Question

Given F1: a force of magnitude 6 N at an angle of 30°
F2: a force of magnitude 8 N at an angle of 50°C

a. Find F1+ F2 analytically (using equations instead of graphing) and write it in the form Fr1i + Fr2 j
b. Find the magnitude FR and θ_resultant

Answer 1

Answer:

13.8 N

$41.44^{\circ}$

Explanation:

$F_1=6\ \text{N}$

$F_2=8\ \text{N}$

$F_1\cos\theta_1\hat{i}+F_1\sin\theta_1\hat{j}\\ =6\cos30^{\circ}+6\sin30^{\circ}\hat{j}\\ =5.2\hat{i}+3\hat{j}$

$F_2\cos\theta_2\hat{i}+F_2\sin\theta_2\hat{j}\\ =8\cos50^{\circ}+8\sin50^{\circ}\hat{j}\\ =5.14\hat{i}+6.13\hat{j}$

$F_R=F_1+F_2=10.34\hat{i}+9.13\hat{j}$

$|F_R|=\sqrt{10.34^2+9.13^2}=13.8\ \text{N}$

The magnitude of the resultant is 13.8 N

Direction is given by

$\tan^{-1}=\dfrac{y}{x}=\tan^{-1}\dfrac{9.13}{10.34}=41.44^{\circ}$

The angle of the resultant is $41.44^{\circ}$