Lab 8 Newton's Law of Gravity Purpose: To study Newton's law of gravity and determine the value of gravitational constant. Theory: Gravity is a natoral phenomenon by which all massive objects (irrespective of how small the mass is) are brought toward one another, including stars, planets, galaxies and even light and sub-atomic particles. Gravity is responsible for many of the structures in the Universe, by creating spheres of hydrogen where hydrogen fuses under pressure to form stars and grouping them into galaxies. On Earth, gravity gives weight to physical objects and Moon's gravity causes the tides in the oceans. Unlike electromagnetic force which can be both attractive and repulsive, gravity is always attractive. Gravity has an infinite range meaning two cbjects always exert some gravitational pull on each other, although its effects become increasingly weaker on farther objects. In 1687 Sir [zaac Newton hypothesized the law of gravitation. It states: m; m; Every mass exerts a force of attraction on every other mass The strength of . this force is directly proportional to the product of their masses and inversely - . proportional to the square of their r separation. Mathematically: The strength of the force is directly proportional to the product of their masses F cemym, (1) The strength of the force is inversely proportional to the square of the distance between them. 1 F = ) Where F iz the strength of the force (or simply force), m) and m) are the masses of the two objects involved and r is the distance between them, and o represents proportionality. Equation (1) and (2) can be combined to get: my ma F=G V= 3 Where \"G' 15 a constant called gravitational constant In metric units, the value of G is G=6.67x 10 N mkg? In this experiment we will verify (1) and (2) and using (3) we will determine the value of "G, You must review the specific detatls of Newton's law of gravity from the textbook before starting fo work on this lab. You can use your textbook. Experimental Procedure: Go to the URL: hitp: phet,cnlnradb,edu en/simulation/gravity-force-lab Click on the simulation to start the experiment. Please play around with the simulation and make yourself familiar with it Part 1: Variation of force with mass In this part we will lock at the variation of force with masses at a fixed distance. Choose a distance between the red and the blue balls. I would recommend a distance between 3 and 6 meters. Distance between the balls is the distance between the centers of mass of the balls. See the picture below. To change the distance between the objects, you can click and drag the balls left and right. To measure distance, place the ruler as shown in the picture. Force on m2 by m1 = 0.000 000 004 3868 N - Force on m1 by m2 = 0.000 000 004 388 N Center of mass a8 9 10 Mass 2 J | g Show vatios. Write down the distance between the balls (r) below. Once you choose a distance, you won't change it until you move to part 2 of the experiment. Choose values for Mass 1 (1) and Mass 2 (ma). T would recommend that you choose masses which are at least 25 kg Write them down in the table below. Also record the force (F) for this two masses. The force is displayed at the top of the simulation. It says 'Force on m2 by m1\" or 'Force on m1 by m2. The two values are the same. Choose two new values for Mass 1 and Mass 2. For both Mass 1 and Mass 2, you can change mass by clicking repeatedly on the left or the right arrow-head as shown in the picture above. You can do the same by simply moving the blue button to left or right. Write down m1, m2 and F in the table below. Repeat the above step until you fill the whole table r= mi (kz) ma(kg) Fm) Part 2: Variation of force with distance In this part we will look at the variation of force with distance for fixed masses. Choose m1 = 100 kg, m> = 90 kg. You won't change the value of masses until you start part 3 of the experiment Choose a distance of 10 m between the two balls (r =10 m) and write down the force in the first row of the table below. Change distance as suggested and fill the table. Please note that this distances are only suggested values. You can choose your own values. If you choose your own values, make sure to change accordingly in the table 1 (m) oo 10 9 Part 3: Determination of gravitational constant In this part we will determine gravitational constant. Equation (3) iz an equation of a straight line when force (F) is plotted against m1 my/r? with 2 slope equal to gravitational constant. So we will find force for different values of m) my/r* and plot our data. Find F" for the following suggested values of my, my and r. Please note that you will vary all three variables (m1, my, and r). The valuer provided are only suggested. You are Jree to choose your own valuss. [f vou choose different values, make sure to change them in the table accordingly. Record *F\" in the right most column_ m1(kg) mz (kg) 1 (m) FQ) 30 20 6.3 40 30 5 70 60 6 100 100 4 80 5 3 65 95 5.5 75 91 2 10 25 1 54 72 36 68 18 28 Data Analysis: Open the excel template Lab &8 Gravity Lgh Template Before you enter any data, first save it as Lab & Gravity Lah Firgt Name Last Name. In cell C3, please enter your first and last name again. Part1: Transfer your data from table in Part 1 in the manual to Part 1 of the excel template In F10 calculate the product mim?2. You can type the formula =C10*D10 and hit enter. Click on F10 again, then come to the lower right corner and drag all the way to F19. You should have mimy calculated for the whole table. Once you calculate all the mimy values, excel should automatically plot your data. How does the graph look like? You must answer the following questions in the \"Results and Conclusion' section of your lab report. o Does the graph has a positive or negative slope? o What does the graph tell you about the variation of force with mass? Part 2: Transfer your data from table in Part 2 in the manval to Part 2 of the excel template. Don't forget to enter the values of m) and my in D26 and D27. In F30 calculate r. You can type the formula =D302 and hit enter. Click on F30 again, then come to the lower right comer and drag all the way to F39. You should have r calculated for the whole table. Onee you calculate all the 1 values, excel should automatically plot your data. How does the graph look like? You must answer the following questions in the 'Results and Conclusion\" section of your lab report. o What's the shape of the graph? o What does the graph tell you about the variation of force with distance or square of distance between the masses? Part 3: Transfer your data from table in Part 3 in the manual to Part 3 of the excel template_ In F48 caleulate m my/r. You can type the formula = B48*C48/D482 and hit enter. Click on F48 again, then come to the lower right corner and drag all the way to F37. You should have r? caleulated for the whole table Once you calculate all the m) my/r* values, excel should automatically plot your data. How does the graph lock lile? The slope of the line would be the experimental gravitational constant. Write the value of the slope in F61. Please note that excel uses the symbol 'E\" for \"multiplied by 10 raised to power'. For example the number 0.0001 which iz actually 110, excel may write simply as 1E-4. In F63 calculate the percentage difference between the given gravitational constant (FG0) and the experimental gravitational constant (F61). You must type your own formula. Fou have calculated percentage difference in many of the previous labs. Save your file. You will upload your excel file into blackboard.