a)A disk between vertebrae in the spine is subjected to a shearing force of 540

Question

a)A disk between vertebrae in the spine is subjected to a shearing force of 540 N. Find its shear deformation taking it to have the shear modulus of 1 109 N/m2. The disk is equivalent to a solid cylinder 0.700 cm high and 4.00 cm in diameter.

b)A moonshiner makes the error of filling a glass jar to the brim and capping it tightly. The moonshine expands more than the glass when it warms up, in such a way that the volume increases by 0.3% (that is, V/V0 = 3 10-3) relative to the space available. Calculate the force exerted by the moonshine per square centimeter if the bulk modulus is 1.6 109 N/m2, assuming the jar does not break.

c)During a circus act, one performer swings upside down hanging from a trapeze holding another, also upside-down, performer by the legs. If the upward force on the lower performer is three times her weight, how much do the bones (the femurs) in her upper legs stretch? You may assume each is equivalent to a uniform rod 30.0 cm long and 1.74 cm in radius. Her mass is 57.5 kg.

Explanation / Answer

Here ,

Force = 540 N

shear modulus , S = 1 *10^9 N/m^2

let the deformation is x

x = F * Lo/( S * A)

x = 540 N * 0.70/(1 *10^9 * 3.141 * (0.035/2)^2)

x = 3.92 *10^-4 cm

the shear deformation is 3.92 *10^-4 cm

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