A 77-kg person standing is standing on one foot on a very smooth gym floor. He i

Question

A 77-kg person standing is standing on one foot on a very smooth gym floor. He is lifting his body by pivoting his foot upwards through a 30.0? angle, balancing all of his weight on the ball of the foot. The forces on the bones from the rest of his body are due to the Achilles tendon and the ankle joint as shown in the figure. The Achilles tendon acts perpen- dicular to a line through the eel and toes; it is this line that has rotated upward through 30.0?. Assume that the weight of the foot is negligible compared with that of the rest of the body. (a) What are the magnitude and direction of the force that the floor exerts on the man?s foot? (b) What is the tension in the Achilles tendon? (c) Find the horizontal and vertical components of the force that the ankle joint exerts on the foot.

Explanation / Answer

let the tension in the tendon=T weight of the body is acting through the ankle joint take moment about the ball of the foot T*(16+4.5)=77*9.81*16*cos(30) T=510.57 N let the forces acting on the foot by the floor=Fx and Fy Fy+T*cos(30)=77*9.81 Fx+T*sin(30)=0 Fx=-255.28 N Fy=313.2 N magnitude of the force that the floor exerts on the foot=sqrt(Fx^2+Fy^2) =404.5 N direction=50.81 degree north of west horizontal component of force that the ankle joint exerts on the foot=0 vertical component=77*9.81=755.37 N

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