Newton Third Law general equation

In summary, we are given a picture with a frictionless table and two masses, m1 and m2, connected by a rope over two pulleys. We need to find the expression for the acceleration of m1, and to do so, we need to determine the forces acting on each mass. After analyzing the forces and applying Newton's 2nd law, we find that the acceleration of m1 is equal to 2mg divided by 4m1 plus m2.
  • #1
bigredd87
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1
I have a picture provided. You can assume that the table is frictionless. I need an expression for the acceleration of m1.
 

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  • #2
We don't do your homework for you. What are the forces on each mass?
 
  • #3
here is what I have so far:

Fnetx for m1 is T=m1a
Fnety for m1 is N-m1g=0

I guess my real dilemma is i don't really know what the forces on m2 are. I believe there is no acceleration constraint since m2 is on the second pulley. Does that mean that the tension and weight are equal to m2a, with m2 having a different acceleration than m1?
 
  • #4
bigredd87 said:
here is what I have so far:

Fnetx for m1 is T=m1a
Fnety for m1 is N-m1g=0
OK. (All you need here is Fnetx.)

I guess my real dilemma is i don't really know what the forces on m2 are.
Treat m2 and its pulley as one object. I see 3 forces acting on it.
I believe there is no acceleration constraint since m2 is on the second pulley.
Of course there is an acceleration constraint, which you need to figure out. When m2 drops X distance, how far must m1 move?

Does that mean that the tension and weight are equal to m2a, with m2 having a different acceleration than m1?
You will apply Newton's 2nd law to m2, just like to m1. Yes, a2 is different from a1, but there is a simple relationship.
 
  • #5
so a2 =-a1? I didn't understand if the mass on the pulley made it different from other problems. So there is tension T from the rope attached to the wall, the weight force m2g, and the tension from m1 which is m1a1?
 
  • #6
bigredd87 said:
so a2 =-a1?
No. (But the minus sign is good.) Answer my question earlier: When m2 drops X distance, how far must m1 move? (Get a piece of string and figure it out.)

I didn't understand if the mass on the pulley made it different from other problems. So there is tension T from the rope attached to the wall, the weight force m2g, and the tension from m1 which is m1a1?
The tension will be the same throughout the rope. The only things exerting a force on m2 are: (1) the ropes; (2) gravity.

Set up an equation for each mass. (After you've found the acceleration constraint.) Then solve them together to find the accelerations.
 
  • #7
ok, so I think I got it now.

a2 = (-1/2)a1

so u have for m2 in y direction:
2T-m2g=m2a2 ; since there are two ropes pulling on m2

i already know that T =m1a1 and the acceleration constraint, so plugging this in i get:
2m1a1-m2g=-m2a1/2

4m1a1-2mg=-m2a1

a1(4m1 + m2)= 2mg

a1=2mg/(4m1+m2)
does this look ok?
 
  • #8
Excellent!
 

Related to Newton Third Law general equation

1. What is Newton's Third Law?

Newton's Third Law 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 is Newton's Third Law represented mathematically?

The general equation for Newton's Third Law is FAB = -FBA, where FAB is the force exerted by object A on object B, and FBA is the force exerted by object B on object A. This equation showcases the equal and opposite nature of the forces.

3. Does Newton's Third Law apply to all types of forces?

Yes, Newton's Third Law applies to all types of forces, including gravitational, electromagnetic, and contact forces. It is a fundamental principle in physics and applies to all interactions between objects.

4. Can Newton's Third Law be observed in everyday life?

Yes, 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 jump, your feet push down on the ground, and the ground pushes back on you, causing you to move upwards.

5. How does Newton's Third Law relate to the conservation of momentum?

Newton's Third Law is closely related to the conservation of momentum. Since the forces between two objects are equal and opposite, the momentum gained by one object is equal to the momentum lost by the other object. This ensures that the total momentum of the system remains constant.

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