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Trava [24]
3 years ago
6

: A pneumatic "cannon" is a device that launches a low mass projectile from a cylindrical tube using pressurized air stored upst

ream of the projectile. The projectile is held in place while the pressurized air is introduced to the cylinder. After the trigger is released, the projectile accelerates down the tube and the pressure upstream of the projectile drops according to the relation.
p = π [ 1 − (x/d)²] /25

where π is the initial (high) pressure in the tube before the trigger is released, x is the distance traveled by the projectile, and d is the diameter of the tube. If we have a 5.0 cm diameter tube, with a projectile initially located 5.0 tube diameters upstream of the tube exit, and the initial pressure upstream of the projectile is 12 bar. Determine the work done by the air on the projectile during the time it is in the tube. Assume that there is no friction between the tube and the projectile.
Engineering
1 answer:
alukav5142 [94]3 years ago
5 0

Answer:

Work done = 125π J

Explanation:

Given:

P = P_i * ( 1 - (x/d)^2 / 25)

d = 5.0 cm

x = 5 * d cm = 25d

Pi = 12 bar

Work done = integral ( F . dx )

F (x) = P(x) * A

F (x) =  (πd^2 / 4) * P_i * (1 - (x/d)^2 / 25)

Work done = integral ((πd^2 / 4) * P_i * (1 - (x/d)^2 / 25) ) . dx

For Limits 0 < x < 5d

Work done = (πd^2 / 4) * P_i  integral ( (1 - (x/d)^2) / 25)) . dx

Integrate the function wrt x

Work done = (πd^2 / 4) * P_i * ( x - d*(x/d)^3 / 75 )  

Evaluate Limits 0 < x < 5d :

Work done = (πd^2 / 4) * P_i * (5d - 5d / 3)

Work done = (πd^2 / 4) * P_i * (10*d / 3)

Work done = (5 π / 6)d^3 * P_i

Input the values:

Work done = (5 π / 6)(0.05)^3 * (1.2*10^6)

Work done = 125π J

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The Java program that accepts a matrix of M × N order and then interchanges diagonals of the matrix is given below:

<h3>Steps:  </h3>
  • 1. We can only interchange diagonals for a square matrix.
  • 2. Therefore, we would have to create a square matrix of size [M × M].
  • 3. We would check whether the matrix is a square matrix or not. If the matrix is square then follow step 3 else terminate the program.
  • 4. Apply logic for interchange diagonal of the matrix some logic is given below.

<h3>Java Code</h3>

//  Java Program to Accept a Matrix of Order M x N &

//  Interchange the Diagonals

import java.util.Scanner;

public class InterchangeDiagonals {

   public static void main(String[] args)

   {

       // declare variable

       int m, n, i, j, temp;

       // create a object of scanner class

       Scanner sc = new Scanner(System.in);

       System.out.print("Enter number of rows ");

       // take number of rows

       m = sc.nextInt();

       System.out.print("Enter number of columns ");

       // take number of columns

       n = sc.nextInt();

       // declare a mxn order array

       int a[][] = new int[m][n];

       // if block it's execute when m is equals to n

       if (m == n) {

           System.out.println(

               "Enter all the values of matrix ");

           // take the matrix inputs

           for (i = 0; i < m; i++) {

               for (j = 0; j < n; j++) {

                   a[i][j] = sc.nextInt();

               }

           }

           System.out.println("original Matrix:");

           // print the original matrix

           for (i = 0; i < m; i++) {

               for (j = 0; j < n; j++) {

                   System.out.print(a[i][j] + " ");

               }

               System.out.println("");

           }

          // perform interchange

           for (j = 0; j < m; j++) {

               temp = a[j][j];

               a[j][j] = a[j][n - 1 - j];

               a[j][n - 1 - j] = temp;

           }

           System.out.println(

               " after interchanging diagonals of matrix ");

           // print interchanged matrix

           for (i = 0; i < m; i++) {

               for (j = 0; j < n; j++) {

                   System.out.print(a[i][j] + " ");

               }

               System.out.println("");

           }

       }

       // else block it's only execute when m is not equals

       // to n

       else {

           System.out.println("Rows not equal to columns");

       }

   }

}

Read more about java programming here:

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