A board with uniform mass density and a mass of 55.0 kg, and length of L = 2.70 m is attached to a hinge at its left end. A box of mass 37.0 kg is placed so that its center is a distance of d = 1.60 m from the left end of the board and the hinge. A vertical rope is attached to the right end of the board. All of this is shown in the figure below, L (a) The figure below shows a free-body diagram for the box. ที FG Which of the following statements is true? ○ The force n forms an interaction force pair with a normal force in the free-body diagram for the board. The forces ñ and FG in the free-body diagram form an interaction force pair. O The force FG forms an interaction force pair with a weight force in the free-body diagram for the board. The figure below shows two different options for extended free-body diagrams for the board. The force F is the force due to the hinge on the board. A n W B n W (b) Which of the statements below is true when considering forces and comparing the extended free-body diagrams A and B in the figure above? O Diagrams A and B can both be valid for forces with F Net = 0. Only diagram A can be valid for forces with F Net = 0. ○ Only diagram A can be valid for forces with Net = 0. ......... Neither diagram can be valid for forces with F Net = 0. (c) Which of the statements below is true when considering torques and comparing the extended free-body diagrams A and B? O Diagrams A and B can both be valid for torques when the pivot point is at the right end of the board. ○ Only diagram A can be valid for torques when the pivot point is at the right end of the board. ○ Only diagram B can be valid for torques when the pivot point is at the right end of the board. ○ Neither diagram can be valid for torques when the pivot point is at the right end of the board. (d) Let's say you want to find the tension in the rope. Based on the information you are given at the start of the problem, which origin, or pivot point, should you choose if you want to use torques to find the tension in the rope? O the left end of the board O the center of the board O the center of the box the right end of the board (e) With the origin, or pivot point, that you identified in Part (d), which of the following statements is true? The torques due to and ñ are negative (CW) and the torque due to F is positive (CCW). The torques due to w and ñ are negative (CW) and the torque due to T is positive (CCW). O The torques due to w and ñ are positive (CCW) and the torque due to T is negative (CW). O The torques due to w and ñ are positive (CCW) and the torque due to F is negative (CW). (f) Determine the sum of the (torque due to the weight of the rod) + (torque due to the normal force from the box on the board) using the pivot point selected from Part (d). magnitude of sum of the two torques = m.N (g) What is the magnitude of the torque due to the tension in the rope when using this same pivot point? magnitude of the torque due to the tension force = (h) Determine the magnitude of the tension in the rope. N m.N (i) Determine the magnitude of the force due to the hinge acting on the board. Hint: There is more than one way to do this! N