The torque generated by each item is the force acting on the item multiplied by the distance to the pin. Thus: T₂ = magr

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The Torque Generated By Each Item Is The Force Acting On The Item Multiplied By The Distance To The Pin Thus T Magr 1 (53.49 KiB) Viewed 10 times

The torque generated by each item is the force acting on the item multiplied by the distance to the pin. Thus: T₂ = magra where ra is the distance from the mass m₂ to the pin. Next we want the torque due to the center of gravity of the meter stick. This is required since the meter stick will induce a torque on itself if the pin is not located at the center of gravity. We assume the meter stick is a perfect meter stick in that it's mass is uniform, so the center of mass is at 50cm. We calculate the torque due to the center of gravity: (3) Teg meggreg where reg is the distance between the center of mass (center of gravity) of the meter stick and the pin. Calculate these quantities (what are the units Torque? Include units on all numbers reported): 72 Teg= Tew= Now we want to calculate the counter-clockwise torque. This will allow us to find the unknown my. The counter-clockwise torque is generated by my and the y-component of the external force, F. This is because forces whose line of action, for instance, Fr, go through the pin do not contribute to torques! (they have zero lever arm). Here Teow is the total counter-clockwise torque in this situation. Tecw = T1+TE, Since we do not know the unknown mass, we determine the torque due to the external force: TF. - FTF-Fsin(0)rF (2) (5) where ry is the distance from where the force is applied on the ruler to the pin. Since we are looking for the y-component of the force (ie, non-parallel) we must multiply by sind. We finally note that our unknown mass creates a torque: T₁ = migri 7₂ +Teg== T1+F (6) where as usual, r₁ is the distance from my to the pin. Calculate TP = We are finally at the point where we can solve for the unknown mass. Since Tew Teow in order for the meter stick to be in equilibrium, we have: We can now use our calculations to determine the unknown torque and given the fact that we know ri, we can determine our unknown mass. Solve for my