Question

Two forces, F1 and F2, act at a point. F1 has a magnitude of 9.80 N and is directed at an angle of α = 62.0° above the negative xaxis in the second quadrant. F2 has a magnitudeof 5.20 N and is directed at an angle of β = 53.7° below the negative x axis in the third quadrant.

a. What is the x component Fx of the resultant force?
b. What is the y component Fy of the resultant force?
c. What is the magnitude F of the resultant force?
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.

Answer 1

Step-by-step explanation:

Fx = F₁ cos62 + F₂cos 53.7

= -(9.8cos 62 + 5.2 cos 53.7 )

= - ( 4.6 + 3.07

= - 7.67 N

Fy = F₁ sin 62 - F₂sin 53.7

= 9.8 sin 62 - 5.2 sin 53.7

= 8.65 - 4.19

= 4.46 N

c )

magnitude of resultant F

= √ ( Fx² + Fy²)

= √ ( 7.67² + 4.46²)

= √ ( 58.83 + 19.89)

= 8.87 N

d )

Tanγ = Fy / Fx

= 4.46 / 7.67

.58

γ = 30° approx .