A mouse and an elephant fall from a height of 3 meters. Will they both suffer th

Question

A mouse and an elephant fall from a height of 3 meters. Will they both suffer the same? To answer this question, we will attempt to estimate the stress applied to the bones of the mouse and the elephant in this scenario.

4a) Write down an equation for the energy of an animal of mass m that falls h meters.

4b) Imagine the legs act jointly as a single spring of spring constant k. How far must the bones of the leg compress to dissipate the energy of the fall? (Write this down as an equation that is a function of the mass of the animal, the height of the fall, and other constants.)

4c) Write down an equation for the spring constant of an animal’s legs, as a function of the combined foot area, leg length, and Young’s modulus of bone.

4h) Who hurts more after the fall – the elephant, or the mouse? Why?

Explanation / Answer

a) Stress= applied force /area

applied force = mg

area of mouse is much smaller than area of elephant and mass of mouse is also less than mass of elephnat, which will result in creating less stress for mouse and less damage for mouse.

4a) Energy = mgh = 1/2 mv^2

b)mgh = 1/2kx^2

x^2 = 2mgh / k

x= sqroot ( 2mgh/k)

c)stress/ strain = Y

F/ area/ change in length / original length = Y

F/ area / x/ L = Y

F ( L)/ (x) (area) = Y

F =kx

K ( L)/ area = Y

K = area (Y)/ L

F = kx

h) elephant = more stress

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