IC-18 Static Equilibrium - online lab (1)

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Apr 3, 2024

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IC-18 E QUILIBRIUM OF A R IGID B ODY Rev 1-1-2023 18.1 OBJECTIVE The purpose of this experiment is to study the conditions that must be satisfied for a rigid object to be in static equilibrium. 18.2 EQUIPMENT Meter stick Support stand Clamps (3) Hooked weights Unknown weight Triple beam balance 18.3 THEORY The torque τ exerted by a force F on a rigid object able to rotate about an axis is given as τ = F d, where d is the lever or moment arm of F about axis. It is equal to the perpendicular distance from axis to F . Torque is a vector quantity that is perpendicular to the plane made by F and d. For rigid bodies in equilibrium, they should not have neither linear nor angular acceleration. This means that two conditions must be satisfied simultaneously; the total force acting on the object is zero and the total torque should also be zero. Hence Σ τ = 0 (1) and Σ F = 0 By convention, torque is positive if the force tends to rotate the object counterclockwise and negative if it ends to rotate clockwise. The apparatus consists of a meter stick balanced about a pivot. The torques are created by weights hung at different locations along the stick by using clamps. Example 1 A meter stick of mass 80 g has its center of mass at the 49 cm position. It is placed in the support stand at the 49 cm position (i.e. at its center of mass). Mass A of 200 g is attached at 40 cm from the fulcrum, and mass B of 450 g is attached at 15 cm form the fulcrum. a) Calculate the torques applied by masses A and B about the fulcrum, and b) Is the meter stick in equilibrium? τ (A) = +0.20*g*0.40 = 0.784 Nm τ (B) = - 0.45*g*0.15 = - 0.6615 Nm Σ τ = 0.20*g*0.40 + n*0 + 0.080*g*0 – 0.45*g*0.15 = 0.784 – 0.6615 = 0.1225 Nm ≠ 0 b) Meter stick is Not in equilibrium 1 A B 40 cm 15 cm 0.20*g 0.45*g 0.080*g n

Example 2 For the same problem, what is the sum of the torques about the left end of the meter stick, which is 0.00 m. Σ F = n – 0.20*g – 0.080*g – 0.45*g n = 1.96 + 0.784 + 4.41 n = 7.154 N Σ τ = -0.20*g*0.09 – 0.080*g*0.49 – 0.45*g*0.64 + 7.154*0.49 = -0.1764 – 0.38416 – 2.8224 + 3.50546 = -3.38296 + 3.50546 = 0.1225 Nm Which is the same as found is Example 1. 18.4 PROCEDURE 1) Using triple beam balance, measure mass of the meter stick without any clamp, mass of the unknown mass, and masses of the clamps 2) Ideally, the center of gravity of the stick should be at the 50-cm mark. However, this is not true in most situations. To find its correct location, use one clamp to balance the stick about the stand until it is horizontal. Record this position of the center of gravity. 3) Hang a 100-g mass from a clamp located at the 10-cm mark and slide the meter stick through the supporting clamp until the stick is balanced on the support stand. Record the position of the point of support. Use this data to calculate the mass of the meter stick and compare it with the measured mass. 2 49 cm 64 cm 9 cm 40 cm 15 cm 0.20*g 0.45*g 0.080*g n

4) Hang a 100-g mass at the 10-cm mark, and hang a 200-g mass from a clamp at the 90-cm mark and slide the meter stick through the support until it is balanced on the support stand. Record the position of the point of support, ‘A’. From the data, calculate the sum of the torques about the point of support ‘A’. Also find the sum of torques about the zero position of the meter stick. 5) Remove the weights and clamps. Balance the meter stick at its center of gravity. Hang an unknown mass (e.g. your keys, or some object from the Lab) at the 90-cm mark. Hang the 200-g mass on the meter stick, and move it on the stick until equilibrium is reached. Record this position. Calculate the mass of the object and compare it with its measured value. 18.5 PRECAUTIONS 1) If the meter stick is too loose in the clamp, tighten the clamp just enough so that the stick slides when you move it, but does not slide off by itself. 2) Don’t mix up the masses of the three hangers. 3) Make sure to include the mass of the hangers in the calculations. 4) Keep away from draughts of air (from the air conditioning) as it makes it harder to balance the stick. 5) If you have to use the weight hangers under the clamps, use a Lab Jack to raise the support stand so that the weights do not touch the table. Do not forget to include the mass of the hangers. 3

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Data: Procedures 1 and 2 grams Measured mass of meter stick 90.5 g Mass of clamp-1 21.9 g Measured mass of unknown mass Mass of clamp-2 25.3 g Center of mass of meter stick 50.0 cm Mass of clamp-3 25.3 g Procedure 3 Position of the 100-g mass 10.0 cm Position of equilibrium 26.8 cm Mass of the stick from method of torques Percent error between calculated and true mass of stick Procedure 4 Position of the 100-g mass 10.0 cm Position of the 200-g mass 90.0 cm Measured Position of equilibrium of meter stick = “A” 59.1 cm Torques Calculation about the point “A”: Position “A” about which the Torques are calculated 59.1 cm Torque about “A” due to the: Meter Stick 0.603 Torque about “A” due to the: 100 g mass 0.081 Torque about “A” due to the: 200 g mass 0.683 Sum of the three torques 0.455 4

Torques Calculation about one end of the meter stick (i.e. at 0.00 m): Torque about 0.00 due to the: Meter Stick Torque about 0.00 due to the: 100 g mass 0.503 Torque about 0.00 due to the: 200 g mass 0.594 Torque about 0.00 due to: Normal Force 0.0877 Sum of the four torques Procedure 5 (stick balanced at its center of mass) Position of 200-g mass 21.3 cm Position of the unknown mass 90.0 cm Mass of unknown mass from method of torques True mass of unknown mass 139.5 Percent error between calculated and true mass 18.6 IC-18 Equilibrium of a Rigid Body REPORT FORM Name: _________________________________ Date: _________________ 18.8 ADDITIONAL RESOURCES http://hyperphysics.phy-astr.gsu.edu/hbase/handb.html https://phet.colorado.edu/sims/html/balancing-act/latest/balancing-act_en.html 18.9 POST LAB QUESTIONS: 1. If a baseball bat (thicker on one side than the other) is cut at the location where it balances, with both sides be of equal weight? Nope it will not be balanced. 2. Can the meter stick be balanced if a mass is attached on one side only? Not possible 5

3. In each of the procedures of this experiment, are all the forces also balanced? If the system is in equilibrium, all the forces have to balance by each other. 4. Why does a tight rope walker carry a long, horizontal bar to keep him balanced? Due to lever 6

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