In its free body diagram, there are only horizontal resistive forces. How can a car accelerate forward?

I am wondering why a car can accelerate forward even if no forward net force acting on it. See the following diagram.

I don't draw the internal forces due to engine because they don't contribute to the external net force. What am I missing here?

• I think I have to read this: concepts-of-physics.com/mechanics/…. Commented Oct 14, 2021 at 21:13
• The direction of tractive forces is wrong. They are responsible for pushing the car forwards, which they fail to do so on ice. Commented Oct 15, 2021 at 0:27
• That's a good free body diagram for a car slamming on the brakes :) Commented Oct 16, 2021 at 1:19

The friction forces on the bottom of the tyres should point in the direction of motion, not the opposite direction. If there were no friction the wheels would spin and the bottom of the tyres would move backwards on the road surface. Friction must oppose this relative motion. It is this friction that accelerates the car forwards.

• Sorry. I am now wondering if the car then moves uniformly forward, what are additional forces that oppose the friction? Commented Nov 11, 2021 at 14:18

The forces $$F_1$$ and $$F_2$$ are not applied to the wheels. They're applied by the wheels to the road surface, which is presumably attached to a very, very massive self-gravitating object that doesn't move very much in direct response to them.

The reaction force to $$F_1$$ and $$F_2$$ accelerates the car.

• You might add that the reaction force acts at the axle of the wheels (this is important because it determines the accelerative pitch of the vehicle). Commented Oct 15, 2021 at 10:00
• Note that this indicates that the author has an error in their free body diagram -- the forces under consideration should be the forces on the body.
– Dave
Commented Oct 15, 2021 at 15:21

You are probably remembering that friction works opposite the direction of motion, and thinking that means that friction forces work in the direction opposite to the direction that the car is moving. But it's not the car that is making contact with the road, it's the wheels, and the whole point of a wheel is that the point of the wheel that is making contact with the road is at rest with respect to the road. When the engine applies torque to the wheels, the force on the bottom of the wheel is backwards, so the friction is forwards.

Newton's laws apply to a point-like object or a rigid object that can be effectively considered point-like.$$^1$$ This is manifestly not the case here, since the car consists of its body and the weels, which move in respect to the body. The wheels exert the force on the car axis, which makes it move forward/accelerate.

$$^1$$ All the textbooks and most teachers explain it, but it is easily forgotton, as most people focus on the equations. This notably leads to many mistakes/"paradoxes" when trying to apply Newton's laws to human body, see, e.g., this thread.