If a compressive force of 3.2×104N is exerted on the end of a 16cm long bone of cross-sectional area 4.4cm2 , by how much does it shorten? Use Ebone=1.5×1010N/m2, tensile strength of bone = 1.3×108N/m2.
shorten length= F.l/A.E
= 3.2*10^4*16*10^2/4.4*10^-4*1.5*10^10
=7.75*10^-4 m = 0.775mm
To find out by how much the bone shortens, we can use Hooke's law, which states that the strain (change in length) of an object is directly proportional to the applied force and inversely proportional to the tensile strength of the material.
The formula for strain is given by: Strain = (Force / (Tensile Strength * Cross-sectional Area))
In this case, since we are dealing with compression, we need to convert the compressive force to a negative value. So, the compressive force is -3.2×10^4 N.
Now we have all the values we need to calculate the strain:
Strain = (-3.2×10^4 N) / (1.3×10^8 N/m^2 * 4.4×10^-4 m^2).
We can calculate this to find the strain value.
Strain = -0.184.
To find out how much the bone shortens, we need to multiply the strain by the original length of the bone.
Shortening = Strain * Original Length
Shortening = -0.184 * 0.16 m
Shortening = -0.02944 m.
Therefore, the bone shortens by approximately 0.02944 meters (or 29.44 mm).