A 110 n force and a 55 n force both act on an object point p. the 110 n force acts at 90 degrees. the 55 n force acts at 0 degrees. what is the magnitude and direction of the resultant force?

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19-08-2017
Physics

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A 110 n force and a 55 n force both act on an object point p. the 110 n force acts at 90 degrees. the 55 n force acts at 0 degrees. what is the magnitude and direction of the resultant force?

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Erythrosin17 Erythrosin17 · Answer 1 · 2017-08-29T14:43:26+02:00

To determine the magnitude and the direction of the resultant force, we assume that the forces are in XY coordinate plane and the angles that are given are from the x axis.

The 110 N force is said to act at 90 deg which means it is along the Y axis. The 55 N force is said to act at 0 deg which means it is along the X axis. so, a right angle is made by the two forces. Thus, the

X component of the resultant force = 55 N
Y component of the resultant force = 110 N
Magnitude of the resultant force would be calculated as follows:
R = √(Fx^2 + Fy^2)
R = √(55^2 + 110^2)
R = √(15125)
R = 123 N
The resultant force would have its terminal side in the x-axis. We calculate angle θ as follows:

tan θ = Fy/Fx
tan θ = 110 N /55 N = 2
θ = arctan(2)
θ = 63.4 degrees
Therefore, the magnitude of the resultant force is 123 N and the direction would be at an angle of 63.4 degrees.