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Solutions to Selected Introductory and Additional Problems: Week 3-4 SOLUTIONS TO SELECTED INTRODUCTORY PROBLEMS (Ch 6) 9. Muscle can generate approximately 90 N of force per square centimeter of cross-sectional area. If a biceps brachii has a cross-sectional area of 10 cm2, how much force can it exert? 90 N (10 cm2) = 900 N SOLUTIONS TO SELECTED ADDITIONAL PROBLEMS (Ch 6) 5. If the fibers of a pennate muscle are oriented at a 45° angle to a central tendon, how much tension is produced in the tendon when the muscle fibers contract with 150 N of force? (106 N) T = (150 N) cos 45° T = 106 N 6. How much force must be produced by the fibers of a pennate muscle aligned at a 60° angle to a central tendon to create a tensile force of 200 N in the tendon? (400 N) 200 N = F cos 60° F = 400 N 7. What must be the effective minimal cross-sectional areas of the muscles in problems 5 and 6 above, given an estimated 90 N of force producing capacity per square cm of muscle cross-sectional area? (1.2 cm2, 4.4 cm2) 106 N / 90 N/cm2 = 1.2 cm2 400 N / 90 N/cm2 = 4.4 cm2 8. If the biceps brachii, attaching to the radius 2.5 cm from the elbow joint, produces 250 N of tension perpendicular to the bone, and the triceps brachii, attaching 3 cm away from the elbow joint, exerts 200 N of tension perpendicular to the bone, how much net torque is present at the joint? Will there be flexion, extension, or no movement at the joint? (0.25 N-m; flexion) Torquenet = Torqueflexion - Torqueextension Tnet = (250 N)(0.025 m) - (200 N)(0.03 m) = 0.25 N-m (flexion) 1 9. Calculate the amount of torque generated at a joint when a muscle attaching to a bone 3 cm from the joint center exerts 100 N of tension at the following angles of attachment: a) 30°, b) 60°, c) 90°, d) 120°, e) 150° (a. 1.5 N-m, b. 2.6 N-m, c. 3 N-m, d. 2.6 N-m, e. 1.5 N-m) Torque = F • sin θ • 0.03 a) T = 100 N sin 30° (0.03) = 1.5 N-m b) T = 100 N sin 60° (0.03) = 2.6 N-m c) T = 100 N sin 90° (0.03) = 3 N-m d) T = 100 N sin 120° (0.03) = 2.6 N-m e) T = 100 N sin 150° (0.03) = 1.5 N-m 2