VectorComponents Worksheet - Copy

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Embry-Riddle Aeronautical University *

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Mechanical Engineering

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Apr 3, 2024

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Vector Components Lab (Worksheet) Name: Hunter Porter Section Number: 1 To start the lab, refer to the lab manual sheet provided. The equipment is shown below: Part 3: ∑ ⃑ F = 0, 3 Forces in 2 Dimensions 1. Use the balance to measure the mass of each of the mass hangers and record them. Make sure you label them with a sticky note. (3 points) Mass Hangers Mass [g] Hanger 1 244.2 g Hanger 2 246.1 g Hanger 3 244 g

2. Keep the first pulley at the 0 ° mark and balance it with the other two pulleys. What angle does each of the forces make with the force aligned with zero mark? (3 Points) Pulley Angle Angle Aligned with Zero Mark [°] Pulley 1 0 Pulley 2 120 Pulley 3 240 3. What angle do the two forces make with each other? (2 Points) Pulley Angle made with each other[°] Pulley 1 to Pulley 2 120 Pulley 2 to Pulley 3 120 4. Imagine the x-axis that cuts the center of the force table from 180 ◦ mark and the 0 ◦ mark. Let the y-axis be perpendicular to that, through the center of the table along the line from 90 ◦ to 270 ◦ . The force aligned with 0 ◦ mark is pointing in the positive x-direction. a. Do the other two forces (not at the 0-degree pulley) point in the positive or negative x-direction? (1 point) Negative b. Do the forces (not at the 0-degree pulley) point in the positive or negative y- direction? (1 point) Positive

Part 4: Vector Components Keep the vectors the way they were in Part 3. 5. What must be true about the y-components of the two off-axis forces for the ring to be in equilibrium? (1 point) They would have to be equal to each other. 6. Add and remove masses to each hanger so that the total mass of each is about 250 g . (As long as all three forces are kept equal, the equilibrium should not be disturbed. You may want to replace the nail to lock the ring while you are adjusting. Don’t forget to include the mass of the hanger itself.) What is the total mass of each of your three hanging masses after the additional mass? (3 point) Hanging Masses Mass [g] Mass 1 250.7 g Mass 2 249.1 g Mass 3 250.5 g 7. You will now alter the force table with an additional pulley. The first pulley will remain at the 0 ° degree mark and the second pulley will remain at an angle . The first and second pulleys should continue to have masses of 250 grams each; you are not adding or removing masses to the first and second pulleys for this part of the experiment. The third pulley should have been at an angle on the force table. Move the third pulley to the 180 ° mark ( - x-axis ). Use the fourth line to create a fourth pulley. Hang the fourth mass hanger from it. Place the fourth pulley at the 270 ° mark ( - y-axis ). The force table will be unbalanced. You will add and remove masses to ONLY the third pulley and the fourth pulley to achieve equilibrium on the force table. You can determine the masses that you need for the components by trial and error, or you can calculate them in advance using Equations 2 and 3 shown below. Confirm that the component replacements for the original vector are equivalent by checking that the ring remains in equilibrium with the nail removed. When you have accomplished this task, you will have split the force that was initially exerted onto the third pulley into its x- and y- component forces. (1) (2) (3)

a. What mass did you need for your x-component? (1 point) 139.7 g b. What do you calculate for the mass of the x-component using Equation 2? (1 point) 139.7 g c. What mass did you need for your y-component? (1 point) 178.1 g d. What do you calculate for the mass of the y-component using Equation 3? (1 point) 178.1 g

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