Lab 6 Hooke's Law Purpose: To use Hooke's law to find the spring constant of an unknown spring and use it to determine the acceleration of gravity of a known celestial object (Moon). Also to determine the gravitational acceleration of an unknown planet and masses of some unknown ohjects. Theory: Hooke's law is a principle of physics that states that the force F needed to extend or compress a spring by some distance x iz proportional to that distance. That is F=kx 0 where k 15 a constant factor, called the spring constant, which is a characteristic of the spring: its stiffness, and x is small compared to the et total possible deformation of the spring. If the spring is compressed too B-JW\\f= much or stretched too much (as shown in the curved portion of the AW o o i O ANV graph i the picture), Hocke's law fails to apply. The region where P ANV e Hocke's law apply is called elastic region Hooke's law i3 a very important and widely-used law in physics and engineering whose applications go far beyond springs and rubber bands. Hooke's law iz extensively used in many branches of science and engineering, and is the foundation of many disciplines such as seismology, molecular mechanics and acoustics. It is also the fundamental principle behind the spring scale, the manometer, and the balance wheel of the mechanical clock. Hocke's Law can be studied by measuring how much known forces stretch a spring. A convenient way to apply a precisely-known force is to let the weight of a known mass be the foree used to stretch the spring. The stretch of the spring can be measured by noting the position of the end of the spring before and during the application of the force. The force can then be calculated from W=mg Which gives: F=mg =kx ) Part 1 - Determining spring constant: If masz (m) and the corresponding stretch (x) are known spring constant (k) can be found. Equation (2) is the equation of a straight line. So plotting force along Y-axis and stretch along X-axis, the spring constant can be found as the slope of the graph. Part 2 - Determining acceleration of gravity: Equation (2) can be rewritten as _kx m= 3 (3) Since spring constant is now known, a graph of mass and & x will have a slope which will be equal to the reciprocal of *g\"_ Part 3 - Determining mass of unknown an unknown object: If an experiment is done in a known environment (o that *2' is known), equation (3) can be directly used to determine the mass of an unknown object. Procedure: Go to Virtual Physics Labs at website: 'hitps:\\phet colorade.edu/sims/html/masses-and-springs/latest'masses-and-springs _en.himl Choose Intro. First play around with the simulation and make yourself familiar with it. s Lo B ol P 0 bt Chesk these. Extension i the length blue and green line. Choase Raad A from the ruler Earth, Moon and placed as shawn here. Planet X from here. Part 1: We will work with spring 1 (see the picture for guidance). Don't change the \"spring constant\" and the "damping' settings. Make sure that 'Earth' is displayed. Check 'Natural Length and 'Equilibriuvm Position'. Place the ruler as shown in the picture. You will record the 'extensions' for each mass. The extension will be the distance between the blue and the green line. Click on the 30 gram mass and drag it to hang from the bottom of the spring-1. To stop the oscillation, vou can click on the \"red\" button left to the spring. After it stops oscillating, read the oscillation. You will measure in cm, but when you enter in excel, you must convert them to meters Record the extension it in table 1. Remove the 50 g mass and replace it first with it with a 100 g mass and then with the 230 g mass. Measure the extension in both cases carefully and record in table 1 case remember that when You tramsfer Vour data to Extension excel, you will change your masses to kilogram and x (cm) extension to meters. This will be true also for Part 2 and 3 Part 2: Extension Click on "Moon' to change the environment to Moon. x (em) We will use the same three masses and record their extensions for each of them as described in Part 1. Record your data below in table 2. Extension x (cm) 30 100 250 To determine the gravity of an unknown planet, click on Planet X Use the same procedure as described above to collect data for this planet. Record your data in table 3. Table 3 Part 3: Click on Earth' again Hang the green, gold and Extension purple maszes one by one and measure the extensions. x (cm) Record vour data below in table 4. Table 4 Data Analysis: Part 1: Open Excel Part 3: In column B of the table in part 1, enter the mass values from table 1 in the manual You must enter your masses in kilogram To convert gram into kilogram_ simply divide it by 1000. For example, 50 g will be 50/1000 kg = 0.05 kg, In column C, calculate the gravitational foree due to the masses. Use the formulaF=m g and g = 9.8 m/s?. You can enter the following formula in C10 =B10*2.8 followed by 'Enter' Click again on C10 and bring your cursor to the lower right corner of C10 and drag it all the way to C12. In column D of the same table, enter the extensions. You must enter your datz in meters. To convert cm to meters, simply divide the number by 100. For example: 70 cm = 70/100 n all the remaining tables vou will enter masses i kg and extensions in meiters. Plot your data with force in the Y-axis and extension in the X-axis. Fit a linear trendline and click to display equations. See lab 2 and 3 vou have forgotten how to do it. The slope of the graph iz the spring constamt Please remember that slope i3 the coefficient of x in the displayed equation. Enter this value in D18, In column B of the table for Moon, enter the mass values from table 2 in the manual Similar to part 1, you must enter your masses in kilogram_ In column C of the same table, enter the extensions in meters. In column D caleulate the quantity kg where k is the spring constant which you noted in D12 and x is the extension (column C). Flot mass (column B) along Y-axis and x (column D) along X-axis. Fit a linear trendline and click to display equations. Record the slope in D34, According to equation (3), the slope must be the reciprocal of acceleration of gravity. In D33 calculate the inverse of D34, Accepted value of acceleration of gravity on the Moon iz about 1.622 m/s?. Calculate the percentage difference of vour experimental result (D33) and the accepted value in D37, Use the formula percentage dif ference = You can type this formula in D37: = ABS(D36-D33)D36*100 Repeat the above steps to calculate the acceleration of gravity in Planet X. Use the data vou had recorded in table 3. Since this is an unlmown planet, you will not calculate any percentage difference. After you find the acceleration of gravity, make a guess what planet is it? You may want to do a google search for it. You must report this in the Results and Conclusion' section of your lab report. In the table for unknown mass, enter the values from table 4 in the manual. Similar to part 2, calculate kx in column D. Using equation (3), the mass can be calculated. Since this part is being done on Earth, vou can divide kg, by acceleration of gravity of Earth (which is 9.8 m/s%) to calculate the mass. Further multiply it by 1000 to express your results in grams. You can enter the following formula in E62 =D62/0.8%1000 followed by \"Enter\" Click again on E62 and bring your cursor to the lower right corner and drag it all the way to C12. All numbers should appear. There is no graph for this part