TORQUE AND ROTATIONAL EQUILIBRIUM, Essays (university) of Health Physics

Download TORQUE AND ROTATIONAL EQUILIBRIUM and more Essays (university) Health Physics in PDF only on Docsity! SCHOOL OF MEDICINE AND HEALTH SCIENCES Bachelor of Science in Public Health Refresher Physics Labs Lab 2: Torque and Rotational Equilibrium of Rigid Body Full Time Labs Report Instructions: After this lab you are required to write a well referenced 7 – 10 pages individual report with the following key features: Cover page [use sample]; Title; Introduction; Aim; Materials/Methods; Results [Summarized]; Discussion; Conclusion, Answers to assigned questions and Reference list. The laboratory report must be typed using Times New Roman font type and size 12. It should have at least 5 references. All citations and references must agree with the tenets of the Harvard Style of Referencing. Hard copies in Word format of your report should be submitted by 9th November 2021. No late submissions will be accepted for whatever reason. Scanned, neat and legible handwritten reports are also acceptable. Lab 2: Torques and Rotational Equilibrium of a Rigid Body Objectives 1. Apply the conditions for equilibrium of a rigid body to a meter stick pivoted on a knife edge wooden pivot. 2. Determine the center of gravity of the meter stick and mass of the meter stick 3. For a given applied force needed to produce equilibrium, compare the theoretically predicted location of the force to an experimentally determined location. Equipment List  Meter stick  Wooden pivot  Laboratory balance and calibrated hooked masses  Thin nylon thread and unknown mass with hook Theory If a force F acts on a rigid body that is pivoted about some axis, the body tends to rotate about that axis. The tendency of a force to cause a body to rotate about some axis is measured by a quantity called torque τ It is defined by: Equation 1 with F the magnitude of the force, and d the lever arm of the force. The units of torque are N–m. Torque caused by a given force must be defined relative to a specific axis of rotation. Figure 1 shows two forces F1 and F2 acting on an arbitrarily shaped body. The axis of rotation is along a line through O perpendicular to the page. The direction of the line of action of each force is shown as a dotted line extended in either direction along the force vector. The lever arm for each force is shown as the perpendicular distance from O to the line of action of the force. In this case there are two torques τ1 and τ 2 acting on the body given by: Equation 2 Experimental Procedure Part 1: Torque due to Known Forces 1. Use the laboratory balance to determine the mass of the meter stick. Record it in the Meter Stick Data Table. 2. Place the meter stick on the wooden pivot. Adjust the position of the meter stick until the best balance is achieved. Record the position of the meter stick as xg in the Meter Stick Data Table. 3. With the meter stick supported at xg, place a mass m1 at distance away from the pivot. Determine and record in Data and Calculations Table 1 the position x2 at which m2 balances the meter stick. Use a small loop of nylon thread to hang the hooked masses at a given position. It may prove helpful to use a very small piece of tape to hold the thread at the desired position. 4. Calculate the lever arm for each force di = │xg – xi│is the position of the ith mass. With the support at the position xg, the meter stick mass has zero lever arm and contributes no torque. Record the values of d1 and d2 in Data and Calculations Table 1. 5. Calculate and record in Data and Calculations Table 1 the value of the torques. The only counterclockwise torque is due to m1 and ∑ τ ccw = m1gd1. The only clockwise torque is due to m2 and ∑ τ cw = m2gd2. Use a value of 9.80 m/s2 for g for these and all other calculations. 6. Calculate the percentage difference between ∑ τ ccwand ∑ τ cw and record it in Data and Calculations Table 1. Part 2. Torque due to Three Known Forces 1. Support the meter stick at xg. Place m1 at 0.100 m, and m2 at 0.750 m. Determine the position x3 at which m3 balances the system. Record the value of x3 in Data and Calculations Table 2. 2. The meter stick mass mo makes no contribution to the torque. Calculate the lever arm for each of the masses and record the values in Data and Calculations Table 2 (di = │xg – xi│) 3. Calculate the values of ∑ τ ccwand ∑ τ cw and record them in Data and Calculations Table 2. 4. Calculate the percentage difference between ∑ τ ccwand ∑ τ cw and record it in Data and Calculations Table 2. Part 3: Determination of the Meter Stick Mass by Torques 1. Place a mass m1 at the 0.100 m position. Move the wooden pivot until the torque exerted by m1g is balanced by the torque of the meter stick weight acting at xg. When the best balance is achieved, tighten the clamp. The position at which the meter stick is supported is xo. Record xo in Data and Calculations Table 3. 2. The values of the lever arms are given by d1 =│x1 – xo│and do = │xg – xo│. Calculate and record the values of d1 and do in Data and Calculations Table 3. 3. For these conditions, ∑ τ ccw=¿m1gd1 and ∑ τ cw = mogdo where mo stands for the assumed unknown mass of the meter stick. Equating the two torques gives mo = m1(d1/do). Calculate and record in Data and Calculations Table 3 this value as (mo)exp. 4. Calculate and record in Data and Calculations Table 3 the percentage error in (mo)exp compared to the meter stick mass determined by the laboratory balance. Data and Calculation Tables Table 1 Mass (Kg) Position (m) Lever arm (m) Torque (N – m) % Difference m1 = x1 = d1 = ∑ τ ccw = ∑ τ cw = m2 = x2 = d2 = Table 2 Mass (Kg) Position (m) Lever arm (m) Torque (N – m) % Difference m1 = x1 = d1 = ∑ τ ccw = ∑ τ cw = m2 = x2 = d2 = m3 = x3 = d3 = Table 3 Support position x0 = (m) Mass (Kg) Position (m) Lever arm (m) mo (exp) = Kg % Error m1 = x1 = d1 = mo = xg = do = Questions 1. Consider the percentage difference between the ∑ τ ccwand the ∑ τ cwfor the first two parts of the laboratory when known forces are balanced. A difference of 0.5% or less is excellent, a difference of 1.0% or less is good, and a difference of 2% or less is acceptable. Based on these criteria, describe your results for the first two parts of the laboratory and defend your statement. 2. Using the same criteria as in Question 1 for the percentage differences, describe your results for the determination of mass of the meter stick in Part 3 of the laboratory. 3. Suppose an experimental arrangement like the one in Part 2 has mass m1 = 0.200 kg at the 0.100-m mark and a mass m2 = 0.100 kg at the 0.750-m mark. Can the system be put in equilibrium by a 0.050-kg mass? If it can be done, state where it would be placed. If it cannot be done, state why not. 4. In Part 1 of the laboratory, what is the value of the force Fs with which the support pushes upward on the meter stick?