Chapter 6.4, Problem 75E

(a)

To determine

To Find: The force required to keep the truck from rolling down the hill in terms of $d$ .

Answer to Problem 75E

The required expression for the force is.

Explanation of Solution

Given:

The gross weight of the truck is 22 metric ton.

The slope is degree $d$ .

Calculation:

From the given data, the force that is required is the product of weight of the truck and the gravitational force parallel to the road as,

  $F=22\sin d$ .

(b)

To determine

To Find: The graphing utility to complete the given table.

Answer to Problem 75E

The complete table is shown in Table 2

Explanation of Solution

Given:

The given tables is shown in Table 1

Table 1

degree	0	1	2	3	4	5	6	7	8	9	10
$\text{Force}$

Calculation:

Consider the expression for the force is,

  $F=22\sin d$

From the above expression the complete table is shown in Table 2

Table 2

degree	0	1	2	3	4	5	6	7	8	9	10
$\text{Force}$	0	0.38	0.77	1.15	1.53	1.92	2.30	2.68	30.6	3.44	3.82

(c)

To determine

To Find: The force perpendicular to the hill when $d=5°$ .

Answer to Problem 75E

The force that is perpendicular to the hill is $21.92$ metric ton.

Explanation of Solution

Consider the expression for the force is,

  $F=22\cos d$

Consider the force perpendicular to the hill when $d=5°$ is obtained as,

  $\begin{array}{c}F=22\cos 5°\\ =21.92\end{array}$

Then, the force that is perpendicular to the hill is $21.92$ metric ton.