# Thread: calculating acceleration from coefficient of friction

1. ## calculating acceleration from coefficient of friction

The floor of a railroad flatcar is loaded with loose crates having a coefficient of static friction of 0.40 with the floor. If the train is initially moving at a speed of 52 km/h, in how short a distance can the train be stopped at constant acceleration without causing the crates to slide over the floor?

2. net force on the crates while stopping will be provided by $F_s$.

the max net force possible would then be $F_{smax} = \mu m g = ma_{max}$

so ... $a_{max}$ has magnitude $\mu g$

using the "no time" kinematics equation ...

$\Delta x = \frac{v_f^2 - v_0^2}{2(-\mu g)}$

3. how would you use it in this situation though?

4. Originally Posted by winterwyrm
how would you use it in this situation though?
The same way skeeter did it. You know the maximum force that friction can have from $f_s = \mu _s N = \mu _s mg$. (Igonre, for the moment that we don't know the mass.) Then using Newton's 2nd Law we get that the maximum acceleration the block can take without sliding is $\sum F = f_s = ma$. Now the mass cancels out so we don't have to worry about it. Thus we get $a = \mu _s g$.

-Dan