a) In terms of F, A, Y, L 0 , and L, what is the formula for stress? In terms of

Question

a) In terms of F, A, Y, L0, and L, what is the formula for stress? In terms of the same variables, what is the formula for strain?

b) Two rods, which have identical cross sections, are made of different materials and have different lengths. The same stretching force is applied to both. One rod, made of material A, stretches 1 cm while the other, made of material B, stretches 2 cm. Can you identify which material has the greater Young’s modulus? Hint: consider the quantities on which Young’s modulus depends on.

c) A human anterior cruciate ligament that has a length equal to 2.7 cm and a steel rod that has a length equal to 54.0 m are subjected to the same stretching force. Both have the same cross-sectional area. Find the ratio of the change in length of the ACL to the change in length of the steel rod. Use YS = 2 x 1011 N/m2 and YACL = 1 x 108 N/m2.

Explanation / Answer

a) stress = F/A

strain = delta_L/Lo

b) we know, delta_L is inversly proportinal to young's modulus.

so, material A the greater Young’s modulus

c)

we know, Y = (F/A)/(delta_L/Lo)

= F*Lo/(A*delta_L)

delta_L = F*Lo/(A*Y)

in both cases A and F are same

so,

delta_L(ACL)/delta_L(S) = 0.027*2*10^11/(54*1*10^8)

= 1

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