A force of 1.00 x 10^2 pounds acts at an angle of 60.0° to the x-axis. (The force is accurate to 3 significant figures.) What are the components of the force along the x-axis? What is the force component along the y-axis?

Fx = 50.0 Pounds : Components of the force along the x-axis

Fy = 86.6 Pounds : Component of the force along the y-axis

Explanation:

Conceptual Analysis

To find the components (Fx, Fy) of the total force (F), we apply the trigonometric concepts for a right triangle, where the perpendicular sides of the triangle are the components (Fx, Fy) of the force (F), the hypotenuse (h) is the magnitude of the total force F and β is the angle that forms the horizontal component with the hypotenuse.

Formulas

cos β : x/h : x: side adjacent to the β angle h: hypotenuse (1)

sin β = y/h : y: side opposite to the β angle h: hypotenuse (2)

Known Data

Known data

F = 1.00 * 10² pounds = 100 pounds : magnitude of total force

β = 60.0° to the x-axis. : Angle that forms the force with the x-axis

Problem Development

We apply the formula 1 to calculate horizontal component (Fx)

cos β : Fx/F

Fx = F cosβ = 100*cos 60° = 50.0 Pounds

We apply the formula 2 to calculate vertical component (Fy)

sin β = Fy/F

Fy = F sinβ = 100*sin 60° = 86.6 Pounds