A child pulls on a box with the force of 60 N directed at an angle of 60 degrees to x axis. What are x and y components of the force?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The child pulls the box with a force of 60 N at an angle of 60 degrees to the x-axis.

As force is a vector quantity and both direction as well as magnitude matter, the force can be split into two components.

The x-component is equal to 60*cos 60

=> 60*0.5

=> 30 N

The y- component is equal to 60*sin 60

=> 60*(sqrt 3)/2

=>30*sqrt 3

The x and y components of the force with a magnitude of 60N at an angle of 60 degrees with the x- axis are 30 N and 30*sqrt 3 N respectively.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

If we'll draw a right angle triangle, whose hypotenuse is the resultant force of 60 N, we'll notice that the angle of 60 degrees is made by the hypotenuse and the horizontal component.

We'll note the requested components as it follows: Fx and Fy.

We'll apply sine function to determine the vertical component.

sin 60 = Fy/F

Fy = F*sin 60 N

Fy = 60*sqrt3/2 N

Fy = 30*sqrt 3 N

Fy = 51.96 N

We'll apply cosine function to determine the horizontal component:

Fx = F*cos 60 N

Fx = 60*1/2

Fx = 30 N

The requested components of the force of 60 N are: Fx = 30 N and Fy = 51.96 N.

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