Chapter 5, Problem 4STP

To determine

To Choose: The correct option.

Answer to Problem 4STP

Option C: $1.58\times {10}^3\text{ N}$

Explanation of Solution

Given:

Mass of the log, $m=1.00\times {10}^3\text{ kg}$

Angle, $\theta ={18.0}^{\text{o}}$

Force by each tractor, $F=8\times {10}^2\text{ N}$

Formula Used:

From Newton’s second law of motion:

  ${\displaystyle \sum F_i=ma}$

Where, m is the mass and a is the acceleration.

Calculation:

Net force along x − axis:

  $F_x=F\cos \theta +F\cos \theta$

Net force along y − axis:

  $F_y=F\sin \theta -F\sin \theta =0$

Force exerted on the log:

  $\begin{array}{c}F\text{'}=F_x\\ =F\cos 9^{\text{o}}+F\cos 9^{\text{o}}\\ =2F\cos 9^{\text{o}}\\ =2\times 8\times {10}^2\text{N}\times \cos {\text{9}}^{\text{o}}\\ =1.58\times {10}^3\text{ N}\end{array}$

Conclusion:

Force exerted by the tractors on the log: $1.58\times {10}^3\text{ N}$ .