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In this particular example shown the image below (from engineering dynamics - Meriam), I do not figure out why the direction of friction is in direction of the translation of the car?

Or I just didn't get it right and the car is slipping down in that situation?

(see hint 2 and 3 on the right hand side of the page)

Meriam - Engineering Dynamics

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The truck is indeed moving up the hill, and the tires are not slipping. There are a couple of ways to see why the friction points in the direction of the motion of the truck. One way is to keep in mind some external agent must be acting on the truck to get it moving to the right. That is, in your free body diagram there has to be some force acting to the right to get the truck accelerating to the right. You might say that the engine and tires are the thing(s) doing this, but keep in mind, if the road was perfectly frictionless, then the truck would just sit there with its tires spinning. As we turn on friction slowly, the truck wouldn't all the sudden start moving backwards, it would start moving forwards. There is a force responsible for this, and its friction.

Another way is to circumnavigate the above all together and note that the truck is pushing on the road down and to the left, hence by Newton's third law, the road must be pushing on the truck up and to the right. The force that points upward on the truck is the normal force, and the force that points to the right is the (static!) friction force.

EDIT: As per your comment you still seem confused, thats fine. In which case, forget the truck for the moment and let me build up the logic more orderly:

(1) First of all, we have to agree how static friction works. Picture a block on a table with a string attached to the middle of it, and you pull that string to the right. Friction is what opposes the motion of a block sliding on the table, and it always points opposite the motion of the block. If the block is sliding its kinetic friction thats opposing it. If the block isn't sliding, its static friction. Static friction opposes whatever motion the pull intends for the object. For example, if you are pulling the block to the right on a friction-full table, and its not moving, the static friction is what points the left that opposes the motion. Its critical that we agree that this is what static friction is, and how it works.

(2) Now replace the block with a wheel so it can rotate where the string it attached to it (that is, it can roll if it wants to). If the table is (perfectly) frictionless, and you pull on the string to the right, the wheel will just slide as the block did.

(3) Now lets say we turn on friction. The very bottom of the wheel wants to go to the right, but it won't - it will stick (i.e. won't slip) because of friction and the wheel will roll. Remember from the block example above friction is the force on a surface that will oppose the motion of the object if there was no friction. The bottom of the wheel wants to slide to the right, so (static!) friction opposes this and points to the left.

If you still have further questions feel free to let me know, but let me know if you disagree with (1), (2), or (3).

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Note that while the car moves to the right, its contact surfaces - the wheels - are rotating clockwise. This means that they are moving to the left at the point of contact. The grip the tires get is a result of the friction force attempting to halt this movement, which means this force is pointed to the right.

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Each wheel interacts with the ground somehow.

The component of the force acting on the wheel directed along the normal to the surface is called "normal force" (and unless the wheel is glued to the ground the direction is always up), and the component of that force directed along the surface is called "friction force" (depending on what the car is doing it could be directed anywhere along the surface, even to the side when the truck's turning). It's just a convention.

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Although the car is moving towards the right, that doesn't matter. (That's a different science used to make the truck go forward when wheels turn clockwise, and it is not the topic of this question.) What matters is that what two bodies actually are interacting with each other that involve the role of friction or it's reaction. It is the lower surface of the wheels and the road.

Now, the universal fact: Friction always opposes the relative motion between the two bodies who are actually interacting with each other and are experiencing either friction or it's reaction.

So, since the lower surface of the wheels is moving towards left (as in the image, the wheels are rotating clockwise), therefore the friction acts towards the right.

P.S. By left, I mean backward, along (parallel to) the road. By right, I mean forward, along (parallel to) the road.

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