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According to Newton's third law, the force acting on object is equal and opposite to the other object that is applying the force. If I push a table with 5N force then table is doing the same. But the table and I have different masses, so how could the force be same? Isn't $F=ma$?

Kyle Kanos
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Suyash Prakash
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4 Answers4

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Suppose you and the table are floating in space. If you push the table it will go in one direction and you will go in the other direction. Your and the table's acceleration will be different so you will end up travelling at different speeds. This is obvious from conservation of momentum. The momentum in the centre of mass frame is initially zero, so after the push your velocity $v$ and the table's velocity $V$ are related by:

$$ MV = mv $$

where $M$ is the mass of the table and $m$ is your mass. Your velocity will therefore be:

$$ v = \frac{M}{m} V $$

If you walk up to a table in your living room and push it then other forces come into play. These include the force on the table legs exerted by the living room floor and the force on your feet exerted by the living room floor. You would need to take these into account to analyse the situation properly.

John Rennie
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Your mass or your acceleration doesn't tell you anything about the forces acting on your body. F=ma simply states that if we add (vector addition) all the force acting on your body then the effect of the net force will be given by your mass times acceleration.
There may be a lot of forces acting on your body but if the net sum of these is zero, the body simply stays the way it was before (doesn't move if it were in rest).
The force exerted by the table in not the only force acting on you while you are pushing it. There is also force due to friction acting on you in opposite direction.
The net effect of these forces combined will give you your mass times acceleration.

sarthak
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This question has to be a duplicate, but just in case it isn't ...

You are confusing the force Newton's third law with the force in Newton's second law. Newton's third law addresses the individual forces on two different objects subject to a common interaction. Newton's second law addresses the net force on one object.

The net force on the book are a result of the gravitational interaction between the book and the Earth as a whole and the normal interaction between the book and the tabletop. Ignoring planet rotation, these cancel one another. The net force on the book is zero. Note that just because these two forces cancel one another does not mean that these are third law action-reaction forces.

The net force on the table is the result of the gravitational interaction between the table and the Earth as a whole, the normal interaction between the legs of the table and the floor, and the normal interaction between the tabletop and whatever is piled atop the table. Ignoring planet rotation, these collectively cancel one another. The net force on the table also is zero.

David Hammen
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Here there are two objects, One is the Person pushing, other is the Table. Both have applied force which is equal to (say) 5N, F=5N.

  • Mass of the Person (say) m=20kg
  • Mass of the Table (say) m'=10kg
  • Acceleration of the Person= a m/s^2**
  • Acceleration of the Table = a' m/s^2
  • Force of the Person and Table= 5N ---- {According to Newton's Third law}
  • Applying Newton's Third law to the Person --- F=ma implies 5=20a

Applying Newton's Third law to the Table --- F=ma' implies 5=10a'

  • You see, acceleration is variable i.e. a is not equal to a' and as the Person has more momentum than of the Table, obviously the Table has to move but Force remaining Equal and Opposite.
Sushant23
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