EGG 131L, Lab 7, Equilibrium of a Rigid Body, 90 points Name: 1. Objective To examine the conditions of the equilibrium of a rigid body by applying the concept of torque. 2. Apparatus Meter stick, a fulcrum with a knife edge, rigid support, a set of known weights, 2 unknown weights, 2 hangers (50 grams each), 2 thread loops, and digital hanging scale. 3. Theory Refer to the section in the textbook concerning the conditions for equilibrium of a rigid body. Recall the formula for calculating torques. Notice torque, displacement and force are all vectors. 4. Preparation 4.1 Read the following article to get some idea about a simple pendulum https://www.mun.ca/physics/undergraduates/fylabs/p1020/experiment6.pdfEGG 131L, Lab 7, Equilibrium of a Rigid Body, 90 points http://www.kingsborough.edu/academicdepartments/physci/Documents/labmanuals/phy11 13/Expe riment10.pdf 4.2 Watch the following videos to see a demonstration for this lab. https://www.youtube.com/watch?v=khmR5DAvhEw https://www.youtube.com/watch?v=do Y2MIsU2aQ 5. Procedure 5.1 Examine the condition of equilibrium 5.1.1 Hang a knife edge on a support stand and place a meter stick in the knife edge which is acting as a fulcrum. Adjust the stick to balance it horizontally (should be around 50-cm mark). Denote the center position (fulcrum) of the knife edge on the stick as O. 5.1.2 Place a known weight (between 200 gr to 600 gr and denote it as A) at an arbitrary point (denote it as p) on the left-hand side of the fulcrum of the meter stick. Place another known weight (between 200 gr and 600 gr, denote it as B, make sure B # A) on the right-hand side of the fulcrum of the meter stick. Move weight B along the meter stick back and forth to find a point where the meter stick will be balanced, and denote the point as q. 5.1.3 Measure the distance between O and p (this distance is called lever arm) as r]; and measure the distance between O and q as 12. 5.1.4 Record A, B, I1, and I2 in the lab report. 5.1.5 In the lab report calculate torque 1 using ri and weight A as T1; and calculate torque 2 using 12 and weight B as T1. From the theory of equilibrium torque 1 should be equal to torque 2. 5.2 Find value of unknown weight 1 5.2.1 Remove the above two weights. Hang unknown weight 1 (denote it as X) at an arbitrary point on the meter stick (denote it as p). Place a weight with a known value (between 200 gr and 600 gr, denote it as C) on the other side of the fulcrum. Move C back and forth to find a point where the meter stick will be in equilibrium, and denote that point as q. 5.2.2. Find the lever arm for C as I'1; and also find the lever arm for the unknown weight as I'x. 5.2.3 Record A, I'1, and I'x in the lab report. 5.2.4 Find the true value of X as M using a balance, and record the value in the lab report. 5.2.5 Calculate the value of unknown weight using C, I'1, and I'x. 2EGG 131L, Lab 7, Equilibrium of a Rigid Body, 90 points 5.3 Find value of unknown weight 2 5.3.1 Remove the above weights from the meter stick. Hang unknown weight 2 (denote it as Y) at an arbitrary position of the stick (denote it as p). Place a weight with a known value (between 200 gr and 600 gr, denote it as D) on the other side of the fulcrum. Move D back and forth to find a point where the meter stick will be balanced. Denote that point as q. 5.3.2 Place the unknown weight on point q. Place a weight with known value (denote it as E) on point p. Adjust the value of E to make the meter stick to be balanced. 5.3.3 Record value of D and E in the lab report. 5.3.4 Find the value of unknown weight Y using the hanging scale and record the value as NV in the lab report. 5.3.5 Find the value of unknown weight Y by taking the square root of the product of two known weights, that is Y = VD . E. 5.3.6 Mathematically derive the above formula in the conclusion part of your lab report. (6 points) 6.4 Find the weight of the meter stick 6.4.1 Place the meter stick on the hanging scale and find the weight (in grams) of the meter stick as Z, and record it in the lab report. 6.4.2 Clamp the knife-edge fulcrum to any place less 50-cm mark of the meter stick, and denote it as x. Find the lever arm due to weight of the meter stick (the difference between x and 50-cm mark). Denote it as I'x and record it in the lab report. 6.4.3 Place a weight with a known value (between 400 gr and 600 gr, and denote it as F) at any point of the meter stick with less than x-cm mark, and denote it as p. 6.4.4 Place another weight with a known value (between 200 gr and 400 gr and denote it as G) on the meter stick with a mark larger than x cm. Move G along the meter stick back and forth until to a point where the meter stick will be in equilibrium. Denote that point as q. 6.4.5 Find the lever arm for weight F as I'1; and then find the torque due to weight F as TA. Find the lever arm for weight G as I'2; and then find the torque due to weight G as TB record them in the lab report. 6.4.6 The difference between the torque due to weight F and the one due to weight G is equal to the torque due to weight of the meter stick Z. Find Z by Z = (TF - TG) + I'x 3EGG 131L, Lab 7, Equilibrium of a Rigid Body, 90 points Lab Report 1. Purpose: (12 points) 2. Data and Calculation: Part 1: (12 points) A B r1 12 Show the formula to calculate torques, and then find the torques Torque 1 = Torque 2 = Part 2: (12 points) C r1 rx M Calculation of experimental value of unknown weight X: Part 3: (14 points) 3.1 The true value of the unknown weight N: 4EGG 131L, Lab 7, Equilibrium of a Rigid Body, 90 points 3.2. The value of weight D: ; the value of weight E: 3.3 Calculation of the experimental value for unknown weight Y: Part 4: (28 points) Z F rx G 12 Torque TA due to weight F = Torque TB due to weight G = The torque due to the weight of the meter stick = The calculation for weight of the meter stick: 3. Conclusion (12 points) 5zoom C 4.4 30cm 95 cm P.2 50 Z = 150 9 7 X true Weight Z =? TO G 309 50VG weight of meter stick 40162 2622 08Lab 7- Raw Data P. 1 15 cm 4.1 50 cm 7ocm P o A = 2009 B = 3509 X 14 cm 50 cm 4 . 2 . 70 cm (true value of x FIC = 50 09 M = 2759 X = ? unknown weight I1 X X X 4.3 step 1 step 2 P O P y = 2 D = 4009 4 = ? E = 560g unknown weight 2 true value q y N = 450g