Why Do We Use Sine for the X-Component in Physics Problems?

[Hemingway]

Homework Statement

I am worried that I don't understand a basic part of figuring out the component forces in the following problem. I have a full worked example but there is a few steps which I don't understand why we use sin for the x component and not cos (understand why I am really worried as it appears to be basic trig :/)

A 58-kg skier is coasting down a 25° slope, as Figure 6.7a shows. Near the top of the slope, her speed is 3.6 m/s. She accelerates down the slope because of the gravitational force, even though a kinetic frictional force of magnitude 71 N opposes her motion. Ignoring air resistance, determine the speed at a point that is displaced 57 m downhill.

Homework Equations

vf = √2(KE_f) / m
= √(2(1/2 mv₀² + Sigma F cos theta s)/m
= √(2(1/2 mv₀² + mg sin 25 - fk s) /m
= √(2(1/2 mv₀² + 170N cos 0 x 57) / 58
= 19m/s

The Attempt at a Solution

This was in my textbook:

a free-body diagram for the skier and shows the three external forces acting on her: the gravitational force , the kinetic frictional force , and the normal force . The net external force along the y-axis is zero, because there is no acceleration in that direction (the normal force balances the component mg cos 25° of the weight perpendicular to the slope). Using the data from the table of knowns and unknowns, we find that the net external force along the x-axis is:

SigmaF = mg sin 25 - f_k
= (58)(9.8)(sin 25)(71)
= 170N

I look at sin and think we are looking at y component. I can't see why we would used sin for x component - can someone explain?

Many thanks

H
x

ps. please forgive formating - each time I use latex it just puts large gaps in the place of symbols :)

 

[Hemingway]

AH! My free body diagram was incorrect - all good don't need a reply. thanks anyway those who read through my problem. Sorry for inconvenience.

 

[Mindscrape]

Friction is a nonconservative force, so you can't use conservation of energy.

Sin is used for the x component because you have to draw a similar triangle for the normal force of the skiier. The angle between the force opposite the normal force and gravity is theta. Then trig will tell you that the x component is mgsin(theta).

 

[Hemingway]

Friction is a nonconservative force, so you can't use conservation of energy.

Sin is used for the x component because you have to draw a similar triangle for the normal force of the skiier. The angle between the force opposite the normal force and gravity is theta. Then trig will tell you that the x component is mgsin(theta).

Thank you very much! This really helped me consolidate my understanding :)