Static_Equilibrium

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College of Business & IT Batkhela, Malakand Agency *

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102

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Mechanical Engineering

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Nov 24, 2024

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pdf

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Uploaded by AgentFangOryx3

Part 1: Conditions of Static Equilibrium Obtain a meter stick or some other long, uniform bar. For example, most broom handles without the brush would work, but a baseball bat would not as the bat is not of uniform width. Measure the length of the pole and use a marker to mark the halfway point. If you are using a meter stick, the halfway point is at the 50 cm mark. Tie a string to your pole at this halfway point and suspend the pole. Alternatively, you can find a tall, thin object to act as a fulcrum. If you have a tall, thin object (less than 1.0 cm) then you can balance your pole on the fulcrum. Adjust the string or fulcrum so that your bar rests perfectly level. You should have two blocks in your lab kit with known masses (please check the lab kit inventory sheet for this information). Tie a rope around each mass and suspend the blocks on either side of the pivot point. Adjust the position of the blocks as necessary so that the pole is perfectly level. Alternatively, you can place the blocks on top of the pole and adjust their positions so that the pole is perfectly level. Take a picture of your system once you have achieved equilibrium. The picture should include a card with your name, date, and section number. Paste the picture in the space below. or or

Measure the distance between the pivot point and the center of each block. Complete the following data table: Calculate the torque exerted by each block on the pole. Show your work. Explain whether your results support or do not support the conditions for static equilibrium. Be specific and use your data to support your claim. Mass of block (kg) Distance from pivot (m) 0.03725 (medium block) 0.04 0.01912 (small block) 0.08 T= (r)(F) (sin theta) Small Block= T= -(0.08 m) (0.01912 kg) (9.8 N/kg) T= -0.01499 N-m T ~ -0.015 N-m Medium block= T= (r)(F) (sin theta) T= (0.04 m) (0.03725 kg) (9.8 N/kg) T= -0.01460 N-m T ~ -0.015 N-m Yes, the results do support the conditions for static equilibrium. For the conditions for static equilibrium, the net force must be zero acting on the object; in addition, the net torque acting on the object is also zero. Here, the conditions are met where the two objects do not cause the rotation clockwise or counterclockwise, hence, it is in equilibrium. In addition, looking at the values, they are equal and opposite to be in equilibrium and be in static equilibrium.

Explain why you do not need to include the weight of your pole in your torque calculations. Part 2: Experimental Determination of Block Mass You should have a block with an unknown mass in your lab kit. Repeat the steps of Part 1 of this lab, but this time, include the block with the unknown mass in your system. You may use all three blocks in this setup, or you may use one block with a known mass in conjunction with the block of unknown mass. Adjust the blocks until the pole is horizontal. Complete the following data table: Determine the mass of the unknown block. Show your calculations below. Part 3: Experimental Determination of Pole Mass Devise a set of procedures that would allow you to use principles of static equilibrium to experimentally determine the mass of your pole. List your procedures below. Be specific. Mass of block (kg) Distance from pivot (m) x 0.089 0.019 0.365 0.037 0.320 The weight of the pole is irrelevant as the torque is the measure of the magnitude of the force and the angle of such force to create a rotational motion. This is the reason why the weight of the pole does not need to be included in the calculations. Sum of T= (r)(mg)+ (r)(mg) + -(r) (mg) = 0 (0.089 m) (X)(9.8 N/kg) +(0.365 m)(0.019 kg) (9.8 N/kg)+ -(0.320m)(0.037 kg)(9.8 N/kg)= 0 0.8722x + 0.0679-0.1160=0 0.8772x=0.048132 X= 0.05487 kg

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Apply your procedures. Create a properly labeled data table for any relevant data. Put your table in the space below. Mass (kg) Distance from the pivot (m) 0.037 0.0460 x- unknown pole mass -0.505 Use your data to calculate the mass of your pole. Show your calculations below. Reflect on the lab. How consistent was your data with your expectations? What worked well and what 1. Find a pole or a tube-like structure that can be suspended. Measure this pole in length and calculate the middle. The middle will be the center of gravity where equilibrium will most likely occur. 2. Balance the pole by tying known mass blocks to one ends of the pole. Ensure that the pole is horizontal and stable by moving the blocks around till in equilibrium, indicating stable equilibrium. 3. Record the distance from the pivot point to the block. Then, calculate the torque by multiplying the mass and the distance. 4. In static equilibrium, the torque and forces and all vertical forces will cancel out and from there the mass of the pole can be found via the tension force. Sum of T= (r)(mg)+ (r)(mg)= 0 (0.0460 m) (0.037 kg) (9.8 N/kg) + (-0.505 m) (x kg) (9.8 N/kg) = 0 X= 0.03370 Kg Tension force (0.037 kg) (9.8 N/kg) W1= 0.3626 N (0.03370 Kg) (9.8 N/kg) W2 = 0.33026 N Tension = W1+ W2 = 0.3626 N + 0.33026 N Weight of the pole is 0.6928N, so then this the pole and block weight pulling down. Hence, the pole weight is 0.6928 kg I believe that the lab was successful and produced results that corresponded with torque theory. The results and data were consistent with the predicted theory of static equilibrium. In parts one and two, the lab portion was easier as the instructions were laid clearly; however, the latter portion of the lab lead to some trial and error from my own procedures which resulted in some issues. In terms of set up, finding a “pole” was