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saul85 [17]
3 years ago
14

A cylindrical specimen of a hypothetical metal alloy is stressed in compression. If its original and final diameters are 30.00 a

nd 30.04 mm, respectively, and its final length is 105.20 mm, compute its original length if the deformation is totally elastic. The elastic and shear moduli for this alloy are 65.5 and 25.4 GPa, respectively.
Engineering
1 answer:
IrinaVladis [17]3 years ago
5 0

Answer:

The original length of the specimen l_{o} = 104.7 mm

Explanation:

Original diameter d_{o} = 30 mm

Final diameter d_{1} = 30.04 mm

Change in diameter Δd = 0.04 mm

Final length l_{1} = 105.20 mm

Elastic modulus E = 65.5 G pa = 65.5 × 10^{3} M pa

Shear modulus G = 25.4 G pa = 25.4 × 10^{3} M pa

We know that the relation between the shear modulus & elastic modulus is given by

G = \frac{E}{2(1 + \mu)}

25.5 = \frac{65.5}{2 (1 + \mu)}

\mu = 0.28

This is the value of possion's ratio.

We know that the possion's ratio is given by

\mu = \frac{\frac{0.04}{30} }{\frac{change \ in \ length}{l_{o} } }

{\frac{change \ in \ length}{l_{o} } = \frac{\frac{0.04}{30} }{0.28}

{\frac{change \ in \ length}{l_{o} } = 0.00476

\frac{l_{1} - l_{o}  }{l_{o}  } = 0.00476

\frac{l_{1} }{l_{o} } = 1.00476

Final length l_{o} = 105.2 m

Original length

l_{o} = \frac{105.2}{1.00476}

l_{o} = 104.7 mm

This is the original length of the specimen.

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Use the case structure in order to do the following tasks. a) Use a five layer case structure in order to do following for a two
Igoryamba

Answer:

The complete answer along with step by step explanation and output results is provided below.

Explanation:

Task a)

#include<iostream>

using namespace std;

int main()

{

  int op;

  double num1, num2;

   cout<<"Enter num1 and num2"<<endl;

   cin>>num1>>num2;  

  // To provide the option of required 5 cases  

  cout << "Select the operation:"

          "\n1 = Addition"

          "\n2 = Subtraction"

          "\n3 = Multiplication"

          "\n4 = Division"

          "\n5 = Negation\n";

  cin >> op;  // user input the desired operation

  switch(op)  // switch to the corresponding case according to user input

   {

       case 1:

           cout <<"The Addition of num1="<<num1<<" and num2="<<num2<<" is: "<<num1+num2;

           break;

       case 2:

           cout <<"The Subtraction of num1="<<num1<<" and num2="<<num2<<" is: "<<num1-num2;

           break;

       case 3:

           cout <<"The Multiplication of num1="<<num1<<" and num2="<<num2<<" is: "<<num1*num2;

           break;

       case 4:        

        while(num2 == 0) // to check if divisor is zero  

        {

           cout << "\nWrong divisor! Please select the correct divisor again: ";

           cin >> num2; // if divisor is zero then ask user to input num2 again

        }

           cout <<"The division of num1="<<num1<<" and num2="<<num2<<" is: "<<num1/num2;

           break;

       case 5:

           cout <<"The Negation of num1="<<num1<<" and num2="<<num2<<" is: "<<-1*num1<<" "<<-1*num2;

           break;

       default:

           // If the operation is other than listed above then error will be shown

           cout << "Error! The selected operatorion is not correct";

           break;

   }

  return 0;

}

Output:

Test 1:

Enter num1 and num2

2

9

Select the operation:

1 = Addition

2 = Subtraction

3 = Multiplication

4 = Division

5 = Negation

1

The Addition of num1=2 and num2=9 is: 11

Hence the output is correct and working as it was required

Test 2:

Enter num1 and num2

8

0

Select the operation:

1 = Addition

2 = Subtraction

3 = Multiplication

4 = Division

5 = Negation

4

Wrong divisor! Please select the correct divisor again: 2

The Division of num1=8 and num2=2 is: 4

Hence the output is correct and working as it was required

Test 3:

Enter num1 and num2

-2

4

Select the operation:

1 = Addition

2 = Subtraction

3 = Multiplication

4 = Division

5 = Negation

5

The Negation of num1=-2 and num2=4 is: 2 -4

Hence the output is correct and working as it was required

Task b)

#include<iostream>

#include<cmath>   // required to calculate square root

using namespace std;

int main()

{

  int op;

  double num;

   cout<<"Enter a real number > 0"<<endl;

   cin>>num;

  cout << "Press 1 for square root:";

  cin >> op;

  switch(op)  // switch to the corresponding case according to user input

   {

       case 1:

          if (num <= 0) // to check if number is less or equal to zero

        {

           cout << "\nError! number is not valid";

           break;   // if number is not valid then terminate program

        }

           cout <<"The square root of num="<<num<<" is: "<<sqrt(num);

// if number is valid then square root will be calculated

           break;

       default:

           // If the operation is other than listed above then error will be shown

           cout << "Error! The selected operation is not correct";

           break;

   }

  return 0;

}

Output:

Test 1:

Enter a real number > 0

6

Press 1 for square root: 1

The square root of num=6 is: 2.44949

Hence the output is correct and working as it was required

Test 2:

Enter a real number > 0

-4

Press 1 for square root: 1

Error! number is not valid

Hence the output is correct and working as it was required

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Explanation:

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