12.) Lab 121_ Rotational Static Equilibrium

Lab 121: Rotational Static Equilibrium A. Introduction: Theory & Objectives According to Newton's laws, an object is stagnant only if all the net forces equal zero. The same applies to torque, which as learned in the previous lab is the force in a circular motion. So to reiterate, an object will not rotate only when all the net torques are equal to zero. However, many times torque isn’t applied directly onto an object, it is applied on an angle. In such cases, the angle at which the torque is applied along the available path of motion is only valid. The equation below, thus entails how torque on an angle can be calculated. τ = ?𝐹?𝑖𝑛θ In this lab, we will explore how various forces applied at different regions and in different magnitudes will affect a strut. Obviously, we will be looking at the strut while it is static and will assign magnitudes to some unknown according to how the other forces impact the system. We will further change the conditions, to see how the unknown’s value changes. We will then further compare our calculations to experimentally found data and understand the mechanisms of torque in static equilibrium. B. Experimental Procedure 1. Set up the two weights on the loop and the string from the top of the stand. 2. Measure the distance from the intersection point to weight 1, weight 2, the point where the string is attached, and the total length. (Labeled them L1, L2, L3 and L4 respectively). 3. Make sure the whole board is at a zero angle and the gravitometer actually measures zero. 4. Given the masses of the two weights, theoretically find the force of tension of the strong. 5. Then press record, after zeroing unattached first, and measure the force of tension experimentally. 6. Record both of those values. 7. Next, move the bar to be at an angle, less than 90, above the horizontal. 8. Measure the angle between the stand, the bar, and the string and the bar. 9. With that given and the connect with, calculate the new theoretical force of tension. 10. Experimentally record the force of tension as well with the force sensors. 11. Lastly, repeat the same process as the previous adjustment but set it to angle below the horizontal. 12. Find the theoretical and experimental force as always.

C. Results: Data & Calculations Part 1: Weight of Rod = .1186 kg Length of strut = .555 m Θ 1 = 56 W 1 = .150 kg L 1 = 30.5 Θ 2 = 0 W 2 = .150 kg L 2 = 50.5 L 3 = 40.5 Calculated Force of Tension: Static Equilibrium - Torque down = Torque Up F w1 + F g + F w2 = F T (.150)(9.8)(.305) + (.1186)(9.8)(.2775) + (.150)(9.8)(.505) = F T (.405) F T = 3.74 N Experimental Force of Tension: F T = 4.2 N Part 2: Θ 1 = 76 W 1 = .150 kg L 1 = 30.5 Θ 2 = 20 W 2 = .150 kg L 2 = 50.5 L 3 = 40.5 Calculated Force of Tension: Static Equilibrium - Torque down = Torque Up F w1 + F g + F w2 = F T (.150)(9.8)(.305)cos(20) + (.1186)(9.8)(.2775)cos(20) + (.150)(9.8)(.505)cos(20) = F T (.405)sin(76) F T = 3.62 N Experimental Force of Tension: F T = 3.5 N Part 3: Θ 1 = 35.5 W 1 = .150 kg L 1 = 30.5 Θ 2 = 22.5 W 2 = .150 kg L 2 = 50.5

E. Conclusion of Experiment In this lab, I learned a lot about how static equilibrium works. I know that for a n object to stay in motion all the upward and downward forces must cancel out. However, when it is regarding a rotating object, it is about all the torque. I found this idea very intriguing, and I think enjoyed setting up both sides of the equation to find the unknown. I love doing simple algebra like this and so to be able to set it up and solve it was satisfying. Additionally, I think I was just able to practice looking at problems and scenarios like this and be able to recognize and assign the various topics in play. When in doubt, I just moved the actual bar to see where it was going to double-check my thinking. I think this lab has helped me do equilibrium problems in class better.