Physics 10 Grade Crystalline and amorphous bodies Application 3

Application 3

Example – 1:

§  A wire 2 m long and 2 mm in diameter, when stretched by weight of 8 kg has its length increased by 0.24 mm. Find the stress, strain and Young’s modulus of the material of the wire. g = 9.8 m/s² .

Problem – 2:

§  A wire of length 2 m and cross-sectional area 10^-4 m² is stretched by a load 102 kg. The wire is stretched by 0.1 cm. Calculate longitudinal stress, longitudinal strain and Youn’s modulus of the material of wire.

Example – 3:

§  A mild steel wire of radius 0.5 mm and length 3 m is stretched by a force of 49 N. calculate a) longitudinal stress, b) longitudinal strain c) elongation produced in the body if Y for steel is 2.1 × 10¹¹ N/m².

Example – 4:

§  A metal wire 1 m long and of 2 mm diameter is stretched by a load of 40 kg. If Y = 7 × 10¹⁰ N/m² for the metal, find the (1) stress (2) strain and (3) force constant of the material of the wire.

Example – 5:

§  What must be the elongation of a wire 5m long so that the strain is 1% of 0.1? If the wire has cross-selection of 1mm² and is stretched by 10 kg-wt, what is the stress?

Example-6:

§  A brass wire of length 2 m has its one end, fixed to a rigid support and from the other end a 4 kg wt is suspended. If the radius of the wire is  0.35 mm, find the extension produced in the wire.  g = 9.81m/s² ,Y = 11 × 10¹⁰ N/m²

Example-7:

§  A wire of length 1.5 m and of radius 0.4 mm is stretched by 1.2 mm on loading. If the Young’s modulus of its material is 12.5 × 10¹⁰ N/m². , find the stretching force.

Example – 8:

§  What force is required to stretch a steel wire 1 cm2 in cross-section to double its length? Y = 2× 10¹¹ N/m². Assume Hooke’s law.

Example – 9:

§  Find the maximum load which may be placed on a tungsten wire of diameter 2 mm so that the permitted strain not exceed 1/1000. Young’s modulus fortungsten = Y = 35 × 10¹⁰ N/m².

Problem – 10:

§  A mass of 2kg is hung from a steel wire of radius 0.5 mm and length 3m. Compute the extension produced. What should be the minimum radius of wire so that elastic limit is not exceeded. Elastic limit for steel is 2.4 × 10⁸ N/m², Y for steel = Y = 20 × 10¹⁰ N/m²

Example – 11:

§  A wire is stretched by the application of a force of 50 kg wt/sq. cm. What is the percentage increase in the length of the wire? Y = 7 × 10¹⁰ N/m², g = 9.8 m/s²

Problem – 12:

§  A compressive force of 4 × 10⁴ N is exerted at the end of a bone of length 30 cm and 4 cm² square cross-sectional area. What will happen to the bone? Calculate the change in length of a bone. Compressive strength of bone is 7.7 × 10⁸ N/m² and Young’s modulus of bone is 1.5 × 10¹⁰ N/m²

Example – 13:

§  The radius of a copper bar is 4 mm. What force is required to stretch the rod by 20% of its length assuming that the elastic limit is not exceeded?  Y = 12 × 10¹⁰ N/m².

Example – 14:

§  Find the change in length of a wire 5m long and 1 mm² in cross-section when the stretching force is 10 kg-wt. Y = 4.9 × 10¹¹ N/m². and g=9.8 m/s² .

Example – 15:

§  Elastic limit is exceeded when the strain in a wire (Y=14 × 10¹¹ N/m² ) exceeds 1/2000. If the area of the cross-section of the wire is 0.02 cm², find the maximum load that can be used for stretching the wire without causing a permanent set.

Example – 16:

§  Elastic limit of steel is exceeded when the stress on given steel wire exceeds 8.26 × 10⁸ N/m². Can a steel wire ( Y = 2 × 10¹¹ N/m² ) 2m long be stretched by 10 mm without exceeding the elastic limit?

Example – 17:

§  Young’s modulus of the material of a wire is 9.68 × 10¹⁰ N/m². A wire of this material of diameter 0.95 mm is stretched by applying a certain force. What should be the limit of this force if the strain is not to exceed 1 in 1000?

Example – 18:

§  The elastic limit of copper is 1.5 × 10⁸ N/m². A copper wire is to be stretched by a load of 10 kg. find the minimum diameter the wire must have if the elastic limit is not to be exceeded.

Example – 19:

§  What would be the greatest length of a steel wire which when fixed at one end can hang freely without breaking? Density of steel = 7800 kg/m³. Breaking stress for steel = 7.8 × 10⁸ N/m².