KIN 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 1 3 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 Position A Position B 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 foot FC hip FM L 0 43 m d 0 08 m knee Rotary component of the force FC from the Cybex machine Muscle force FM required to hold this position KIN 430 Problem Set 2 5 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 KIN 430 Problem Set 3