Question

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?

Answer 1

Answer:

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