# Kinetic friction in an accelerating Frame of Reference

## Main Question or Discussion Point

Can the kinetic friction be in the direction of acceleration? I am thinking of the example of a box on a flatbed truck accelerating to the right from rest. The box accelerates to the left due to the inertial force as seen by an observer on the truck where the kinetic friction is opposite to the direction of this inertial force and assuming that the inertial force is greater than the kinetic friction.
My difficulty is trying to understand how would the kinetic friction be the cause of acceleration as seen by the ground? any clarification would be appreciated.

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sophiecentaur
Gold Member
The best way to approach this would probably be to believe there is an answer, for a start. The secret would be to look at all the forces involved.
In this case, with no friction, the truck would accelerate more than with friction. ( The box would just be left behind and fall off.) When there is friction, the force on the truck from the box will oppose its acceleration. No violation of 'direction'. The box will accelerate, of course, because the force on it is in the appropriate direction.

My difficulty is trying to understand how would the kinetic friction be the cause of acceleration as seen by the ground? any clarification would be appreciated.
I suppose you mean here the acceleration of the box.
For the ground observer the box accelerates to the right, under the action of the friction force between the box and the truck's bed.
This acceleration is smaller than the acceleration of the truck itself so the box is left behind by the moving truck.

Thank you sophiecentaur and nasu for the clarification.

Dale
Mentor
My difficulty is trying to understand how would the kinetic friction be the cause of acceleration as seen by the ground? any clarification would be appreciated.
In many cases an object is acted on by three forces: gravity, the normal force, and friction. If the ground is level then the normal force cancels out gravity and the net force is equal to the friction force. In such cases the friction will always be the cause of the acceleration, and the friction force must be in the same direction as the acceleration.

It is clear that friction is the cause of deceleration but in the above example it is causing acceleration and not deceleration as seen by an observer on the ground.

sophiecentaur
Gold Member
Perhaps you could look at the Energy situation rather than getting distracted by the use of the words acceleration and deceleration. 'Deceleration' is no more than negative acceleration and both are due to forces. The actual direction of a force is not necessarily linked to the Energy transfer.

The friction between two surfaces will produce two equal and opposite forces. The force on the box is equal and opposite to the force on the truck. The box is being accelerated because a force acts on it and it gains kinetic energy. So friction is taking some energy from the truck and transferring it to the box - plus there is some heat as a consequence of the slipping over the truck floor. The total amount of KE after the event will be less than before - so your worry about the apparent paradox is groundless; friction causes loss of energy as usual. The details of forces and directions are, actually, not relevant.

Dale
Mentor
It is clear that friction is the cause of deceleration but in the above example it is causing acceleration and not deceleration as seen by an observer on the ground.
There is nothing which prevents friction from causing acceleration. After all, that is how both cars and feet work.

sophiecentaur