Calculating Stopping Distance for a Moving Truck and Box to Prevent Sliding

AI Thread Summary
To prevent the box from sliding in a moving truck, the deceleration of the truck must not exceed the friction force between the box and the truck's floor. The coefficient of static friction is 0.40, which is crucial for calculating the maximum deceleration. As the truck decelerates, if the deceleration matches or surpasses the friction force, the box will slide. The discussion highlights the importance of understanding Newton's laws in this context. Proper calculations are necessary to determine the least stopping distance to ensure the box remains stationary.
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The coefficent of static friction between the floor of a truck and a box resting on it is 0.40. The truck is traveling at 82.9 km/hr. What is the least distance in which the truck can stop and ensure that the box does not slide?

No idea where to even start...
 
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Doesn't seem like they gave you enough info to solve this quantitatively.
In order for the box to not move it cannot meet or exceed the friction force. This is force is equal to the coefficient of friction*mass of the box*acceleration (gravity).

The truck and the box are already moving and according to Newton an object in motion tends to stay in motion, so when the truck slows (negative acceleration) the box will slide if the deceleration is an equal or greater magnitude than the friction force between the truck and the box.

I hope this helps. I confused myself writing it so if you have any questions please feel free to ask.
 
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