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A surgeon is using material from a donated heart to repair a patient’s damaged aorta and needs to know the elastic characteristics of this aortal material. Tests performed on a 16.0-cm strip of the donated aorta reveal that it stretches 3.75 cm when a 1.50-N pull is exerted on it.

(a) What is the force constant of this strip of aortal material?

(b) If the maximum distance it will be able to stretch when it replaces the aorta in the damaged heart is 1.14 cm, what is the greatest force it will be able to exert there?

Short Answer

Expert verified

a) The force constant of the aorta is 40 N/m .

b) The force on the aorta when the stretch is 0.0114 m is 0.456 N .

Step by step solution

01

Identification of given data

The given data can be listed below,

  • The length of the aorta is,l=16cm .
  • The force exerted on the aorta is,F=1.50N .
  • The stretch in the aorta is,x=3.75cm .
02

Concept/Significance of force.

When describing a physical motion or movement, the term "force" alludes to strength or energy. It is physical motion or movement that demonstrates strength or vigour.

03

Determination of the force constant of the aorta strip of aortal material

The force constant of the aorta is given by,

F=kxk=Fx

Here, F is the force on the aorta, and x is the stretch in the aorta.

Substitute all the values in the above,

k=1.50N0.0375m=40N/m

Thus, the force constant of the aorta is 40 N/m .

04

(b) Determination of the greatest force will be able to exert there when the maximum distance of stretch is 1.14 cm

The force on the aorta is given by,

F = kx

Here, k is the force constant, and x is the maximum distance of stretch.

Substitute all the values in the above,

F=40N/m1.14m10-2m1cm=0.456N

Thus, the force on the aorta when the stretch is 0.0114 m is 0.456 N .

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