ovided data. will measure the tal force on it must vanish, i.e. the vector sum 'in question is a knot of string that is being You should have ended up with units of Kg .m $2 , the SI unit for force. To make life easier, we define a Newton, N, as N = kg .m You will use N for force units for the remainder of the lab. 6. On the protractor template sheet (last sheet of lab procedure), draw vector arrows for F, and F2 . You will need a coordinate system and a scale conversion factor. Place the origin of the coordinate system at the center of the template with 0 as the x* axis and use a scale conversion factor of 1 N =6 cm. Be sure to label your vectors and include SI force units. Once you are satisfied with your arrows, darken them so that they visually stand out. 7. Now we want to experimentally determine 1) where we need to place a third pulley, and 2) how much mass we should place on its hanger so that the string knot is directly above the center of the table. In other words, we want the magnitude and direction of a third force which will center the string. We will call the force associated with this mass F, . Here is a hint: You can get a feel for the direction of F, by pulling its string so that the knot is centered. As for how much mass, you will have to find this by trial and error. In order to verify that you have correctly centered the knot, do the following: a) Check that the third string is parallel to the force table and only touching its pulley. b) Check that all strings are the same distance above the force table and parallel. c) If these are satisfied, gently nudge the string and see if the knot returns to the center. If not, you need to make some adjustments to the magnitude and/or direction of the third force. 8. Using your experimental value for F3 , draw F, (using the same scale) on the protractor template sheet. 9. Record all your data in a data table. Don't forget units! (see in red on protractor template sheet) 10. Express all three vectors in unit vector notation. 1 1. Let's check our results. Later we will show that a centered knot requires the following mathematical relationship between the three force vectors: F, + F2 + F; =0 There are a couple of ways to check our results: a) In a graphical analysis (tip to tail, triangle, or parallelogram method), adding three vectors to zero means that the three vectors form the sides of a closed triangle. Graphically add your three vectors and see if they form a closed triangle. Do this on the protractor template sheet. b) In the component method, a zero vector has x and y components of zero. In other words, EF. =0 and _F, =0. Add the x and y components of your three forces and see how close each sum comes to zero. Here is a quick way to find a maximum percentage error, which assesses the precision of your results. highest of the two ( )F) values percentage factor = -x 100% smallest magnitude of three forces 12. Now let's find the theoretical values for the mass and angle. Using your experimental values for F, and F2 and the equation in step 10, mathematically calculate the magnitude and direction of F3.h. Find a percent difference between this theoretical value and the experimental value for | F, |, the magnitude. Show all your work.002 061 170 180 210 220 130 140 150 160 230 120 250 100 110 100 90 - 8 260 270 280 290 300 310 32 320 340 20 40 330 340 350 30 20 0 10 Protractor Template Experimental Data: You would notice that the hanger itself has a mass of 5g so that would need to be added for each force. A previous group experimentally determined that the third force used a mass of 53g added to the hanger at an angle of 320.002 061 170 180 210 220 130 140 150 160 230 120 250 100 110 100 90 - 8 260 270 280 290 300 310 32 320 340 20 40 330 340 350 30 20 0 10 Protractor Template Experimental Data: You would notice that the hanger itself has a mass of 5g so that would need to be added for each force. A previous group experimentally determined that the third force used a mass of 53g added to the hanger at an angle of 320