16. Elasticity and Vibrations

Question 1

Relation between deformation and stress

Answer 1

• when a force is applied to an object, there is a resulting deformation
• stress leads to strain and deformation

Question 2

What are the 3 types of stress?

Answer 2

1. Tensile Stress - leads to a change in the objects length
2. Shearing stress - leads to the twisting and changes the angle of the object
3. Hydraulic stress - leads to a change in the objects volume

Question 3

What is the opposite of tensile stress?

Answer 3

Compressive stress (contraction)

Question 4

When do we describe the response of an object as being ‘elastic’?

Answer 4

• When a material responds to external forces (stress) with a linear deformation (strain)
•When the change in length of an object increases linearly with stress
sigma = Y(∆L/L)

Y - Young’s modulus , the stretchability of a material

Question 5

What happens when the strain is greater than the elastic limit?

Answer 5

The object undergoes permanent plastic deformation

- irreparable damage once the material ruptures

Question 6

When is a material considered to be a ‘plastic’?

Answer 6

When it responds to stress in a non-linear fashion

•plastic deformations are irreversible

Question 7

What is the shear stress?

Answer 7

Defined as the tangential force per unit area of a sheared face.
•leads to shear strain and a deformation that can be quantified by either
- the angle theta or
- by the ratio of the displacement ∆x to the height (thickness of the object)

ref. shear modulus

Question 8

What is hydraulic stress?

Answer 8

•When a force is applied perpendicular to the surface of an object from all sides.
• The resulting hydraulic strain is defined as the ratio of the volume change to the initial volume
• Bulk modulus (compressibility of a material)

Question 9

Explain how aneurysms occur and the what equation can be used to describe it.

Answer 9

Caused by a weakened blood vessel
• the tissue responds to the same blood pressure with larger strain
• results in blood vessel ballooning from hydraulic stress

1. the ballooning decreases the speed of the blood flowing through the vessel
2. this increases the pressure and strain

Question 10

What is hooke’s law?

Answer 10

• applied in the elastic regime of a material when the stress and strain are linearly proportional
• k: spring constant (stiffness of a string)

Question 11

How do you determine the work done to move an object away from equilibrium?

Answer 11

Area under the force vs position curve

Question 12

What is the amplitude when referring to a vibrating object?

Answer 12

The maximum displacement of a vibrating object

Question 13

What terms are given to system which obey Hooke’s law tor produce repetitive motion?

Answer 13

Vibration, oscillation, or periodic motion

Question 14

What is a restoring force?

Answer 14

The force required to hold the object away from equilibrium