You have decided to sit on an 8 m3cubic marshmallow As a res

You have decided to sit on an 8 m^3-cubic marshmallow. As a result of the stress you exerted on the cube, the marshmallow has doubled in dimensions in both the x-direction and y-direction. Young\'s modulus for the marshmallow is given as 200Pa; take your weight to be 70kg. Take z to be the direction of the stress. Calculate Poisson\'s ratio. Calculate the stress in the x-direction assuming the modulus of elasticity is the same in all directions. Is this compression isotropic?

Solution

Solution :

The dimensions of marshmellow are 2*2*2 m

a) Poissons ratio = lateral strain / linear strain

Lateral strain (Y- direction ) = 1 since the dimesions in doubled

Lateral strain = change in dimension / original dimension = (2y-y)/y = 1

Similary Linear strain(Xdirection ) = 1

Hence poissons ratio = 1/1 = 1

b)

Stress in x-direction = Elastic modulus * Linear strain = 200 Pa *1 = 200 Pa

c) Yes the compression is isotropic since the properties are same along all the three directions