Do all cases of Newton's third law follow both the strong and weak forms?

In summary, Newton's third law has two forms: the weak form states that the forces exerted by two particles on each other are equal in magnitude and opposite in direction, while the strong form states that the forces must not only be equal and opposite, but also lie on the straight line joining the particles. However, there are cases where both forms fail to hold, such as with magnetic forces. In these cases, the forces may still obey the weak form, but not the strong form.
  • #1
ehrenfest
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[SOLVED] Newton's third law

Homework Statement


My book gives two forms of Newton's Third Law:
Weak Form: The forces exerted by two particles [itex]\alpha[/itex] and [itex]\beta[/itex] on each other are equal in magnitude and opposite in direction
Strong Form: The forces exerted by two particles [itex]\alpha[/itex] and [itex]\beta[/itex] on each other, in addition to being equal and oppositive, must lie on the straight line joining the two particles.

Here are my questions:
1) Is it true that there are cases IN WHICH BOTH THE STRONG FORM AND THE WEAK FORM FAIL TO HOLD?
2) My book says that for example, magnetic forces, those forces exerted on a moving charge q in a magnetic field [itex]\mathbf{B}[/itex] [itex](\mathbf{F}=\mathbf{q}v \times \mathbf{B})[/itex], obey the weak form, but not the strong form. I don't understand why that obeys the weak form. What are the two particles?

Homework Equations


The Attempt at a Solution

 
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  • #2
1.
Consider two identical charges moving along the x and y axes with same speed away from the origin. The electrical forces between them is repulsive, but now just find out how the magnetic forces between them behave. You don't have to calculate -- just roughly think of the charges as currents and find the direction of the associated magnetic fields like we do for currents.

The total force of one on the other is equal to the force of the other on the former, but they are not opposite. So, this violates both weak and strong.

2.
Consider one charge and the wire in which current is flowing that makes the magnetic field B. Or simply a magnet and a charge near one of the poles, moving in a direction perpendicular to the axis of the magnet. The force on the charge is perpendicular to the plane containing B and v. The force on the magnet is opposite, but not collinear. So, the weak form holds.
 
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1. What is Newton's third law of motion?

Newton's third law of motion states that for every action, there is an equal and opposite reaction. This means that whenever an object exerts a force on another object, the second object exerts an equal and opposite force back on the first object.

2. How does Newton's third law apply to everyday life?

Newton's third law can be observed in many everyday situations. For example, when you push a door, the door pushes back on you with an equal force. When you walk, your feet exert a force on the ground and the ground exerts an equal and opposite force back on your feet, propelling you forward.

3. What are the different forms of Newton's third law?

The different forms of Newton's third law include action and reaction forces, reaction at a distance, and action and reaction within a system. Action and reaction forces occur between two objects in contact, while reaction at a distance involves forces acting on objects that are not in direct contact. Action and reaction within a system refer to the internal forces between different parts of a system.

4. Can Newton's third law be violated?

No, Newton's third law is a fundamental principle of physics and cannot be violated. However, it may not be noticeable in certain situations, such as when forces are balanced or when one force is significantly greater than the other.

5. How does Newton's third law relate to conservation of momentum?

Newton's third law is closely related to the principle of conservation of momentum. According to this law, the total momentum of a closed system remains constant. Since action and reaction forces are equal and opposite, they cancel each other out and do not change the total momentum of a system. This means that momentum is conserved in all interactions, in accordance with Newton's third law.

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