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Hello :) The questions are in the image.
(p.s. Please tell me where to label for part a)

Answer
Hello Isabel,

Interpretation of the write-up is required. The way it is written, you could consider that the torques on the plank are unbalanced. But the only way to calculate W requires the assumption that the system forces and torques are balanced so that the system is in equilibrium.

a. The weight, W, is already on the image. The other forces are from the weight of the plank, Wp, and the upward force from cone X, let's call that force Fx. Cone Y is not providing a force now that W is involved.

The force Wp can be considered to be concentrated at the middle of the plank. So Wp should be shown pointing down 2.25 m from either end. The value of Wp is 2.0 kg*g.

b. The force Fx is calculated using the above assumption of equilibrium. The weight W provides an anti-clockwise torque, Tw. The force W is applied 1.0 m from the pivot. The sum of torque Tw and the torque, Tx, (which is provided by Fx) must be zero. (Another way of saying that is that the 2 torques must be equal and opposite.) The force Fx is applied 0.95 m from the pivot. If it was acting alone,  W would cause anti-clockwise rotation. By convention, the polarity of an anti-clockwise torque is given a positive sign. So the clockwise torque due to the weight of the plank is considered negative.
anti-clockwise torque + clockwise torque = 0
W*1.0 m - Wp*0.95 m = 0
Plug in the value for Wp and solve for W.

I hope this helps,
Steve

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Steve Johnson

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I would be delighted to help with questions up through the first year of college Physics. Particularly Electricity, Electronics and Newtonian Mechanics (motion, acceleration etc.). I decline questions on relativity and Atomic Physics. I also could discuss the Space Shuttle and space flight in general.

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I have a BS in Physics and an MS in Electrical Engineering. I am retired now. My professional career was in Electrical Engineering with considerable time spent working with accelerometers, gyroscopes and flight dynamics (Physics related topics) while working on the Space Shuttle. I gave formal classroom lessons to technical co-workers periodically over a several year period.

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BS Physics, North Dakota State University
MS Electrical Engineering, North Dakota State University

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