Chapter 1, Problem 28RE

a

To determine

The data for the given table.

Explanation of Solution

Given:

The diagram for the spring and the force is given as:

  

The equation is given as:

  $F=\frac{5}{4}x,0\le x\le 20$

The table is given as:

  

Here, x is the stretch in the spring in inches from the natural length and F is the force required to do so.

Using the given equation of the F , for the each value of the x , F can determined by substituting the value of x as shown below:

  $\begin{array}{l}F=\frac{5}{4}x\\ \text{For:}\\ x=0\Rightarrow F=0\\ x=4\Rightarrow F=5\\ x=8\Rightarrow F=10\\ x=12\Rightarrow F=15\\ x=16\Rightarrow F=20\\ x=20\Rightarrow F=25\end{array}$

The table is drawn as:

  

b

To determine

To sketch: The graph for the model.

Explanation of Solution

Given:

The diagram for the spring and the force is given as:

  

The equation is given as:

  $F=\frac{5}{4}x,0\le x\le 20$

Drawing the graph using the table:

  

c

To determine

The force required for the stretching of the spring upto 10 inches using the graph.

Explanation of Solution

Given:

The diagram for the spring and the force is given as:

  

The equation is given as:

  $F=\frac{5}{4}x,0\le x\le 20$

The graph is drawn as:

  

Now, at 10 inches draw the perpendicular line to the x- axis, where the line will meet the graph that will be the value of the force required as shown below:

  

Therefore, 12.5 pound force is required for the stretching of the 10 inches.