Force with regard to 0 acceleration

[joel amos]

Premise: Ball A is accelerated on a level, frictionless plane until it reaches a velocity of 5 m/s. Ball A travels at 0 acceleration until it collides with Ball B.

Statements:
1. According to F = ma , Ball A cannot produce a force at 0 acceleration.
2. Upon collision, Ball A applies a force on Ball B.

From what I've learned, both of the statements are true. However, they clearly contradict each other. What's the cause of my confusion?

 

[hokhani]

Once the ball A hits the ball B, its velocity will change and hence it will have acceleration and therefore apply force to B.

 

[WannabeNewton]

1. According to F = ma , Ball A cannot produce a force at 0 acceleration.

Just because a given object is not itself accelerating doesn't mean it can't exert a force on something else. If I place a book on top of a table then it isn't accelerating but it exerts a downward force on the table. Similarly let's say we have some particle A traveling with some constant velocity towards some particle B, which is also traveling at some constant velocity towards A. When A collides with B, A exerts some force on B and by Newton's 3rd law B will exert an equal and opposite force on A.

 

[joel amos]

Once the ball A hits the ball B, its velocity will change and hence it will have acceleration and therefore apply force to B.

But wouldn't the acceleration of Ball A be negative upon impact, causing the force applied to be negative. If the force is negative, wouldn't that mean that Ball B moves in the opposite direction?

 

[hokhani]

According to the third Newton's law, it doesn't matter to say A applied force to B or vice versa.

 

[Doc Al]

Statements:
1. According to F = ma , Ball A cannot produce a force at 0 acceleration.

Newton's 2nd law tells you that 0 acceleration means zero net force. During its travel at constant velocity, the net force on the ball must be zero.

2. Upon collision, Ball A applies a force on Ball B.

And Ball B applies an equal and opposite force on Ball A. Once the collision happens, it's no longer true that there is 0 net force on Ball A or that its acceleration is zero.

From what I've learned, both of the statements are true. However, they clearly contradict each other. What's the cause of my confusion?

No contradiction at all. They describe different situations.

 

[Doc Al]

But wouldn't the acceleration of Ball A be negative upon impact, causing the force applied to be negative. If the force is negative, wouldn't that mean that Ball B moves in the opposite direction?

If you call the original direction of motion of Ball A the positive direction, then Ball B will exert a negative force on Ball A. Which means that Ball A will be accelerated in the negative direction (slowing it down).

And Ball A exerts a positive force on Ball B, giving Ball B a positive acceleration.

 

[joel amos]

If you call the original direction of motion of Ball A the positive direction, then Ball B will exert a negative force on Ball A. Which means that Ball A will be accelerated in the negative direction (slowing it down).

And Ball A exerts a positive force on Ball B, giving Ball B a positive acceleration.

Thanks!

 

[Lsos]

There really is no distinction between "acceleration" and "deceleration" from an F=ma standpoint. Negative and positive values only mean that the direction is different, but it's still "acceleration". Pressing on the gas pedal, stepping on the brake pedal, or going around the Earth in a satellite are all the same from an F=ma standpoint.