Question

The Hebrides Macaque sleeps upside down, hanging off of tree branches by its thick, strong tail. The body-length, mass, tail length, and tail diameter (or 'thickness') is measured in a population of these monkeys. The dimensions for a particular juvenile specimen are as follows:

Body length: 35 cm
Mass: 13 kg
Unstrained tail length: 30 cm
Tail thickness: 3 cm

(a) Assuming that the tail is essentially cylindrical and acts under tension as an elastic material with Young's modulus 4.5××1066 N/m22, what is the approximate length of the srained tail as the monkey sleeps?

l strained =  

(b) What is the strain, ϵϵ, of the tail as the juvenile monkey sleeps?

ϵϵ =

(c) It is found that as these monkeys grow, all aspects of their bodies grow isometrically with the exception of tail thickness, which grows to maintain a constant sleeping-posture strain (i.e. so that the tail experiences the same strain, when the monkey is hanging by the tail). What would you expect the length and thickness of the tail to be of a large adult of mass 45 kg?
(For simplicity, presume that the tail's contribution to the body mass is ignorable.)

Adult Tail Length =  
Adult Tail Thickness =  

Answer 1

(a) body mass m = 13 kg

unstrained tail length L = 30 cm = 0.3 m

tail thickness d = 3 cm = 0.03 m

young's modulus E = 4.5 x 10^6 N/m^2

Solution:

Weight of body w = mg = 13 x 9.81 = 127.53 N

since the tail is cylindrical so radius of tail r = d/2 = 0.015 m

stress can be defined as;

Also, stress is directly proportional to strain, therefore

increase in length,

strained length of tail;

(b) find strain;

(c) mass of adult monkey M = 45 kg

weight W = Mg = 45 x 9.81 = 441.45 N

since strain is given as same, therefore;

Now stress;

thus,

Adult tail length;