Newton's 3rd law and an impulse

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Discussion Overview

The discussion revolves around the application of Newton's third law and the concept of impulse in the context of a superball and a tomato of the same mass dropped onto a bathroom scale. Participants explore the differences in force readings on the scale due to the elastic and inelastic properties of the two objects upon impact.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant asserts that both the superball and tomato, having the same mass, should exert the same force on the scale due to gravitational force, questioning why the scale shows different readings.
  • Another participant introduces the concept of elastic versus inelastic collisions, suggesting that the deformation of the superball and tomato affects the force measured by the scale.
  • It is noted that while both objects have the same initial momentum, the force experienced during impact depends on their stiffness and other characteristics.
  • A participant explains that force is related to the rate of momentum transfer, which varies based on impact and rebound velocities, as well as the duration of the collision.
  • One participant acknowledges the difference in forces experienced by the two objects and questions the applicability of F=ma in this scenario, leading to a discussion on how acceleration and force can differ during collisions.
  • Another participant mentions that the tomato undergoes permanent deformation, implying that energy is lost as heat, which affects the scale's reading differently than the superball.

Areas of Agreement / Disagreement

Participants express differing views on the application of Newton's laws in this scenario, particularly regarding the impact of object properties on force measurements. There is no consensus on the reasoning behind the differing scale readings, and multiple competing explanations are presented.

Contextual Notes

Participants highlight the importance of understanding the properties of materials (elasticity, stiffness) and their effects on momentum transfer during collisions, which are not fully resolved in the discussion.

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?
 
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WilliamLeung said:
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?
 
WilliamLeung said:
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.
 
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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.
 
phinds said:
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
Dale said:
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?

jbriggs444 said:
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.
 
WilliamLeung said:
You mean they hit the scale the scale with different force
Yes. That is what I mean.

WilliamLeung said:
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.
 
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.

Vidar
 

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