Mechanical properties of solid bodies Presentation (1)

Mechanical properties of solid bodies

Today’s Theme:

Learning Objectives

To define Young’s modulus under elastic deformation;

Success Criteria

Students have achieved the objective if they are able to
Know the correct definitions for the three terms (stress, strain, and Young's modulus);
explain the relationship between the values (stress, strain, and Young's modulus);
solve problems using the Young's modulus formula;
Analyze the strain of wires of different cross-sections and lengths.

Example

A rigid bar AB of negligible mass is suspended horizontally from two long, vertical wires as shown in the diagram. One wire is made of steel and the other of brass. The wires are fixed at their upper end to a rigid horizontal surface. Each wire is 2.5 m long but they have different cross sectional areas.
When a mass of 16 kg is suspended from the centre of AB, the bar remains horizontal. The Young modulus for steel = 2.0 x 1011 Pa. The Young modulus for brass = 1.0 x 1011 Pa.
What is the tension in each wire?
If the cross sectional area of the steel wire is 2.8 x 10-7 m2, calculate the extension of the steel wire.
Calculate the cross-sectional area of the brass wire.
The brass wire is replaced by a steel wire of the same dimensions as the brass wire. The same mass is suspended from the midpoint of AB.
Which end of the bar is lower?
Calculate the vertical distance between the ends of the bar.

Example

A rigid bar AB of negligible mass is suspended horizontally from two long, vertical wires as shown in the diagram. One wire is made of steel and the other of brass. The wires are fixed at their upper end to a rigid horizontal surface. Each wire is 2.5 m long but they have different cross sectional areas.
When a mass of 16 kg is suspended from the centre of AB, the bar remains horizontal. The Young modulus for steel = 2.0 x 1011 Pa. The Young modulus for brass = 1.0 x 1011 Pa.
What is the tension in each wire? 78.4 N
If the cross sectional area of the steel wire is 2.8 x 10-7 m2, calculate the extension of the steel wire. 0.0035 m
Calculate the cross-sectional area of the brass wire. 5.6 x 10-7 m2
The brass wire is replaced by a steel wire of the same dimensions as the brass wire. The same mass is suspended from the midpoint of AB.
Which end of the bar is lower? Side A
Calculate the vertical distance between the ends of the bar. 0.175 cm

Vocabulary

Respectively, compress, extend, spring (force) constant, apparatus, load, natural length, elastic potential (strain) energy, equilibrium, free oscillation, springs in parallel, springs in series

A

D

D

A

C

A

D

C

D

B

B

B

C

Summary Reflection

Answer the following questions:
1) What is strain?
2) What is stress?
3) What is the Young modulus and how can you calculate it from a graph?
4) Where does elastic deformation end and plastic deformation begin?