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2/19/2014 Assume: d = 7 cm, θ = 30°, the muscle can produce 60 N of force per cm2, and the cross sectional area of the muscle is 13.33 cm2… What is torque? Torque is the turning effect created by an eccentric force, about an axis, expressed as units of force × units of length (Nm). Our muscles produce joint torque that enables our segments to rotate about our joints. 1. What is the compressive component of the quadriceps force (FC)? 2. What is the rotary component of the quadriceps force (FR)? 3. How much torque is created by the quadriceps force (TQ)? 4. How does the patella increase the mechanical capabilities of the quadriceps? 5. How might internal (muscle) knee extension torque be related to ACL injury? Fb rb FC FQ d θ FR Net Joint Torque d = 7 cm; θ = 30°; CSAQ = 13.33 cm2. Create a free-body diagram representing the upper extremity (upper arm, forearm, and hand) in the following circumstances: Solve for the following: 1. Compressive component of the quadriceps force (FC) 2. Rotary component of the quadriceps force (FR) 3. Torque created by the quadriceps force (TQ) 4. Also, how does the patella increase the mechanical capabilities of the quadriceps? 5. How might the knee extension torque be related to ACL injury? upper 1. You are holding 3 gallons of water (Fww = 111 N) in your right hand: shoulder abduction = 90°, with your wrist and elbow in anatomical position FC FQ 3. Your deltoid is the only active muscle force (Fd): it inserts at an angle of 15° above the humerus and at a horizontal distance of 0.15 m from your shoulder joint d θ Answers: FC = 692 N; FR = 400 N; and TQ = 28 Nm 2. Water weight acts at a horizontal distance that is 0.60 m from your shoulder joint 4. Your arm weighs 40 N (Faw): this weight acts at a horizontal distance of 0.30 m from the shoulder joint FR 5. The bucket is in static equilibrium (ΣF = 0; ΣT = 0). Calculate: Answers 1. Torque produced by the deltoid in order to hold the water in static equilibrium 1. Deltoid Torque = 78.6 Nm 2. Deltoid force, including the resultant, rotary, and compressive components 2. Force produced by the deltoid = 2024 N (rotary = 524 N; compressive = 1955 N) 3. Compressive (horizontal) shoulder joint reaction force (JRFX) 3. Compressive (horizontal) shoulder joint reaction force = 1955 N 4. Shear (vertical) shoulder joint reaction force (JRFY) 4. Shear (vertical) shoulder joint reaction force = 373 N 5. Resultant shoulder joint reaction force (JRF) 6. How might you decrease the shoulder joint reaction force? 5. Resultant shoulder joint reaction force = 1990 N, 10° below the horizontal axis 6. How might you decrease the shoulder joint reaction force? Adduct the humerus (lower the water) 1 2/19/2014 Some A 1.5-kg forearm is horizontal and flexed 90˚ relative to a vertical upperarm, while holding a 5-lb weight in the hand (the forearm center of mass is 13 cm away from the elbow joint). Although not a perfect assumption, assume that the biceps brachii is the only muscle force acting on the forearm. The angle of insertion for the biceps brachii is 45˚, and the insertion point is 3 cm from the elbow joint. If the 5-lb weight is 30 cm away from the elbow, calculate the following: 1. Torque, due to the force that is produced by the biceps brachii. Answer: 8.63 Nm. 2. Force (resultant, rotary, and compressive) that is produced by the biceps brachii. Answers: 407 N, 288 N, and 288 N. 3. Magnitude and direction of the joint reaction force, applied by the upper arm to the forearm. Answers: 382 N, ~41˚ below a horizontal axis. Torque, due to muscle force is influenced by joint angle F × r = Torque, due to muscle force, is highly dependent upon joint angle. Notice how the perpendicular distance related to the muscle force changes as joint angle changes. Mechanical advantage (ME), within a biomechanical context: T Typeequationhere. Mechanical advantage is a ratio of perpendicular distances, or moment arms: internal over external ri re FE 2