Question number 4.

Lab #2 Static Equilibrium Experiment: Force Table. Name _____ Objectives: 1. You will test the concept of static equilibrium using 3 trial situations given below. 2. Practice combining vectors mathematically. The rst condition for static equilibrium states that the sum of forces in a system = 0 ...mathematically 2 F = 0. 2'. is a capital sigma and stands for summation, and 1-5 represents a vector force. Procedure: - 1. Set up the force table with the given vectors (situations I, II and III) following the demonstrated procedure to determine the equilibrant vector. Do not calculate anything more than determining'how much mass you added! The equilibrant is the force required to put the system into static equilibrium (i.e. balance the table). The resultant is the sum of the given forces. The resultant's magnitude is the same as that of the equilibrant, but its angle is 180 from the angle of the equilibrant. The resultant is that force that would result if all the given vectors are replaced by a single vector that we call the resultant. ' 2. Each time you set up the force table and believe it is balanced, displace the centering ring slightly off center. Move the ring only enough so that it remains where you put: it and does not \"snap\" back toward center. 'Move' it in different directions and observe; Think about a real force in the system allows you to do this. See questions 1_ and 2- under analysis and'questions. . ' ' ' \" ' ' . ' ' ' 1. Force 1 = 120.0 g @. 30.0" NW3? the hangermass=50 g, so here, for example, yeu ' will add 70.0 g to the hangertoobtainthe'desired mass. ' . Force 2 = 220.01g @ 95:00 W 3 Equilibrant force (g) .i w 302.09 . Naming ' Z uilibrant angle- ' i i angle (180 from equilibrium; 1 1'7'3-'5fDa ' . V 254350659 . Equilibrant force (g) 470.0 g Resultant force (g) 470.0g Equilibrant angle 188 Deg Resultant angle 8 Deg III. Force 1 = 180.0 g @ 130.0 Force 2 = 280.0 g @ 0.0 Force 3 = 310.0 g @-120.0 Equilibrant force (g) 137 g Resultant force (g) 137 g See 3. and 4. below Equilibrant angle 96.0 Deg Resultant angle 276 Deg 3. For situation III under load then overload the equilibrant just enough to cause the centering ring to move. You'll have to do this fairly gently. Record both overload and under load amounts. These are the excess amounts, not the totals. Overload amount (g) - 8.0g Under load amount (g) = 7.0g 4. Restore the equilibrant in situation III to the original value. Now move III's equilibrant's pulley slowly to one side until the centering ring moves. Repeat but move the pulley to the opposite side. Record these two angles. Angles will be positive. A(angle) left = 4.5 Deg A(angle) right = 4.0 Deg Analysis and Questions 1. What real force in this system do the overload and underload masses in step 3 approximately measure? In step three, the overload and underload masses measure strength and friction 2. Why are you able to change the angle slightly and keep the system in static equilibrium? You are able to change the angle slightly and keep the system in static equilibrium, because there is no exact measurement. 3. Based on information found in steps 3 and 4 of the procedure calculate the %uncertainty in the measurement. This experimental uncertainty does not represent how much your result deviates from an accepted or calculated value; it represents how wellyou know the measurement. Use the average of the overload/under load masses found in step 3 and the measured equilibrant mass along with the average A(angle) divided by 180 to perform the calculation. Note: using 180 gives the smallest possible uncertainty in angle. See the example below to help you understand the calculation. Example. The measured equilibrant is 200 g, the overload is 25 g and the underload is 15 g. The average mass uncertainty is (25 + 15)/2 -20 g. The % uncertainty in mass = 20/200 * 100 = 10%. The two deviations in angles (left and right) are 5 and 7 degrees for an average of 6 degrees. The %uncertainty in angle is 6/180 * 100 = 3.33% for a total uncertainty of 13.33%. Calculate the actual experimental uncertainty in the space below. 8 +7 = 15/2 = 7.5g 7.5/137 x 100 = 5.4744% = 7.8354% = 7.8% uncertainty 4.5 + 4 = 8.5/2 = 4.25g 4.25/180 x 100 = 2.361% 4. On separate paper, using the component method calculate the magnitude and direction of the resultant for all 3 situations. Comment on how well your calculations match your experimental results. Is the calculated result for situation III within the %error determined in step 2 above? Record measured and calculated values in the following table. Attach your calculations. Procedure Experimental | Calculated Experimental Calculated Experimental resultant (g) resultant (g) resultant angle uncertainty angle