Answer to Question #274335 in Physics for Jame

Question

Joey and his friends are pushing a piece of driftwood which they will be using in their landscaping project. They pushed the wood by applying the following forces:

Joey: 5 N, north

Friend 1: 2.2 N, west

Friend 2: 3.86 N, 55° north of west

What is the net force applied by Jerry and his friends on the wood?

Answer 1

Let's find $x$- and $y$-components of the net force:

$F_{net,x}=5\ N\times cos90^{\circ}+2.2\ N\times cos180^{\circ}+3.86\ N\times cos(180^{\circ}-55^{\circ})=-4.41\ N,$$F_{net,y}=5\ N\times sin90^{\circ}+2.2\ N\times sin180^{\circ}+3.86\ N\times sin(180^{\circ}-55^{\circ})=8.16\ N.$

We can find the magnitude of the net force from the Pythagorean theorem:

$$F_{net}=\sqrt{F_{net,x}^2+F_{net,y}^2},$$ $$F_{net}=\sqrt{(-4.41\ N)^2+(8.16\ N)^2}=9.27\ N.$$

We can find the direction of the net force from the geometry:

$$\theta=tan^{-1}(\dfrac{F_y}{F_x}),$$ $$\theta=tan^{-1}(\dfrac{8.16\ N}{-4.41\ N})=62^{\circ}\ N\ of\ W.$$