Question

1. A 500 N force applied to a box at a 50 degree angle above the horizontal surface. Find the x and y
components. Use the cheat sheet located in your blue resource folder, and show all work.

Answer 1

Answer:

The x and y components of the 500 N-force are 321.394 newtons and 383.023 newtons, respectively.

Explanation:

At first we present a figure describing the situation explained on statement, the x and y components of the force are determined by the following trigonometric expressions:

$F_{x} = F\cdot \cos \alpha$ (1)

$F_{y} = F\cdot \sin \alpha$ (2)

Where:

$F$ - Magnitude of the force, measured in newtons.

$\alpha$ - Direction of the force above the horizontal surface, measured in sexagesimal degrees.

If we know that $F = 500\,N$ and $\theta = 50^{\circ}$, then the components of the force is:

$F_{x} = (500\,N)\cdot \cos 50^{\circ}$

$F_{x} = 321.394\,N$

$F_{y} = (500\,N)\cdot \sin 50^{\circ}$

$F_{y} = 383.023\,N$

The x and y components of the 500 N-force are 321.394 newtons and 383.023 newtons, respectively.