Question

You want to move a heavy box with mass 30.0 kg across a carpeted floor. You pull hard on one of the edges of the box at an angle 30∘ above the horizontal with a force of magnitude 240 N, causing the box to move horizontally. The force of friction between the moving box and the floor has magnitude 41.5 N . What is the box's acceleration just after it begins to move?

Answer 1

Answer:

a=$5.54m/s^{2}$

Explanation:

The net force, $F_{net}$ of the box is expressed as a product of acceleration and mass hence

$F_{net}=ma$ where m is mass and a is acceleration

Making a the subject, a= $\frac {F_{net}}{m}$

From the attached sketch,  

∑ $F_{net}=Fcos\theta-F_{f}$ where $F_{f}$ is frictional force and $\theta$ is horizontal angle

Substituting ∑ $F_{net}$ as $F_{net}$ in the equation where we made a the subject

a= $\frac {Fcos\theta-F_{f}}{m}$

Since we’re given the value of F as 240N, $F_{f}$ as 41.5N, $\theta$ as $30^{o}$ and mass m as 30kg

a= $\frac {240cos30-41.5}{30.0}=\frac {166.346}{30.0}=5.54m/s^{2}$