Question

Components of a Force

A man pushes a lawn mower with a force of $30lb$ exerted at an angle of $30°$ to the ground. Find the horizontal and vertical components of the force.

Short answer

The horizontal component of the force $F_H=15\sqrt{3}$and the vertical component of the force is $F_V=-15$

Step-by-step solution

Step 1. Given information

A force is given with magnitude of $30lb$ acting at angle of ${30}^{°}$

Step 2. Concept used

First we have to write force into vector form. To do this, we need direction and the modulus of vector. A vector in component form can be written as-

$v=a_{1}i+a_{2}j$

Where $a_1=\left|v\right|\cos \theta \&a_2=\left|v\right|\sin \theta$

$a_1$ is the horizontal component and $a_2$is the vertical component.

Step 3. Calculation

Horizontal component of force can be written as-

$\begin{array}{l}{F}_H=\left|F\right|\cos \theta \\ F_H=30\cos {30}^{°}\\ =30\times \frac{\sqrt{3}}{2}\\ =15\sqrt{3}\end{array}$

And the vertical component is-

$\begin{array}{l}{F}_V=\left|F\right|\sin \theta \\ F_V=-30\sin {30}^{°}\\ =-30\times \frac{1}{2}\\ =-15\end{array}$