# Where does the block get the energy from?

Let there be a block of mass $m$ on a frictionless surface. A boy of mass $M$ exerts an invariant force $F$ on the block & does positive work on the block by displacing it by $d$. By Law of Conservation of Linear Momentum , the block will also exert same force $F$ on the boy but in the opposite direction and will do positive work by displacing the boy by $\frac{m}{M} .d$ .

Now one thing that confuses me: From where does the block get the energy required to do positive work on the boy? I am sure it is definitely not its kinetic energy otherwise, the velocity of the block would decrease. The boy uses the energy he got from his food to do positive work on the block. But from where does the block get the energy for doing positive work on the boy?? Please help.

• In this case I think the block do so for its inertia. According to 1st law of motion, when we are going to change the state of motion( i.e. rest or moving) we have to apply force on it. In this case when the boy exerts a force on a block, the block also give the same and opposite forces on the boy which is the reaction force and its appears due to the Inertia property of the matter. This reaction force does a positive work on the boy. – Rajesh Sardar Nov 12 '14 at 3:47
• Have I written anything different. Yes the reactive force of the block does positive work on the boy. But from where does it get the energy for doing this work?? – user36790 Nov 12 '14 at 4:02

## 1 Answer

All the Energy involved here comes from the boy. This is no different than jumping: the force involved in doing so propels you upwards and the Earth downwards, but no Energy came from Earth. In your example no Energy can be spontaneously produced by the block.

The fact that Newton's third law expresses the action and reaction forces appearing together does not imply the Energy involved comes from different sources in a similar way.

You could even account for internal forms of Energy, like its elastic deformation. For example, jumping in a trampoline: although the jumper gains Energy from its elastic deformation, the movement was triggered by the jumper and the way he shapes his body in synchrony with the trampoline's movement allows him to maximize the Energy gain, but again all the Energy involved here was produced by the jumper (and gravitation helps, but not as a spontaneous agent).