PHYSICS S.S ONE (ELASTICITY)

THIRD TERM 

WEEK: 2

ELASTICITY

 Elasticity is the ability of a substance to regain its original shape and size after being distorted by an external force.

Elastic material is one that regains its original shape and size after the distorting force has been removed.

Hooke’s law states that provided the elastic limit of an elastic material is not exceeded, the extension, e, of the material is directly proportional to the load or applied force, F.

F α e

F=ke. Force is measure in Newton (N), extension is measure in metre.

TERMS IN ELASTICITY

Elastic limit: is the limit of force beyond which the stretched wire does not return to its original length when the stretching force is removed.

Yield point: is the point beyond the elastic limit in which the elastic limit in which the elastic material has yielded all its elasticity permanently and has become plastic.

Elastic constant or stiffness: of an elastic material is the force required to give unit extension.

Example: A spring 20 cm long is stretched to 25 cm by a load of 50 N. what will be its length when stretched by 100 N assuming that the elastic limit is not reached.

Solution

F= ke,   k = ,     k =  ;     k =  ;    k = 1000Nm-1

F = k e ; e =  ;   e =  ;  e = 0.1m ;  e = 10cm

Tensile stress: is the ratio of the force to the area. Stress =   ; the unit is Nm-2

Tensile strain: is the ratio of the extension to original length.  Strain =  . It has no unit.

Young’s modulus =  ;      Y    =     

Work done in stretching or compressing a material is the same as the energy stored in the material or its elastic potential energy, and is given by

W = F e  (maximum force) X extension

W =  k e2

EXAMPLE

1. A nylon string has a diameter of 2 mm, pulled by a force of 100 N. Determine the stress!

Known :

Force (F) = 100 N, Diameter (d) = 2 mm = 0.002 m, Radius (r) = 1 mm = 0.001 m, The stress = ?

Solution :

Area :

A = π r2

A = (3.14)(0.001 m)2 = 0.00000314 m2

A = 3.14 x 10-6 m2

2. A cord has original length of 100 cm is pulled by a force. The change in length of the cord is 2 mm. Determine the strain!

Known :

Original length (l0) = 100 cm = 1 m, The change in length (Δl) = 2 mm = 0.002 m, The strain = ?

Solution :

3. A string 4 mm in diameter has original length 2 m. The string is pulled by a force of 200 N. If the final length of the spring is 2.02 m, determine : (a) stress (b) strain (c) Young’s modulus

Known :

Diameter (d) = 4 mm = 0.004 m, Radius (r) = 2 mm = 0.002 m

Area (A) = π r2 = (3.14)(0.002 m)2

Area (A) = 0.00001256 m2 = 12.56 x 10-6 m2

Force (F) = 200 N

Original length of spring (l0) = 2 m

The change in length (Δl) = 2.02 – 2 = 0.02 m

Wanted : (a) The stress (b) The strain c) Young’s modulus

Solution :

(a) The stress 

(b) The Strain

(c) Young’s modulus

4. A string has a diameter of 1 cm and the original length of 2 m. The string is pulled by a force of 200 N. Determine the change in length of the string! Young’s modulus of the string = 5 x 109 N/m2

Known :

Young’s modulus (E) = 5 x 109 N/m2, Original length (l0) = 2 m, Force (F) = 200 N

Diameter (d) = 1 cm = 0.01 m, Radius (r) = 0.5 cm = 0.005 m = 5 x 10-3 m

Area (A) = π r2 = (3.14)(5 x 10-3 m)2 = (3.14)(25 x 10-6 m2)

Area (A) = 78.5 x 10-6 m2 = 7.85 x 10-5 m2

Wanted : The change in length (Δl)

Solution :

Young’s modulus formula :

The change in length :

5. A concrete has a height of 5 meters and has unit area of 3 m2 supports a mass of 30,000 kg. Determine (a) The stress (b) The strain (c) The change in height!    Acceleration due to gravity (g) = 10 m/s2. Young’s modulus of concrete = 20 x 109N/m2

Known :

Young’s modulus of concrete = 20 x 109 N/m2, Initial height (l0) = 5 meters, Unit area (A) = 3 m2

Weight (w) = m g = (30,000)(10) = 300,000 N

Wanted : (a) The stress (b) The strain (c) The change in height!

Solution :

(a) The stress

(b) The Strain

ASSIGNMENT

An elastic body of circular area of 60cm2 which extended by 0.53cm when a load of 50N is applied. Calculate (a) stress  (b) the work done by the force (c) the young’s modulus, if strain = 7.5.

[ans (a) 83.33N/m2  (b) 0.1325J  (c) 11.1 N/m2]

 

 

 

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