1. A 23 kg boy sits 1.5 m from the axis of rotation of a seesaw. At what distance from the axis of rotation must a 21 kg boy be positioned on the other side of the axis to balance the seesaw? [Ans: 1.6 m]
2. Two people push on opposite sides of a swinging door. Person A exerts a force of 40 N at a perpendicular distance of 20 cm from the hinge, and person B exerts a force of 30 N at a perpendicular distance of 25 cm from the hinge. What is the resultant torque acting at the hinge; which way will the door swing? [Ans: T = 0.5 Nm; swings toward person B]
3. How much force must be produced by the elbow flexor muscles at a perpendicular distance of 3 cm from the axis of rotation of the elbow to support a weight of 200 N at a perpendicular distance of 25 cm from the elbow? [Ans: 1667 N]
4. A therapist applies a lateral force of 80 N to the forearm at a distance of 25 cm from the axis of rotation of the elbow. The biceps brachii attaches to the radius at a 90 degree angle 3 cm from the elbow joint center. How much force is required of the biceps (FM) to stabilize the arm in this position? (Hint: Sum of Torques = 0) [666.7 N] What is the magnitude of the reaction force (FR) of the humerus on the ulna? (Hint: Sum of Forces = 0) [586.7 N]
5. Tendon forces Ta and Tb are exerted on the patella. The femur exerts force F on the patella. If Tb = 80 N, what are the magnitudes of Ta and F if no motion occurs at the joint? (Hint: Consider the forces in the horizontal and vertical directions separately. Since no movement occurs, the sum of forces is equal to zero. You now have two equations and two unknowns.) [Ans: Ta = 44.8 N, F = 86.1 N]
6. A volleyball player's 3.7 kg arm moves at an average angular velocity of 15 radians/s during the execution of a spike. If the average moment of inertia of the extending arm is 0.45 kgm2, what is the average radius of gyration (k) for the arm during the spike? [Ans: 0.35m]
7. A 60 kg diver in a full layout position (position 1), with a transverse plane radius of gyration (k) of 0.5 m, leaves a springboard with an angular velocity of 4 radians/s. What is the diver's angular velocity when she assumes a tuck position (position 2), reducing her radius of gyration to 0.25 m? [Ans: 16 radians/s]
Position 1
Position 2
8. A man carries a 3 m, 32 N board over his shoulder. If the board extends 1.8 m behind the shoulder and 1.2 m in front of the shoulder, how much force must the man apply vertically downward with his hand at 0.4 m in front of his shoulder to stabilize the board in this position? (Assume the weight of the board is evenly distributed throughout its length.) [Ans: 24 N]
9. A patient rehabilitating a knee injury performs knee extension exercises while wearing a 15 N weight boot. Calculate the amount of torque at the knee by the weight boot for each of the four positions shown, given a distance of 0.4 m from the knee joint center to the center of mass of the weight boot. [Ans: 0 Nm; 3 Nm; 5.2 Nm; 6 Nm]
