Question

a ball is subject to two forces F1 and F2. The magnitudes of the two forces are 45.0 N and 70.0 N respectively. In the figure below you can see the free body diagram in the ball.

Answer 1

Answer:

• F1.x ≈ -28.93
• F1.y ≈ 34.47
• F2.x = 70
• F2.y = 0
• (F1+F2).x ≈ 41.07
• (F1+F2).y ≈ 34.47
• |F1+F2| ≈ 53.62
• ∠(F1+F2) ≈ 40.0°

Explanation:

A suitable calculator can show you the vector components and their resultant in polar or rectangular format. (See attached.) 2D vectors are conveniently treated as complex numbers, which is why the y-component values are shown as imaginary.

(The 50° angle measured from the -x axis is equivalent to 130° measured from the +x axis, which is the reference we're using here.)

If you'd like to compute the vector components by hand, they are ...

  (x, y) = magnitude×(cos(angle), sin(angle))

This notation is sometimes abbreviated magnitude cis angle, a reference to the complex number form x+yi.