Question

Four forces act on an object, given by A = 37.3 N east, B = 49.3 N north, C = 70.7 N west, and D = 68.7 N south. (Assume east and north are directed along the +x-axis and +y-axis, respectively.)

(a) What is the magnitude of the net force (in N) on the object? _______N

(b) What is the direction of the force? (Enter your answer in degrees counterclockwise from the +x-axis.) _________° counterclockwise from the +x-axis

Answer 1

Given:

A = 37.3 N along east

B = 49.3 N along north

C = 70.7 N along west

D = 68.7 N along south

(a)

resultant force of A and C is Fac = C – A = 70.7 – 37.3 = 33.4 along -ve x axis

resultant force of B and D is Fbd = D – B = 68.7 – 49.3 = 19.4 along -ve Y axis

the total force, F = (Fac² + Fbd²)^1/2 = (33.4² + 19.4²)^1/2 =38.62 N

the magnitude of the net force on the object, F = 38.62 N

( b)

Let θ be the angle between -ve x axis and total force F, then

Tanθ = Fbd/Fac = 19.4/33.4 = 0.5808

Angle θ = tan^-1 0.5808 = 30.1⁰ counter clockwise from -ve x axis = 212.1⁰ counter clockwise from +ve x axis

The direction of the resultant force is θ = 212.1⁰ counter clockwise from +ve x axis