# If an object rests on a table, not accelerating, how much work do both the object and the table do?

Obviously, the net work done is zero, because there's no motion, but is the proper way to look at it that both the object's gravity and the table's normal force do zero work, or that one does positive work and one an equal amount of negative work?

• For simplicity's sake, let's say the both the object's center and the table's lie along the y-axis, and that they meet on the x-axis, at the origin. I don't see how that changes the quantity of work done by or on either, though. – SquarerootSquirrel Mar 14 '15 at 20:23
• My guess is that some of the electrons are doing some work depending on which electron degenerating star, neutron star or black hole you are on. – Jitter Mar 14 '15 at 20:45

Work is linked with energy transfer, giving the energy that a certain force gave or took from the object, usually in the form of kinetic energy. It can also relate to potential energy in conservative forces.

In your case there is no energy transfer (no movement, $\Delta x=0$) so it doesn't make sense to talk about work here.

If it is what you are saying then remember that work done here is neither negative nor positive however "work" doesn't exist here. We define Work as the product of the component of Net force acting on the body and the distance through which Force is exerted. You can say that the Force of gravity and Normal force are cancelling effects of each other since they are one is positive and one is negative $(\vec{F_G}=\vec{-F_N})$ but not Work done is cancelled since it doesn't exist there. Don't take it be like,

$W_G=-W_N$, where $W$ stands for Work done.

Now see mathematically,

Since book is not moving,

$\vec{F_G}=\vec{-F_N}$

$\implies$ $\vec{F_G}+\vec{F_N}=0$ where $N$ stands for $Normal$

We know,

$Work=F_n \times S \times cos(\theta)$ where, $n$ stands for $Net$ and,

$S=0$

$F_n=0$

Hence,

$Work=0$

You are confused little bit. Don't think of negative and positive work here as it even doesn't exist. Work would exist if any of the two forces or net force would make body to cover a distance or body would cover distance against their field.