A uniform rod of mass m,= 173 g and length L = 100.0 cm is attached to the wall with a pin as shown. Cords are attached to the rod at the r₁= 10.0 cm and r₂ = 90.0 cm mark, passed over pulleys, and masses of m₁ = 256 g and m₂ = 157 g are attached. Your TA asks you to determine the following. (a) The position r3 on the rod where you would suspend a mass m3 = 200 g in order to balance the rod and keep it horizontal if released from a horizontal position. In addition, for this case, what force (magnitude and direction) does the pin exert on the rod? Use standard angle notation to determine the direction of the force the pin exerts on the rod. Express the direction of the force the pin exerts on the rod as the angle 0F, measured with respect to the positive x-axis (counterclockwise is positive and clockwise is negative). x See if you can find a convenient point which can serve both as the origin of the coordinate system and as the point about which we wish to determine the torques. m x See if you can write a condition for rotational equilibrium statement that will allow you to determine the position on the rod where we need to suspend the mass my in order for the rod to remain stationary when released from a horizontal position. N See if you can write a condition for translational equilibrium statement that will allow you to determine the magnitude and direction of the force the pin exerts on the rod. 8 = (b) Let's now remove the mass m3 and determine the new mass m4 you would need to suspend from the rod at the position r4 = 20.0 cm in order to balance the rod and keep it horizontal if released from a horizontal position. In addition, for this case, what force (magnitude and direction) does the pin exert on the rod? Express the direction of the force the pin exerts on the rod as the angle Of, measured with respect to the positive x-axis (counterclockwise is positive and clockwise is negative). F₂ m4= Fp= 8F = kg N 0 (c) Let's now remove the mass m4 and determine the mass ms you would suspend from the rod in order to have a situation such that the pin does not exert a force on the rod and the location rs from which you would suspend this mass in order to balance the rod and keep it horizontal if released from a horizontal position. mg = /5 = kg m