What is the minimum stopping distance of a truck with locked brakes?

[DrummingAtom]

Homework Statement

A truck is moving on a level street with speed V_o when the brakes lock (the tires don't roll and skid). Find the minimum stopping distance of the truck in terms of V_o, g, and the coefficient of kinetic friction μ_k.

Homework Equations

W = F*d
W = K₂-K₁
K = 1/2mv²

The Attempt at a Solution

Ok, I think I got this one because want to make sure because when I'm plugging in numbers at the end it seems a little strange.

I started with W = K₂-K₁ and K₂ will be zero because it's stopped at that point.

W = -K₁

I took that -g = n and applied it to the left side, was that step right?

-F*d = -K₁

-F*d = -1/2mV_o²

Solving for d gives:
$$d = \frac{-\frac{1}{2}mV_{o}^2}{-m\mu_{k}g}$$

Then after rearranging:

$$d = \frac{V_{o}^2}{2\mu_kg}$$

Now here's where I'm a little confused, if what I did was right. How can the final equation not have mass? A semi would certainly take a longer distance to stop than a Geo Metro. That's why this equation is so bizarre to me. I'm guessing this is why my Professor assigned this problem, haha. Thanks for any help.

 

[tiny-tim]

Hi DrummingAtom!

Now here's where I'm a little confused, if what I did was right. How can the final equation not have mass? A semi would certainly take a longer distance to stop than a Geo Metro. That's why this equation is so bizarre to me. I'm guessing this is why my Professor assigned this problem, haha. Thanks for any help.

No, your professor thinks this result is perfectly natural …

all the forces are proportional to m, so m doesn't matter.

(btw, air resistance is proportional to size, not mass, so if you include air resistance, the mass does matter)

I'm afraid you're the bizarre one! ​

 

[DrummingAtom]

Haha, thanks.