Question

A force of 150N acts on a particle at an angle of 30 degrees to the horizontal. Find the horizontal and vertical components of force.

Answer 1

This explanation from Physics/Geometry

60o |

|

| Fy (the vert. comp.)

↑

← 30o |

Fx (the horizontal componenet)

F = √(Fx2 + Fy2)

Fy = 50 · cos 60o = 50 · (1/2) = 25 N

Fx = 50 · cos 30o = 50 · (√3)/2 = 25√3 N

I see, that vector sign did not appear in my comment above, so the vector equation is

→ → →

F = 50 cos 30o i + 50 cos 60o j

Answer 2

Answer:

The horizontal component of force = 130 N

The vertical component of force = 75 N

Explanation:

• The force is, F = 150 N
• The angle of force to the horizontal surface = 30°
• Horizontal Component of a force: Horizontal component of a force is the force which is applied parallel to the horizontal axis.

         If the force is 'F'. The angle is Ф.

         Then the horizontal component of force will be = FcosФ

         Here F = 150 N and Ф = 30°

         So horizontal component of force = 150 × cos30°

                                                                  = 150 × $\frac{\sqrt{3} }{2}$

                                                                  = 75√3 = 129.9 ≈ 130 N

• Vertical Component of a force: Vertical component of a force is the force which is applied perpendicular to the horizontal axis.

         If the force is 'F'. The angle is Ф.

         Then the horizontal component of force will be = FsinФ

         Here F = 150 N and Ф = 30°

         So horizontal component of force = 150 × sin30°

                                                                  = 150 × $\frac{1 }{2}$

                                                                  = 75 N