A Pickup Truck and a bit of Friction

[Bachi234]

Homework Statement

A pickup truck with a steel bed is carrying a steel file cabinet. If the truck's speed is 27 m/s, what is the shortest distance (m) in which it can stop without the file cabinet sliding? (Use µs = 0.8 for the coefficient of static friction of steel on steel.)

Homework Equations

F=ma

The Attempt at a Solution

Well, to start I made a force diagram and concluded that, as usual, the normal force equals the weight. That only leaves me to worry about the x-axis, the push speed and the friction. But, I'm not sure where to go and I don't remember how to convert velocity into force since velocity isnt' a force. And I can't find the acceleration. Thank you in advance for any help and/or hints!

~Bachi

 

[tiny-tim]

Welcome to PF!

A pickup truck with a steel bed is carrying a steel file cabinet. If the truck's speed is 27 m/s, what is the shortest distance (m) in which it can stop without the file cabinet sliding? (Use µs = 0.8 for the coefficient of static friction of steel on steel.)
…
F=ma
…
Well, to start I made a force diagram and concluded that, as usual, the normal force equals the weight. That only leaves me to worry about the x-axis, the push speed and the friction. But, I'm not sure where to go and I don't remember how to convert velocity into force since velocity isnt' a force. And I can't find the acceleration.

Hi Bachi! Welcome to PF!

Hint: first, use your F = ma to find how much acceleration is needed to make the cabinet slide (you don't need velocity for this part).

Then use that acceleration to find the stopping distance.

 

[Bachi234]

Thank you for your welcome =)

How would you use F = ma to find the acceleration when you don't have the mass?

 

[tiny-tim]

How would you use F = ma to find the acceleration when you don't have the mass?

Hi Bachi234!

Just call the mass m, and write out the equations …

you'll find that everything has an m in it (like mg), and you can just divide by m.

Have a go!