Question

Two forces act on an object. The first force has a magnitude of 17.0 N and is oriented 58.0º counter clockwise from the x-axis, while the 2nd force has x and y components (-19.0 N, 12.5 N). Express the magnitude and direction of the net force. a) 28.7 N, 70º

b) 36.8 N, 70º
c) 28.7 N, 110º
d) 36.8 N, 110º

Answer 1

option a is correct

net force = 28.7 N and 70º

Step-by-step explanation:

given data

first force= 17.0 N

angle = 58.0º

2nd force = -19.0 N and 12.5 N

to find out

magnitude and direction net force

solution

we know here 1st force is at angle 58.0º is 17 N

so here x component of force is F1 cosθ and y component of force is F1 sinθ

so 1st force

x component of force = F1 cosθ = 17 cos(58) = 9.0086 N ...............1

y component of force = F1 sinθ = 17 sin(58) = 14.4168 N ..............2

and 2nd force

x component of force = -19 N .................3

y component of force = 12.5 N ..................4

so net force is

net force = √(Fx²+Fy²)

net force = √((9-19)²+(14.41+12.5)²)

net force = 28.7 N

and

magnitude

tanθ = Fy / Fx

tanθ = 26.92 / 10

θ = 70º

so option a is correct