Chapter 8 Problems1, 2, 3 = straightforward, intermediate, challenging = full solution available in Student Solutions Manual/Study Guide = co ached solution with hints available at www.cp7e.com = biomedical applicationSection 8.1 Torque 1. If the torque required to loosen a nut that is holding a flat tire in place on a car has a magnitude of 40.0 N m, what ∙minimum force must be exerted by the mechanic at the end of a 30.0-cm lug wrench to accomplish the task? 2. A steel band exerts a horizontal forceof 80.0 N on a tooth at point B in Figure P8.2. What is the torque on the root of the tooth about point A? Figure P8.23. Calculate the net torque (magnitude and direction) on the beam in Figure P8.3 about (a) an axis through O perpendicular to the page and (b) an axis through C perpendicular to the page.Figure P8.34. Write the necessary equations of equilibrium of the object shown in Figure P8.4. Take the origin of the torque equation about an axis perpendicular to the page through the point O.Figure P8.45. A simple pendulum consists of a small object of mass 3.0 kg hanging at the end of a 2.0-m-long light string that is connected to a pivot point. Calculate the magnitude of the torque (due to the force ofgravity) about this pivot point when the string makes a 5.0° angle with the vertical. 6. A fishing pole is 2.00 m long and inclined to the horizontal at an angle of 20.0° (Fig. P8.6). What is the torque exerted by the fish about an axis perpendicular to the page and passing through the hand of the person holding the pole? Figure P8.6Section 8.2 Torque and the Two Conditions for Equilibrium Section 8.3 The Center of Gravity Section 8.4 Examples of Objects in Equilibrium 7. The arm in Figure P8.7 weighs 41.5 N. The force of gravity acting on the arm acts through point A. Determine the magnitudes of the tension force tF in the deltoid muscle and the force sF exerted by the shoulder on the humerus (upper-arm bone) to hold the arm in the position shown.Figure P8.78. A water molecule consists of an oxygen atom with two hydrogen atoms bound to it as shown in Figure P8.8. The bonds are 0.100 nm in length, and the angle between the two bonds is 106°. Use the coordinate axes shown, and determine thelocation of the center of gravity of the molecule. Take the mass of an oxygen atom to be 16 times the mass of a hydrogen atom.Figure P8.89. A cook holds a 2.00- kg carton of milk at arm’s length (Fig. P8.9). What force BF must be exerted by the biceps muscle? (Ignore the weight of the forearm.)Figure P8.910. A meterstick is found to balance at the 49.7-cm mark when placed on a fulcrum. When a 50.0-gram mass is attached at the 10.0-cm mark, the fulcrum must be moved to the 39.2-cm mark for balance. What is the mass of the meter stick? 11. Find the x- and y-coordinates of the center of gravity of a 4.00-ft by 8.00-ft uniform sheet of plywood with the upper right quadrant removed as shown in Figure P8.11. Figure P8.1112. Consider the following mass distribution, where x- and y-coordinates aregiven in meters: 5.0 kg at (0.0, 0.0) m, 3.0 kg at (0.0, 4.0) m, and 4.0 kg at (3.0, 0.0) m.Where should a fourth object of 8.0 kg be placed so that the center of gravity of the four-object arrangement will be at (0.0, 0.0) m? 13. Many of the elements in horizontal-bar exercises can be modeled by representing the gymnast by four segments consisting of arms, torso (including the head), thighs, and lower legs, as shown in Figure P8.13a. Inertial parameters for a particular gymnast are as follows:Segment Mass (kg)Length (m)rcg (m)I (kg-m2)Arms 6.87 0.548 0.239 0.205Torso 33.57 0.601 0.337 1.610Thighs 14.07 0.374 0.151 0.173Legs 7.54 — 0.227 0.164Note that in Figure P8.13a rcg is the distance to the center of gravity measured from the joint closest to the bar and the masses for the arms, thighs, and legs include both appendages. I is the moment of inertia of each segment about its center of gravity. Determine the distance from the bar to the center of gravity of the gymnast for the two positions shown in Figures P8.13b and P8.13c. Figure P8.1314. Using the data given in Problem 13 and the coordinate system shown in Figure P8.14b, calculate the position of the center of gravity of the gymnast shown in Figure P8.14a. Pay close attention to the definition of rcg in the table. Figure P8.1415. A person bending forward to lift a load “with his back” (Fig. P8.15a) rather than “with his knees” can be injured by large forces exerted on the muscles and vertebrae. The spine pivots mainly at the fifth lumbar vertebra, with the principal supporting force provided by the erector spinalis muscle in the back. To see the magnitude of the forces involved, and to understand why back problems are common among humans, consider the model shown in Fig. P8.15b of a person bending forward to lift a 200-N object. The spine and upper body are represented as a uniform horizontal rod of weight 350 N,pivoted at the base of the spine. The erector spinalis muscle, attached at a point two-thirds of the way up the spine, maintains the position of the back. The angle between the spine and this muscle is 12.0°. Find the tension in the back muscle and the compressional force in the spine.Figure P8.1516. When a person stands on tiptoe (a strenuous position), the position of the foot is as shown in Figure P8.16a. The total gravitational force on the body, gF, is supported by the force n exerted by the floor on the toes of one foot. A mechanical model of the situation is shown in Figure P8.16b, where T is the force exerted by the Achilles tendon on the foot and R is the force exerted by the tibia on the foot. Find the values of T, R, and θ when Fg = 700 N.Figure P8.1617. A 500-N uniform rectangular sign 4.00 m wide and 3.00 m high is suspended from a horizontal, 6.00-m-long, uniform, 100-N rod as indicated in Figure P8.17. The left end of the rod is supported by a hinge, and the right end is supported by a thin cable making a 30.0° angle with the vertical.(a) Find the tension T in the cable. (b) Find the horizontal and vertical components of force exerted on the left end of the rod by the hinge.Figure P8.1718. A window washer is standing on a scaffold supported by a vertical rope at eachend. The scaffold weighs 200 N and is 3.00 m long. What is the tension in each rope when the 700-N worker stands 1.00 m from one end? 19. The chewing muscle, the masseter, is one of the