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?
b) 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 bicep must generate a force of 1568 N to hold a 20 kg object with the elbow flexed at 90°. The object is lifted by 3 cm at a velocity of 60 mm/sec when the bicep muscle shortens by the same amount. The human arm has a short bicep lever arm requiring larger forces to lift objects, but provides greater range of motion and agility.

Step-by-step explanation:

To find the force that Dora's bicep muscle must generate to hold a 20 kg object at a 90° angle, we use the concept of torque (τ = r x F). Since the torque produced by the weight of the object is equal to the torque produced by the biceps muscle, we can set them equal: (rweight x Fweight = rbicep x Fbicep). The distance from Dora's palm to her elbow is 32 cm (rweight), the weight of the object is 20 kg, which equates to 196 Newtons (Fweight, considering g = 9.8 m / s2), and the distance from her elbow to her biceps insertion is 4 cm (rbicep). So, the necessary force that Dora's biceps must generate is 1568 N.

When Dora's biceps muscle shortens by 3 cm at a velocity of 60 mm / sec, the distance by which Dora lifts the object is 3 cm, and the object's linear velocity is 60 mm / sec, the same as the muscle's shortening velocity, since the forearm's motion is directly caused by the biceps contraction.

Discussing the functional advantages and disadvantages of the human arm design, we note that the relatively short lever arm of the biceps muscle means larger forces are required to lift objects, which can be seen as a disadvantage. However, this arrangement allows for a greater range of motion and agility, which are functional advantages especially in complex tasks such as manipulation of tools or objects.