oolx xblob Rotational Equilibrium AM. go: grams A Song vitolry M3 : Mas's of the hanger I what you add to the hanger 709 B M2: 70.9 Center of mass whoruler with clamps = 49.5cm Mass of the ruler - 19209 Mass of the clamps - 22. 09, 21 89 22.79 stamp Clamps = 10cm, 40 0m, 90 cm Xers center ofthe rulers mass only Angle of string of clamp C= 350 Angles 01 7 35 40 Angle of OC 102 = 85 0 therulers 8 50 Of= 35 0 Angle of string on clamp- 350 AndISIS A TX CM= MR x XRet MAX XACT MB* XB tmc + XC. MR IMA AMB timePhysics 151 Rotational Equilibrium Name: Objective: In this laboratory you will study an object in rotational equilibrium. Set up a meter stick with three clamps suspended between two pulleys as shown. * The masses Mass of the ruler m, = Mass of the clamp m Mass of the clamp mg = Mass of the clamp m * Position of the clamps c X, = center of the ruler's mass only * Angles kg kg kg kg v 111 Xg = center of the ruler's mass only * Angles 2. ANALYSIS Locate the center of mass of the combination of ruler and clamps A, B, C, which is x_. This is not the center of mass of the meter stick, x,, which should be at about 50 cm or 0.50 m. Make a scale drawing of your experimental setup. The drawing should be to scale spatially, i.e. correct angles and points of application of the forces. The drawing should also represent all of the forces to scale. a. b Set up an x-y coordinate system horizontally and vertically (the direction of gravity). In this coordinate system, find > F_and }'F . Note that at point A, we have and . Similarly, at point C, we have and . Also, at point B, we have . So now we are ready to do our calculations: For YF wehave F, +F_ = Our percent error is For Y F_ we have: s and and our percent error is . (Optional) C. Now we calculate the sum of the torques about the support point near the end of the meter stick. Since which end to use is not specified, I recommend using support point A. Then we proceed as follows: Then for our torques we have: So now our net torque is And our percent error is . Now we ask you to calculate the torques about the center of mass of the stick plus clamps. In this case, d.,; = 0. The other distances need to be recalculated accordingly. Also, which forces produce positive torques (tend to rotate counterclockwise) and negative torques (tend to rotate clockwise) will be different. Thus: A Therefore: T+ = ' T_ + ' ZT = And the percentage error is %A = Page 2 of 2