UNIT 4
Worksheet 1 Static Equilibrium
Worksheet 1 Static Equilibrium Answers
Worksheet 2 Mechanical Properties of Solids
Worksheet 2 Mechanical Properties of Solids Answers

 

 

Mechanical Properties of Solids

Worksheet 2 Mechanical Properties of Solids
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ex1 1. A horizontal beam of aluminum 2.0 cm X 2.0 cm cross-section projects 10.0 cm from a wall. A 100 kg object is suspended from the end of the beam. The shear modulus of aluminum is 3.0 X 1010 Nm-2. Neglecting the rod’s mass, find (a) the shear stress on the rod and (b) the vertical deflection of the end of the rod.
Fig 1.1
 
 
 
ex1 2. (a) Twelve identical wooden greenheart columns of cross-section 25.0 cm X 25.0 cm and 3.00 m above ground support a structure of mass 60000 kg. Assuming that the load is distributed uniformly, calculate the (i) strain of each column and (ii) the compression of each column above ground.
Shear Modulus of Greenheart Wood = 2.00 X 109 Nm-2
(b) Each column is buried firmly in a concrete cuboid 1m X 1m X 1m. having mass 2500kg. If this structure rests on a layer of sand 2.0 am deep, with Young's modulus 5.00 X 107 Nm-2, by how much has the building sink after construction? Assume the sand layer rests on an incompressible rock and ignore friction with the sides of the concrete base.
Fig 2.1 (Greenheart House on the Essequibo River in Guyana)
 
ex1

What do we know?
Mass of structure = 6.00 X 104 kg
Cross-sectional Area of column = [2.50 X 10-1 m]2 = 6.25 X 10-2 m-2
Length of column = 3.00 m
Young's Modulus of Greenheart Wood = 2.00 X 1010 Nm-2
Cross-sectional Area of concrete base = [1 m]2 = 1 m2
Length of sand column = 2.00 m
Young's Modulus of Sand = 5.00 X 107 Nm-2

What can we infer?
W = mg, where am is the mass of the object.
Weight of structure Ws= 6.00 X 104 N
Weight on each column Wc= 5.00 X 105 N
Weight on each column + concrete base Wc+b= 5.00 X 105 N

Plan to solve:
We know Stress = [[Force] / [Cross Sectional Area]]
Young's Modulus = [[Stress] / [Strain]]
Strain = [[ΔL] / [L]]

So we can get ΔX if we calculate Strain

 
ex1 3. (a) The steel jack used to raise a pickup truck has four identical struts 3.00 cm X 3.00 cm X 30.0cm long and 2.00 mm thick.
(a) What is the stress on the struts when it raises a mass of 500kg and the separation of the struts is 90°.
(b) Calculate the strain each strut.
(c) Calculate the compression of each strut.
ex1

 

 
4. A steel cable 30 m long has a diameter of 3.0 cm and supports an elevator of mass 1200 kg.
(a) What is the largest load that not permanent stretch the elevator cable if the Yield strength of Steel is 2.00 X 108 Nm-2?
(b) If the Young's Modulus of steel is 2.0 X 1011 Nm-2, how much will the cable stretch before it deforms?
 
ex1 5. A steel wire of length 5.0 m and cross-sectional area 3.0 X 10-5 m2 stretches by the same amount as a copper wire of length 4.0 m and cross-sectional area of 4.0 × 10−5 m2 under a the same load. What is the ratio of the Young’s modulus of steel to that of copper?
 
   
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Concept by Kishore Lal. Programmed by Kishore Lal... Copyright © 2015 Kishore Lal. All rights reserved.