Question

Three forces with magnitudes of 360 newtons, 200 newtons, and 360 newtons act on an object at angles of −30°, 45°, and 135° respectively, with the positive x-axis. Find the direction and magnitude of the resultant force. (Round your answers to one decimal place.) direction ° magnitude N

Answer 1

Answer:293.45 N ,

`\theta =47.38^(\circ)`

Step-by-step explanation:

Given

Three force of magnitude 360 N, 200 N, 360 N at an angle of
`-30^(\circ),`
`45^(\circ), 135^(\circ)` w.r.t to x axis.

Resolving forces in x and y direction

`R_x=360cos30+200cos45+360cos135=198.605 N`

`R_y=360sin(-30)+200sin(45)+360sin(135)=216.04 N`

Net Force replace these three force is

`R_(net)=√((R_x)^2+(R_y)^2)`

`R_(net)=√(198.605^2+216.04^2)=293.45`

For direction

`tan\theta =(R_y)/(R_x)=(216.04)/(198.605)=1.087`

`\theta =47.38^(\circ)` w.r.t to x axis