Horizontal force on a bicycle dependent on center of mass?

[Imperial Sky]

Hello!

If I pedal a bicycle, where is the force that moves the bike forward horizontally applied?
Is it the bottom of the back wheel or the center of the back wheel?

When the force applied to that point is F, does all that force goes into horizontal acceleration, or does some of that force go vertically agaisnt gravity, because there is an angle between the horizontal force and the center of mass? Would the actual horizontal force then be F*cos(a) ?

If anyone could help I would be thankful.

 

[rcgldr]

Newton third law pairs: at the contact patch, the tire exerts a backwads force onto the ground, the ground exerts a forward force onto the bike. At the tire's axle, the tire's axle exerts a forward force onto the bike, the bike exerts a backwards force onto the tire's axle (the bike may be accelerating).

There's also a torque at the rear wheel. This may result in a wheelie, but the forwards force on the bike remains the same, even it the force vector does not go through the center of mass of the bike.

Another example of this is a horizontal force applied to the end of a veritcal rod in space, absent any other forces. The linear motion follows Netwon's law, force = mass x acceleration or acceleration = force / mass, even if the force is not applied at the center. Since the other part of the Newton third last pair is a reaction force, then in order to generate that force at the end of the rod, the point of contact experiences a greater amount of acceleration since it rotates while the center of mass accelerates horizontally.