KIN 430 - Problem Set 1KIN 430 – Biomechanics Spring Semester 2018 Problem Set #4 (20 points) – Due on Monday, April 30, 2018, in class To receive full credit, you must hand the completed problem set directly to one of the course instructors (do not slip it under a door or leave it in the front office) Answer the following questions by placing your answers in the spaces provided. Do all of your calculations on separate sheets of paper, clearly indicating which calculations go with which problem. Staple the separate sheets of paper to this problem set before you turn it in. You must show your calculations to receive full credit, even if you have the correct answers. Don’t forget to include proper units! 1. (4 pts.) A power lifter performs a dead lift, raising a barbell with a mass of 255 kg through a vertical displacement of 0.53 m above the ground, giving the barbell 1325.82 J of potential energy. The power lifter then releases the barbell, letting it drop to the ground. Determine the magnitude of the vertical velocity of the barbell right as it reaches the ground using both a mechanical energy approach and a projectile motion approach. Be sure to show your work for both approaches. [Use 9.81 m/s2 for g and assume the barbell was at rest right before it was dropped.] Vertical velocity using mechanical energy approach ______________ Vertical velocity using projectile motion approach ______________ 2. (4 pts.) As a person is extending their arm, their biceps, brachialis and triceps muscles generate forces about their elbow joint (ignore any other muscles that act about the elbow). At one point during the movement the magnitudes of the forces in two of the muscles were: biceps = 486 N and triceps = 1873 N. The magnitudes of the muscle moment arms about the elbow joint were: biceps = 0.042 m, brachialis = 0.028 m, and triceps = 0.032 m. What is the force generated by the brachialis muscle if the net joint torque is -32.6 N m? If the brachialis force was zero, what would the magnitude of the net joint torque be? (Note: a negative torque means a net extension torque at the elbow joint.) Brachialis muscle force if net joint torque is -32.6 N m ____________ Net joint torque if brachialis muscle force is 0 N ____________KIN 430 - Problem Set 23. (4 pts.) A figure skater who weighs 730 N is spinning about her longitudinal axis during a jump at a rate of 4.93 rad/s in position A. If her radius of gyration in position A is 0.18 m what is her angular momentum? If she pulls her arms in toward her chest, decreasing her radius of gyration to 0.13 m in position B, what will her angular momentum be, and what will her angular velocity be in radians per second and revolutions per second? (Note: 2 radians equals 1 revolution) Angular Momentum in A ______________ Angular Momentum in B ______________ Angular Velocity in B in radians per second ______________ Angular Velocity in B in revolutions per second ______________ 4. (4 pts.) Your personal training client is doing leg curls to exhaustion on a Cybex machine when she gets “stuck” at a 90 knee joint angle (see figure below). The force exerted by the Cybex machine (FC) on her leg is 425 N, directed at an angle of 62 relative to the tibia (angle ) and the distance from her knee joint to the point where the force is applied is 0.43 m (distance L). For this problem, assume the weight of the shank and foot is negligible and that the muscle force (FM) acts perpendicular to the tibia in this position with a moment arm of 0.08 m (distance d) relative to the knee. What is the magnitude of the rotary component of the force (FC) from the Cybex machine, and how much force do the muscles (FM) need to generate to hold this position? Rotary component of the force (FC) from the Cybex machine ______________ Muscle force (FM) required to hold this position ______________ d = 0.08 m FM L = 0.43 m FC hip knee foot  Position A Position BKIN 430 - Problem Set 35. (4 pts.) During the propulsion phase of a vertical jump a person generated a knee joint extension torque that averaged 176 Nm. Over the propulsion phase, the knee joint angle changed from being flexed 50 to being flexed only 5 right at takeoff. The duration of the propulsion phase was 0.29 s. Determine the angular mechanical work and power generated at the knee joint. (In this problem, full extension of the knee would be 0 and larger negative values mean a more flexed knee. So -5 means the knee is flexed 5 and -50 means the knee is flexed 50. Remember: 2 radians equals 360) Angular mechanical work _____________ Angular mechanical power