# Pushing force with friction

1. Nov 10, 2014

### PiRho31416

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.

2. Nov 11, 2014

### Simon Bridge

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;$$a=0.538\text{m/s}^2$$

3. Nov 11, 2014

### PiRho31416

Simon,

Thanks so much! :)