What Is The Frictional Force That Opposes This Motion

Does friction oppose the motion? If yes, why does it help in the motion of a cycle?

Friction does NOT always oppose the motion. Examples:If you are sliding across the floor, your forward sliding motion will be opposite the friction with the floor, which will slow you down.If you get on a raft in a river, friction between the raft and the river current will speed you up because the friction will push on the raft in the same direction as the raft’s motion.With an auto tire, the tire pushes back on the road and so in reaction, the road will push forward on the tire and the car, causing it to speed up.

Why does friction act in a direction opposite to the direction of motion?

Sometimes friction does act in the direction of motion. It depends on whether we are talking about static or kinetic friction.Kinetic friction is a result of two surfaces sliding with respect to each other. That friction tends to resist the relative motion. Most of the time, that means that the frictional force on some object is in the opposite direction of its motion - that is, it tends to slow it down. Think of a block sliding on a horizontal surface, the frictional force opposes the motion. (But there is a case where the kinetic friction can be in the direction of the motion - and, in fact, can cause an acceleration in that direction. But I’ll get to that in a bit.)Static friction is the frictional force that acts between two surfaces that are not in relative motion. Static friction doesn’t oppose motion, but rather opposes forces. That is, it is a force that opposes a force that is trying to cause sliding. Think again of a block on a table - but at rest. If you try to push the block, but don’t push hard enough to move it, you are pushing against static friction. And that friction is just enough to oppose the force you apply and hence there is no net force on the block. If you push slightly harder, the frictional force increases just enough to keep it from sliding. Only after you exceed some maximum value of that static friction will the block slip.But under what circumstance can friction be in the direction of the motion? Suppose that block we were talking about is at rest with respect to a horizontal surface which itself is accelerating to the right. If the block does not slip, it is accelerating to the right with the surface. So the frictional force on the block (static friction, since there is no slipping) is in the direction of the motion.If there is slippage between the accelerating surface and the block, the block is still accelerating, but not at the same rate as the surface. So in that case, the friction on the block is kinetic friction - and is in the direction of the motion.Are there other cases? Of course. You could not walk across the room if static friction against your shoes didn’t act in the direction you are walking. You push against the floor and the floor pushes back. Your car would not accelerate if your tires did not push against the pavement and the pavement pushed against your tires. The force that accelerates your car is the static friction against your tires in the direction you are accelerating.Friction is subtle.