Force — Question 3

Question 3

Oblique forces may cancel one component

Force A is 10 N at $30^\circ$ above positive x. Force B is 10 N at $30^\circ$ below positive x.

1. Find both component pairs.

2. Find the resultant.

3. How would the resultant change if B were reversed?

Question 3 - Solution

Oblique forces may cancel one component

(a) Resolve with signed angles.

$$\vec A=10(\cos30^\circ,\sin30^\circ)=(5\sqrt3,5)\,\mathrm N,\quad\vec B=(5\sqrt3,-5)\,\mathrm N$$ $\vec A=(5\sqrt3,5)$ N and $\vec B=(5\sqrt3,-5)$ N.

(b) Sum along common axes.

$$\boxed{\vec R=\vec A+\vec B=(10\sqrt3,0)\,\mathrm N}$$ $\vec A+\vec B=(10\sqrt3,0)$ N, a $17.321$ N force along positive x.

(c) Reverse both components of B.

$$\vec R_{\mathrm{reversed}}=\vec A+(-\vec B)=(0,10)\,\mathrm N$$ $\vec A-\vec B=(0,10)$ N, pointing along positive y. Reversal is not merely changing the sign of the angle; it changes the entire vector.