A Pickup Truck and a bit of Friction

AI Thread Summary
To determine the shortest stopping distance for a pickup truck carrying a steel file cabinet without it sliding, the coefficient of static friction (µs = 0.8) is crucial. The discussion emphasizes using the equation F = ma to find the necessary acceleration to prevent sliding, despite initial confusion about converting velocity into force. Participants suggest treating mass as a variable, allowing for simplification in calculations. The focus remains on deriving acceleration from frictional forces and then applying that to calculate stopping distance. This approach ensures a clear understanding of the physics involved in the problem.
Bachi234
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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
 
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Welcome to PF!

Bachi234 said:
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! :smile:

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. :smile:
 
Thank you for your welcome =)

How would you use F = ma to find the acceleration when you don't have the mass?
 
Bachi234 said:
How would you use F = ma to find the acceleration when you don't have the mass?

Hi Bachi234! :smile:

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. :wink:

Have a go! :smile:
 

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