# Why doesn’t friction cause a ball to move in the opposite direction?

When we toss a ball onto a wall, upon collision, by Newton’s third law, the reaction force on the wall would cause the ball to rebound, coming back to us. This is because this force is in our direction.

However, if we roll a ball on a floor with a lot of friction, it just slows to a stop. We know that friction acts in the opposite direction to motion. Wouldn’t this be synonymous to the first scenario and cause the ball to move in the opposite direction?

• One difference is that the line of action of the frictional force does not pass through the centre of mass of the ball when it is rolling on a floor. – Farcher Aug 18 '18 at 7:02
• @Farcher That looks like it should be an answer – David Z Aug 18 '18 at 7:02
• Where would the energy that makes ball move in the other direction come from? At some point the ball will stop, so there will be no relative motion between the ball and the floor - meaning that the kinetic friction will be zero. – Andrei Geanta Aug 18 '18 at 20:54
• Once the ball has stopped, what is the "opposite direction"? – Stéphane Rollandin Aug 20 '18 at 14:03
• What if the coefficient of friction is negative? – N. Steinle Aug 20 '18 at 16:42

Firstly, the first scenario works because the reaction force directly cuts through the centre of mass of a ball, and that the wall being a rigid body will not move. On the other hand, frictional force doesn’t do that, and merely acts on the side of the box, at most generating a torque. For instance, if we slide a box on a surface with high friction, the box will fall forward rather than move forward.

Friction can be said to be a function of the force exerted upon the ball. It is hence directly proportional to the applied force. The greater the force applied, the greater will be the frictional force you experience but only in the opposite direction. Thus, when the exerted force is zero, frictional force is naturally zero.

The real problem is not only in the direction of the friction force, but also in its dissipative nature. It removes kinetic energy from a moving body irreversibly, so when the body stops, it has no energy to move anywhere.

No, it is not synonymous to the first scenario, because friction is a resisting force, relative to the motion of an object, it converts kinetic energy into thermal energy. At the moment that the object loses all its kinetic energy, the friction force will stop instantaneously, not having any force on the object to make it move in the opposite direction.

One analogy that I like is:

Consider the object in motion like a car. Imagine that the friction is like the car's brakes, old brakes, that only function partially. The brakes take away kinetic energy from the car, but as soon as it stops there is no energy left to be taken away, so the brakes no longer have an influence on the car's motion. This way the vehicle will not go backward, in the same way, that the object will not move in the opposite direction as it was initially.

I don't know if this is too much eli5, but I hope it helped you visualize. [my first answer here on StackExchange :)].

To simplify the problem, we could replace a ball by a hockey puck on ice and ask why it bounces back, when it hits a wall, but just slows down in the absence of serious obstacles.

One possible way to think about it is that a puck, as it slides across the ice, undergoes gazillions of micro-collisions with gazillions of micro-obstacles. Each micro-collision takes away a tiny fraction of the puck's kinetic energy as the puck either a) pushes a micro-obstacle out of the way or b) jumps over it.

This outcome of individual collisions is possible because the obstacles are a) easily moved or b) small in comparison to the radius of the puck's edge, which results in an oblique contact and allows the puck to proceed forward with a minor hick-up.

Conversely, if an obstacle was straight and tall enough (in comparison with the radius of the puck's edge) and, at the same time, strong enough to withstand the push, the puck would not have any way to proceed forward and all its kinetic energy would be lost at once, some of it to the heat and some of it converted to the elastic energy stored between the puck and the obstacle, which, in turn, would quickly be converted back to the kinetic energy of the reflected puck.

So, we can say that, although the force of friction is directed against the motion of the puck and the combined work performed during multiple micro-collisions, associated with friction, is equal to the initial kinetic energy of the puck, a specific nature of individual collisions, as described above, makes it impossible to stop the puck at once and send it back.

The line of action of the frictional force does mot pass through the centre of mass of the ball when it is rolling on a floor.

• Wouldn’t it still hit the ball on the sides? Also, why doesn’t it roll after slowing to a stop? – Electricboy Aug 18 '18 at 12:23
• @Electricboy Once the ball stops there is no relative motion between the ball and the floor and so the frictional force is zero. – Farcher Aug 18 '18 at 17:09

Both scenarios are collisions and should be handled as such rather than by the third law. The first case is an elastic collision against huge mass. The second one is complete plastic collision where kinetic energy is lost to friction.

If you insist on using forces, you need to apply impulse-momentum equations. In the second scenario, friction force will gradually reduce momentum. Once at rest, no force will be applied to reverse the motion.

• Throwing a stone on a wall causes not much bouncing;
• throwing a pillow on a wall causes no bouncing;
• throwing a tennis ball on the wall causes much bouncing.

The ball bounces back because of the elasticity of the object's own material (or of the wall for that matter - think of a trampoline).

At impact the normal force pushes back until all kinetic energy in the ball is depleted.

1. If elastic, that kinetic energy is stored as elastic energy. That energy makes the ball want to "spring back" to its original form, causing a spring-back force on the wall. The wall responds with another normal force causing it to bounce.
2. Were there no elasticity, then none of the initial kinetic energy is stored as elastic energy (it may be lost as heat, vibrations, sound etc.). Then the normal force doesn't act anymore after the kinetic energy is depleted, since there is no spring-back force for it to respond to.

Friction works in the same way and you do see elastic materials such as soft rubbers that show a spring-back effect due to friction elastically deforming the touching area. But friction by its very nature, dissipates the kinetic energy as heat and therefore doesn't allow for much of it to be stored elastically.

See, friction is not an actual force. It's a pseudo force. Friction comes into action whenever a body is acted upon by an external force. It itself does never come into action. When a ball is staying on a rough surface, at first there is no friction between the surface and the point of contact. As soon as an external force is applied on it friction comes into play and helps the ball to rotate and to move without sleeping in the direction of the application of force if and only if the couple generated by the applied force about the centre is greater than the couple generated by the frictional force at the centre. It doesn't help the ball to move forward itself. And hence the fact.

• Friction is an actual force... The external force acting on the object is what we call friction in those scenarios. Friction resists relative movement, and can act as an external force on a system you analyze; but that doesn't make it a pseudo-force. – JMac Aug 20 '18 at 16:07