Chapter 1, Problem 59A

(a)

To determine

The curve by plotting the values from the table that fits all the points.

Answer to Problem 59A

The curve of the all the points is shown in figure (1).

Explanation of Solution

Given Info:

Force (N)	Distance (cm)
5	24
10	49
15	75
20	99
25	120
30	145

Calculation:

  

Figure (1)

(b)

To determine

Description of the resulting curve.

Answer to Problem 59A

The resulting curve shows a linear relationship between the distance and the force.

Explanation of Solution

Introduction:

The relating between the quantity on the vertical axis and horizontal axis describes the resulting curve.

The distance in the curve varies with the force for constant time. The equation of the curve between the distance and force is a straight line that is a linear equation.

Conclusion:

Thus, the resulting curve in the figure (1) is linear curve.

(c)

To determine

The equation relating the distance with force.

Answer to Problem 59A

Explanation of Solution

The curve in the figure (1) shows a line. The equation of the resulting curve is,

  $d=kF$

Here,

• $k$ is the slope of the curve.
• $d$ is the distance.
• F is the force.

(d)

To determine

The constant in the equation and the unit of the equation.

Answer to Problem 59A

The constant is the slope of the resulting curve and the unit of the constant is $\text{cm}/\text{N}$ .

Explanation of Solution

Introduction:

In part (c), the equation represents the slope of the curve. Unit of constant is defined as the ratio of quantity units along the axis from vertical axis to horizontal axis.

The constant in the equation is the slope of the line. The slope is the ratio of the vertical change with the horizontal change. The vertical change is the distance and the horizontal change is the force. The unit of the constant is $\text{cm}/\text{N}$ .

Conclusion:

Thus, the constant is the slope of the resulting curve and the unit of the constant is $\text{cm}/\text{N}$ .

(e)

To determine

The distance travelled by the object.

Answer to Problem 59A

The distance travelled by the object is $110\text{cm}$ .

Explanation of Solution

Given Info:

The force on the object is, $F=22\text{N}$

The constant of the line is, $k=5\text{cm}/\text{N}$ .

Formula Used:

The expression to calculate the distance travelled is,

  $d=kF$

Calculation:

Substitute the values in the above expression.

  $\begin{array}{c}d=\left(5\text{cm}/\text{N}\right)\left(22\text{N}\right)\\ =110\text{cm}\end{array}$

Thus, the distance travelled by the object is $110\text{cm}$ .