive when F
points in the same direction as the displacement.
When, as in the case of a spring, the force is variable, the total work done by a
force cannot be simply calculated using this formula, but must instead be calculated by an
integral.
Eq. 3
Hookes Law 2
For an ideal spring, this becomes as follows
Eq. 4
If your force is always in the same direction as the displacement, the dot product may be
treated as simple multiplication. In addition, for sufficiently closely-spaced data points,
the integral can be treated as a summation and the total work can be calculated piece
wise. If you measure the force at many positions, xn, between x0 = 0 and xf, you can
estimate the amount of work done during any interval. The total work done in moving
the system from x0 to xf is then the sum of work done in the little intervals. The estimate
of the work done in a small interval is the average force in that interval times the distance
in that interval.
Eq. 5
Eq. 6
In general, the area of a trapezoid is given by the formula:
?????????????????????????? = 1
2 (????????1 + ????????2) ? ?????????? Eq. 7
Procedure
1. Go to the following website: https://phet.colorado.edu/sims/html/masses-and- springs/latest/masses-and-springs_en.html
2. Pick Intro. 3. Play around with this version for a bit. Please try the following:
a. Put a large mass on one spring, and a small mass on the other spring. Which spring bounces faster (high frequency)? You can use the
stopwatch (in the box on the right) if you want to time 10 bounces to
compare.
b. Hit the stop button for both springs without removing the masses to stop the bouncing. Which mass has stretched the spring down farther (large
displacement, x)? You can use the ruler (in the box on the right), or you
can turn on the Natural Length and Equilibrium Position lines, but you
dont have to do this.
c. Hit the reset button in the bottom right (orange with a circle arrow). Use the slider to change one the spring constant of one spring to large, and the
other to small. Put the two 100g masses, one on each spring. Now which
spring bounces faster?
https://phet.colorado.edu/sims/html/masses-and-springs/latest/masses-and-springs_en.html
https://phet.colorado.edu/sims/html/masses-and-springs/latest/masses-and-springs_en.html
Hookes Law 3
d. Hit the stop button again. Which spring is stretched further?
e. If you had an unknown weight, what are two ways you could determine its weight using the springs?
f. Make a guess at the mass of the blue unknown weight. Explain your reasoning.
4. Now switch to the Lab setup — look at the bottom edge, you should see four tabs, Intro, Vectors, Energy, and Lab. Pick Lab.
5. In this version of the setup, youll see that you can change the orange mass using the slider at the top, or can type in different masses.
6. Pick a value for the spring constant, and write down the position of the spring constant slider (you can number the tickmarks 1 at the left and 10 at the right).
Your spring constant slider value is: __________
7. In the upper right, click to turn on the Displacement and Natural Length checkbox. It may be useful to also turn on the Movable Line checkbox.
8. Drag the ruler from the right to next to the spring.
9. Select 8 different masses that you will investigate for your spring, within the range of masses available.
10. For each mass, record the mass, and the displacement in Table 1.
11. Calculate the force, making sure to use the mass in kg to do so.
12. In MS Excel or Google Sheets, create a graph of F (vertical axis) vs. x (horizontal axis).
13. As in the Graphing lab, fit a trendline to your graph, and display the equation and the R^2.
14. Determine the slope of your trendline. This slope is the spring constant k in N/m.
15. Using your trendline and either Equation 3 or Equation 4, determine a formula for the work. From this formula calculate the total work done to stretch the spring.
Hookes Law 4
16. Using your data and Equations 5 and 6 (that is, area under the curve using trapezoids), calculate the total work done to stretch the spring.
17. Determine the percent difference between this value and the one from Step 15.
18. If your percent difference is over 20%, you probably have an error.
19. Share data for steps 6-16 with a classmate who picked a different value for the slider. Make sure to use their name in your lab report.
Questions
In your lab report, include the questions from Step 3 with letters A-F.
1. Did you or your classmate (Step 19) have a stiffer spring (larger spring constant)?
2. Which spring stretched farther, the stiffer spring or the less stiff spring?
3. Which spring had a graph with a steeper slope?
4. Why do Steps 15 and 16 give different values? Which do you think is closer to the actual value, and why?
5. In the real world, what do you think would happen to the graphs for the springs if you continued to add mass until the metal started bending?
6. In the real world, what do you think would happen to the graphs for the springs if you continued to add mass until the metal broke?
7. Rubber bands do not quite follow the pattern established by your springs. If you had a rubber band, at first when you add just a small amount of mass, it would lengthen a
lot as it straightens out. Then it would behave similarly to a spring. And lastly it
would break. Sketch what you think this force vs. displacement graph would look
like.
Hookes Law 5
Data Table 1: Spring #1
Spring Constant slider value: __________
# Added mass ( ) Force applied to the
spring ( )
Displacement of spring
from equilibrium
( )
0 0 0 0
1
2
3
4
5
6
7
8
Spring Constant #1 from slope of trendline = _______________(______)
Work done according to Trendline and
integration (Step 15)
_________________(_____)
Work done according to data and
summation (Step 16)
_________________(_____)
Percent difference between the two values
_________________(_____)
Hookes Law 6
Data Table 2: Spring #2
Copy this data from a classmate.
Spring Constant slider value: __________
# Added mass ( ) Force applied to the
spring ( )
Displacement of spring
from equilibrium
( )
0 0 0 0
1
2
3
4
5
6
7
8
Spring Constant #2 from slope of trendline = _______________(______)
Work done according to Trendline and
integration (Step 15)
_________________(_____)
Work done according to data and
summation (Step 16)
_________________(_____)
Percent difference between the two values
_________________(_____)
Lab developed by Andria Schwortz from a lab by Ray Johnson (Quinsigamond Community College,
Worcester, MA).
Applied Sciences
Architecture and Design
Biology
Business & Finance
Chemistry
Computer Science
Geography
Geology
Education
Engineering
English
Environmental science
Spanish
Government
History
Human Resource Management
Information Systems
Law
Literature
Mathematics
Nursing
Physics
Political Science
Psychology
Reading
Science
Social Science
Liberty University
New Hampshire University
Strayer University
University Of Phoenix
Walden University
Home
Homework Answers
Blog
Archive
Tags
Reviews
Contact
twitterfacebook
Copyright © 2022 SweetStudy.com
