This picture is from Physics for Scientists & Engineers 4th edition by Giancoli

Question

This picture is from Physics for Scientists & Engineers 4th edition by Giancoli (Ch. 5, p. 117).

According to the book, F(G) = mg is resolved into its components F(Gx) and F(Gy).

I understand how F(Gy) = -mg*cos(theta).

However, I don't understand how F(Gx) = mg*sin(theta)?

When I look at the angle furthest to the right (the angle of the slope to the horizontal), sin(theta) = [opposite/hypotenuse] = F(G)/F(Gx), so solving for F(Gx) should = mg/sin(theta), yet they say that it = mg*sin(theta).

Can you please explain how F(Gx) = mg*sin(theta)?

Also (I don't know if I have to do this as a separate question so let me know), can you please explain to me how they know that the angle between F(Gy) and F(G) is the same as the angle furthest to the right (the angle made between the slope and the horizontal (the angle furthest to the right was the only angle they gave in the picture in the problem)?

Explanation / Answer

You need to remember that the hypotenuese is the longest side of a triangle.  You always multiply a sine or cosine function with the hypotenuese for components of a vector.

As for the angle you can use some sort of right angle law.  I think it's easiest if you look at the triangle formed with the horizontal, the x-axis and the fg vector.  This is okay because we are only concerned with the directions.  Since you know theta and you know that fg is perpindicular to the ground the other angle is θ-90. 

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.