# What happens to energy used by reaction force?

Suppose a person pushes a rock. The person is exerting a force and his energy is used in burning up of fats and converted to thermal energy. But which energy is used by the rock's reaction force.?

None.

A force doesn't require energy.

The wall spends no energy in just holding back. Just like a table spends no energy in simply holding up a book.

The human body is complicated. In order to be able to apply the pushing force, muscles will contract etc. This requires energy. But this is not a general rule.

If you are pushing the rock on the ground, the energy of the push dissipates due to friction with the ground. The energy will then the $$W = - \int_{x_1}^{x_2} F_f\;dx$$ where $F_f$ is the force of friction. Also, pushing a rock uphill for example will increase its potential energy that can later be restored by letting it roll downhill. Finally, pushing a rock in space will simply increase its kinetic energy; after the push, the rock will fly away from you with a constant velocity. To recap, depending on the conditions of the surroundings (is there a potential? is there friction?), the energy exerted on the rock will be transformed into different forms.

• No, the rock is not moving. I know that there is frictional force but what happens to the energy of the rock. It has some potential energy, but it doesn't move. The rock exerts force, so what happens to the energy? – Aditya Agarwal Feb 23 '15 at 9:06
• Well if the rock is not moving, there is no change in energy in the first place. Placing an object on a table for example has at least two forces acting on it, the gravitational force acting downwards and the force from the table that pushes the object upwards. Since the object is not moving, none of the forces are doing any work. Similarly, in your example, the static friction counteracts the force you push with. Replace your arm with a spring, it will be more clear that the spring is not doing any work and therefore no energy is exchanged. – ahemmetter Feb 23 '15 at 9:27
• That is what the problem is. There is conversion of energy in our body. Sweat is coming, fats are being burnt (Thermal Energy). But the rock is not sweating i.e. there is no conversion of energy. So how is there no conversion of energy even when its is applying a reaction force.? – Aditya Agarwal Feb 23 '15 at 13:51
• As long as you are pushing and nothing is happening, you are basically just overcoming static friction. As far as I know, there are a couple of theories how friction happens at a microscopic scale, but the short answer would be that your energy is overcoming static friction. Some might go into heating up the rock, deforming it and maybe exerting a torque on it. – ahemmetter Feb 23 '15 at 14:15
• A force can overcome a force but how an energy can overcome a force? – Aditya Agarwal Feb 25 '15 at 8:08