[Physics] Normal reaction – force without acceleration

newtonian-mechanics

When a body lies on the surface of the Earth it is under the influence of gravity. The force on the body due to gravity causes it to exert a force on the ground and the normal reaction acts in the opposite direction causing the resultant force on the body to be zero.

However, how can the body exert a force on the ground when it does not have any acceleration? Since force equals mass times acceleration how does a body without acceleration experience a force?

Best Answer

When a body lies on the surface of the Earth it is under the influence of gravity. The force on the body due to gravity causes it to exert a force on the ground and the normal reaction acts in the opposite direction causing the resultant force on the body to be zero.

Correct

However, how can the body exert a force on the ground when it does not have any acceleration? Since force equals mass times acceleration how does a body without acceleration experience a force?

But you do have an acceleration, $g$, which you stated in the first paragraph (the force on the body due to gravity...). And this force is equal and opposite to the normal force: $$ \mathbf F_{g} = -\mathbf F_N \\ mg\left(-\hat{z}\right) = -mg\hat{z} $$ That the net force is zero only means that the object is not accelerating, not that there are no forces acting on it.

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