(e) Use your origin (pivot point) from Part (d) to determine the sum of the (torque due to the weight of the rod) + (torque due to the tension from the lamp). sum of the torques due to the board and lamp = direction of the sum of torques: O positive (CCW) O negative (CW) m.N (or N·m) (f) Determine the magnitude of Ty, the vertical component of the tension force in the wire supporting the rod. magnitude of Ty = N (g) What is the magnitude of the force of tension in the supporting wire? Remember you know the angle the wire makes with rod. magnitude of = | N (h) What is magnitude and direction of TX? magnitude of T = direction of T = ---Select--- ✓ N (i) Depending on the numbers you have for your problem, your tip-to-tail vector sum of forces, ignoring the force due to the hinge, looks like one of the two drawings below. BOTH drawings are valid scenarios for this system. 〒 W 〒 W Redraw both of the tip-to-tail vector sums, but rectangularize your drawings and add the hinge force so that the F Net = 0. Both of your drawings should include Tx, Ty, Ĥx, and Hy Based on your two rectangularized free-body diagrams, and taking the variables w, Tx and Ty to be POSITIVE numbers in the statements below, which ONE OR MORE of the following statements is/are true in general (not just for your specific numbers) for this system? ☐ Яx must point to the left, toward the wall. If Ty>(TL+w) then Hy points down. If Ty < (TL + w) then Hy points up. Ax must point to the right, away from the wall. ☐ Ay must point up. (j) What is the magnitude and direction of the vector Hy? magnitude of H = direction of x=---Select--- V (k) What is the magnitude and direction of the vector Hy for the numbers in your version of this problem? magnitude of y = direction of Hy =-Select- v N A lamp of mass m₁ = 21.0 kg hangs at the end of a rod of mass mR = 14.0 kg and length L = 1.60 m. The left end of the rod is attached to a hinge that is fixed to a wall. A cable, also anchored to the wall, is connected to the rod at a distance d = 1.30 m from the wall. The cable makes an angle = 51.0° with the rod, as shown in the drawing. The rod is well-behaved (!) and has a uniform mass density. d A (a) The figure below shows a free-body diagram for the lamp. T wire-lamp G,earth-lamp What is the magnitude of T wire-lamp? N (b) The figure below shows four options for the extended free-body diagram for the rod. The force labeled T is the interaction force pair to the tension force from Part (a). A is the force due to the hinge acting on the rod. A ↑ Hy C HY HX w↓ W B Ꮎ ↓ w Hy D Hy Ꮎ HX W T₁ Which option is consistent with the rod being in static equilibrium for forces? HINT: You might try using tip-to-tail vector sum of forces, or you might draw an extended free-body diagram for the rod of your own and compare it with the four options. |---Select--- ☑ (c) The figure below shows an extended free-body diagram for the rod, with only the vertical, or perpendicular components of the force vectors. These are the components that will contribute to the torque acting on the rod. ↑HY Ty W T If you want to calculate y using torques, which is the best choice of origin, or pivot point? O the left end of the rod O the right end of the rod O the center of the rod O the location of the support wire