Question

11 mark for review a ring is being pulled by three ropes in different directions in a horizontal plane. the magnitude and direction of each force exerted on the ring is represented in the diagram. which of the following correctly describes the direction, if any, of the sum of the force vectors exerted on the ring within the plane shown? a the sum of the force vectors is zero. b the sum of the force vectors is in the +x - direction. c the sum of the force vectors is in the +y - direction. d the sum of the force vectors has components in both the +x - direction and the +y - direction.

Explanation:

Step1: Resolve forces into components

For the 10 N force at 45°:
$F_{1x}=- 10\sin45^{\circ}\text{ N}\approx - 7.07\text{ N}$, $F_{1y}=10\cos45^{\circ}\text{ N}\approx7.07\text{ N}$
For the 10 N force at 60°:
$F_{2x}=10\sin60^{\circ}\text{ N}\approx8.66\text{ N}$, $F_{2y}=- 10\cos60^{\circ}\text{ N}=- 5\text{ N}$
The third - force of 20 N is along the +x - direction, so $F_{3x} = 20\text{ N}$, $F_{3y}=0\text{ N}$

Step2: Calculate the sum of x - components

$F_{x}=F_{1x}+F_{2x}+F_{3x}=-7.07 + 8.66+20=21.59\text{ N}$

Step3: Calculate the sum of y - components

$F_{y}=F_{1y}+F_{2y}+F_{3y}=7.07-5 + 0=2.07\text{ N}$

Answer:

D. The sum of the force vectors has components in both the +x - direction and the +y - direction.