A 65 kg person is standing on the balls of their feet (the metatarsal bones), as

Question

A 65 kg person is standing on the balls of their feet (the metatarsal bones), as shown in the figure. Assume that the person has their weight equally distributed on each foot. The force of the tibia acting on the ankle is labelled as FL and acts on a lever arm of 9.4 cm with respect to the pivot point (indicated by the triangle). The gastrocnemius muscle is attached to the upper leg bone (the femur) and the heel through the Achilles tendon, and produces a force on the heel, labelled as FA, which acts on a lever arm of 14.1 cm.

(a) What class of lever does this situation represent?

(b) Find the forces FL and FA acting on the leg to keep the person balanced. Hint: The person doesn’t become heavier from standing on the balls of their feet. (6 marks)

(c) Why is force of the tibia on the ankle substantially larger than half the person’s weight?  

Explanation / Answer

from balancing equation of force

we can write

Fbody + Fa = FL

65 * 6.8 * 1/2 + Fa = Fl

by using torque balance

FL * 9.4 = FA * 14.1

FL = Fa* 14.1/9.4

Fa * 14.1/9.4 - Fa = 65* 9.8 * 1/2

1/2 * 65* 9.8 = Fa * 14.1/9.4 - Fa

Fa = 65* 9.8 = 637 N

FL = FA * 14.1/9.4

FL = 955.5 N

Since FL is acting near to the pivot point while FA is acting far away from pivot point

since the distance is different

so the force required to balance the torque has to be different

smaller the distance higher the force and far the point lesser the force required

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.