Question

A student attaches a rope to a 20.0 kg box of books. He pulls with a force of 90.0 N at an
angle of 30.0° with the horizontal and walks to the left. The coefficient of kinetic friction
between the box and the sidewalk is 0.500. Find the acceleration of the box.

Answer 1

Problem:

A student attaches a rope to a 20.0 kg box of books. He pulls with a force of 90.0 N at an angle of 30.0° with the horizontal and walks to the left. The coefficient of kinetic friction between the box and the sidewalk is 0.500. Find the acceleration of the box.

Solution:

According to the figure above and second Newton's law:

$$\left\{ \begin{array}{l} N + F \sin \theta = m g \\ F \cos \theta - \mu N = m a \end{array} \right.$$

Where $\theta = 30$ degrees;

N – normal force;

mg – gravitational force;

$\mu = 0.5$ – friction coefficient;

a – acceleration;

F=90 N – pull force;

Thus,

$$a = \frac {F}{m} (\cos \theta + \mu \sin \theta) - \mu g = 0.12 \frac {m}{s ^ {2}}$$

Answer: $a = 0.12\frac{m}{s^2}$