Question

A Discuss the possibility of fracture of two leg bones that have a length of about 70cm and an average area of

about 4cm

2 when a 80kg person jump from a height of 300cm.

Noting: The breaking stress of the bone ϬB =1.5×108 N/m2 , and

Young’s modulus for the bone is Y=1.5×1010 N/m2

Answer 1

Answer: The bones won't fracture.

Step-by-step explanation: Stress, in Physics, is a quantity describing forces that can cause deformation. Strain is the measure of how muc an object can be stretched or deformed. The ratio between stress and strain is called Young's modulus or elastic modulus

Breaking Stress of Bone is the maximum stress a bone can take before a rupture occur.

To determine if a person will break his/her bones by jumping from a height, we determine the energy necessary for that jump and compare it with the energy necessary to break a bone.

The energy for breaking a bone is calculated as

`E=(Al_(0)\sigma_(B)^(2))/(2Y)`

A is the area in m²

l₀ is length in m

`\sigma_(B)` is breaking stress in N/m²

Y is Young's modulus in N/m²

Calculating energy to break a bone:

`E=(4.10^(-4).7.10^(-1).(1.5.10^(8))^(2))/(2.(1.5.10^(10)))`

`E=210` J

This is the energy necessary to break one leg bone, so as there are 2, energy will be 420 Joules.

Potential energy gained by jumping is calculated as

E = m.g.h

m is mass in kg

g is acceleration due to gravity in m/s²

h is height in m

Calculating

E = 80.(9.8)(0.3)

E = 235.2 J

Comparing the two energies, potential energy for jumping is less than maximum energy a bone can absorve without breaking, so the leg bones won't suffer a fracture.