# Biophysics Problem 9

The mass in the diagram slides along a horizontal frictionless floor, pulled by the force $F$ as shown. What is the acceleration?

#### First Step

You should be able to find the net force in the horizontal direction and then substitute into Newton's second law $(F=ma)$ to find the acceleration.

Since there is no friction, the only horizontal force is the horizontal (or $'x'$) component of the $30\;N$ force.

#### Calculations

Remember, the force $F$  made an angle of $37^\circ$ with the horizontal.

Also, the magnitude of $F$ is $30\;N.$

The horizontal component could be represented by $F_x$
or $F_H$

$\text{Since}\; \cos 37^\circ = F_H/F \\ F_H = F \times \cos 37^\circ \\ = (30\; N) \times 0.8 \\ = 24\; N$

Now calculate, using Newton's second law, the magnitude of the acceleration.

Newton's second law is  $F = ma.$

Where $F$ is understood to be the net force in the direction of the acceleration. In this case, there is only one force, in the right direction, and that is the force  $F_H = 24 \;N.$

$\text{Therefore,} \; F = m\times a \\ 24\; N = (12\; kg) \times a \\ a = 2 \; m/s^2 \; \text{to the right}$