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

13.8 N

`41.44^(\circ)`

Step-by-step 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|=√(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)=(y)/(x)=\tan^(-1)(9.13)/(10.34)=41.44^(\circ)`

The angle of the resultant is
`41.44^(\circ)`