Newton's 3rd law and an impulse

[WilliamLeung]

If I have a superball and a tomato of the same mass in my hand, and I let it go.
The only force acting on my superball and tomato is gravitational force.
F=ma, they have same mass so they will hit the bathroom scale with the same force.
According to Newton's third law, the bathroom scale will exert the same force to both my superball and tomato.
This force should be the value show in the bathroom scale.
However, the bathroom scale will show the force of the superball is twice than that of the tomato.
Why is this deduction wrong?

 

[phinds]

If I have a superball and a tomato of the same mass in my hand, and I let it go.
The only force acting on my superball and tomato is gravitational force.
F=ma, they have same mass so they will hit the bathroom scale with the same force.
According to Newton's third law, the bathroom scale will exert the same force to both my superball and tomato.
This force should be the value show in the bathroom scale.
However, the bathroom scale will show the force of the superball is twice than that of the tomato.
Why is this deduction wrong?

Do you understand the difference between elastic and inelastic collisions? If not, I suggest you read up on them. Does your superball deform on impact to the same extent that the tomato does?

 

[Dale]

F=ma, they have same mass so they will hit the bathroom scale with the same force

This is not correct. They will have the same initial momentum on impact, but the force depends on their stiffness and other similar details.

 

[jbriggs444]

Force is equivalent to rate of momentum transfer per unit time. A bathroom scale measures the average rate at which momentum is delivered to its upper surface. The total amount of momentum delivered in a collision will depend on both the impact velocity and the rebound velocity, i.e. how elastic the collision is. The rate at which momentum is delivered will depend on the duration of the collision, i.e. how hard the object is.

 

[WilliamLeung]

Do you understand the difference between elastic and inelastic collisions? If not, I suggest you read up on them. Does your superball deform on impact to the same extent that the tomato does?

I do

This is not correct. They will have the same initial momentum on impact, but the force depends on their stiffness and other similar details.

You mean they hit the scale the scale with different force and I can not calculate the force by simply using F=ma?

Force is equivalent to rate of momentum transfer per unit time. A bathroom scale measures the average rate at which momentum is delivered to its upper surface. The total amount of momentum delivered in a collision will depend on both the impact velocity and the rebound velocity, i.e. how elastic the collision is. The rate at which momentum is delivered will depend on the duration of the collision, i.e. how hard the object is.

I understand what you mean, but I am asking why is my reasoning wrong.

 

[Dale]

You mean they hit the scale the scale with different force

Yes. That is what I mean.

I can not calculate the force by simply using F=ma?

Newton's 2nd law remains valid. Since the force is different during the collision the acceleration will also be different during the collision. If you know one, then you can calculate the other.

 

[Low-Q]

Since the tomato isn't exactly elastic, but suffers from permanent deformation after impact, I guess that lots of the kinetic energy is released as heat, and will therefor not affect the scale in the same way as the superball is doing.
In addition, we're talking about G-forces which is very different between a stiff and a soft object.

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