Question

The distance from Dora’s palm to the center of her elbow joint is 32 cm and the distance from her elbow to the insertion of her biceps muscle is 4 cm. Assume that the biceps muscle is at Lo when the elbow is flexed 90 and that Lo = 24 cm. Also, assume that the biceps muscle is parallel-fibered and has no angle of pennation. a) Dora would like to hold a 20 kg object statically in her hand with her elbow flexed at 90. What is the amount of force that must be generated by the biceps muscle to accomplish this goal?

As Dora lifts the object, her biceps muscle shortens 3 cm (a bit over 1”) in ½ of a second, i.e. the muscle shortening velocity is 60 mm/sec. For this muscle movement, how far does Dora lift the object? How fast does the object move?

c) Consider your responses to parts a) and b) and discuss the functional advantages and disadvantages of the design of the human arm.

Answer 1

The muscle makes an angle p with the arm

tan(p) = 24/4 = 6 ; p = 80.5 deg

angle between the verticle and the muscle = 19.5 deg

The weight pulls down the arm

muscle force has to generate opposite force to keep it in equilibrium

verticle comp[onent of muscle force F_v = FCos(19.5) = 0.99F

taking moments of the forces about the center of the joint

4*0.99F = 32*20000g

F = 161616 N

b) The new position of the arm , shortened length of the muscle form similar triangles as shown above, let h be the height by which th arm is lifted. then

32/4 = h/3

lift height h = 32*3/4 = 24 cm

c) The advantgae is by shortening a small length of the muscle the arm can lift alarger height, the disadvantage is the muscle has to generate a larger force.