Applying Newton's Second Law

A \(\text{10}\) \(\text{kg}\) box is placed on a table. A horizontal force of magnitude \(\text{32}\) \(\text{N}\) is applied to the box. A frictional force of magnitude \(\text{7}\) \(\text{N}\) is present between the surface and the box.

1. Draw a force diagram indicating all of the forces acting on the box.

2. Calculate the acceleration of the box.

Step 1: Identify the horizontal forces and draw a force diagram

We only look at the forces acting in a horizontal direction (left-right) and not vertical (up-down) forces. The applied force and the force of friction will be included. The force of gravity, which is a vertical force, will not be included.

Step 2: Calculate the acceleration of the box

Remember that we consider the \(y\)- and \(x\)-directions separately. In this problem we can ignore the \(y\)-direction because the box is resting on a table with the gravitational force balanced by the normal force.

We have been given:

Applied force \({F}_{1}=\text{32}\text{ N}\)

Frictional force \({F}_{f}=-\text{7}\text{ N}\)

Mass \(m=\text{10}\text{ kg}\)

To calculate the acceleration of the box we will be using the equation \(\vec{F}_{R}=m\vec{a}\).Therefore: \begin{align*}\vec{F}_R &= m\vec{a} \\\vec{F}_1+\vec{F}_f &= (\text{10})\vec{a} \\ (\text{32}-\text{7}) &= (\text{10})\vec{a} \\\text{25} &= (\text{10})\vec{a} \\\vec{a} &= \text{2.5}\text{ m·s$^{-2}$}\ \text{to the left.}\end{align*}