Question

Two forces, F1 and F2, act at a point, as shown in the picture. (Figure 1) F1 has a magnitude of 8.00 N and is directed at an angle of α = 62.0 ∘ above the negative x axis in the second quadrant. F2 has a magnitude of 5.60 N and is directed at an angle of β = 52.8 ∘ below the negative x axis in the third

A) What is the x component Fx of the resultant force?

Express your answer in newtons.

B) What is the y component Fy of the resultant force?

Express your answer in newtons.

C) What is the magnitude F of the resultant force?

Express your answer in newtons.

D) What is the angle γ that the resultant force forms with the negative x axis? In this problem, assume that positive angles are measured clockwise from the negative x axis.

Express your answer in degrees.

Answer 1

here,

a)

the x-component Fx of the resultant force , Fx = -(F1 * cos(alpha) + F2 * cos(beta))

Fx = - ( 8 * cos(62) + 5.6 * cos(52.8)) N

Fx = - 7.14 N

b)

the y-component Fy of the resultant force , Fy = (F1 * sin(alpha) - F2 * sin(beta))

Fy = ( 8 * sin(62) - 5.6 * sin(52.8)) N

Fy = 2.6 N

c)

the magnitude F of the resultant force , F = sqrt(Fx^2 + Fy^2)

F = sqrt(7.14^2 + 2.6^2) = 7.6 N

d)

the angle that the resultant force forms with the negative x axis , gamma = arctan(Fy /Fx)

gamma = arctan(2.6 /(7.14)) = 20.01 degree