# Josh pushes on a 70 kg box in the positive direction with a force of 50 N. Marissa pushes on the box in the negative direction with a force of 35 N. If the force of friction is 2N, what is the acceleration of the box?

Jul 9, 2018

I get approximately $0.186 \setminus {\text{m/s}}^{2}$.

#### Explanation:

We see that Josh's force vector neutralizes all of Marissa's force vector and then gives an additional boost of $50 \setminus \text{N"-35 \ "N"=15 \ "N}$. Assuming that the frictional force was opposite to Josh's push, i.e. towards Marissa's direction, then the total force in favor of Josh will be $15 \setminus \text{N"-2 \ "N"=13 \ "N}$.

To find the acceleration, we use Newton's second law of motion, which states that,

$F = m a$

where:

• $F$ is the force exerted in newtons

• $m$ is the mass of the object in kilograms

• $a$ is the acceleration in meters per second squared

So, we get:

$a = \frac{F}{m}$

$= \left(13 \setminus \text{N")/(70 \ "kg}\right)$

$= \left(13 {\textcolor{red}{\cancel{\textcolor{b l a c k}{\text{kg""m/s"^2)/(70color(red)cancelcolor(black)"kg") \ (because 1 \ "N"-=1 \ "kg m/s}}}}}^{2}\right)$

$\approx 0.186 \setminus {\text{m/s}}^{2}$