# Pushing force with friction

I just want to check to see if I did the problem correctly.

A person pushes a 2.0 kg box across a flat, horizontal surface with a force of 5.0 N for 4.0 m. Determine the acceleration of a box if the friction coefficient is 0.2.

Determine the acceleration of the box if the friction coefficient is 0.2.

First, we need to find the static force.
$$F_s= \mu F_n = (0.2) (2 \cdot 9.81) = 3.924 \ N$$

Then, we need to find the net force.
$$F_{net} = 5 \ N - 3.924 \ N = 1.076 \ N$$

Then, finally, the acceleration of the box is:
$$F=ma \Rightarrow 1.076 = (2 \ kg) \ a \Rightarrow \boxed{a=0.538 m/s^2}$$

Is that right? Any help is appreciated.

Simon Bridge
Homework Helper
The 5N force was horizontal?
Than that was just about perfect.

It is best practice to do the algebra before putting the numbers in.
So: From Newton's second law: $$F+\mu mg = ma \implies a=\frac{F+\mu mg}{m}$$... F=5N, ##\mu##=0.2, and m=2kg;$$a=0.538\text{m/s}^2$$

Simon,

Thanks so much! :)