How Is Force Calculated in Trigonometric Free Body Diagrams?

[SLStudent]

Homework Statement

a person is exerting 300 Newton force on the handle of a shovel that makes an angle of 60 deg with the horizontal ground. the component of the 300 newtion force that acts perpendicular to the ground is apporximately what?
possible answers+ 350N 150N 260N 300N

Homework Equations

??

The Attempt at a Solution

not really an attempt but 260N because the resultant would be longer than the component if you can give the Equation i could probly figure it out.
thanks

 

[Brian-san]

It's just setting up trigonometric relations between the parallel/perpendicular components. The 300N force will form the "hypotenuse" of this right triangle.

 

[tomcue]

for the answer, but I think you may have misunderstood the question. The homework statement is asking for the approximate value of the component of the 300 Newton force that acts perpendicular to the ground, not the resultant force. To find this value, we need to use trigonometric functions.

The equation we can use is:

Fperpendicular = F * sinθ

Where F is the force applied (in this case, 300 Newtons) and θ is the angle between the force and the ground (in this case, 60 degrees).

So, the approximate value of the component of the 300 Newton force that acts perpendicular to the ground would be:

Fperpendicular = 300 * sin60 = 300 * 0.866 = 259.8 Newtons, or approximately 260 Newtons.

I hope this helps! Remember, to solve problems like this, it's important to understand the concepts of trigonometry and how they relate to forces and angles. Keep practicing and you'll get the hang of it!