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When we lift and hold an object for a long time why does our hand pain though no work is being done?

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When an object is lifted and held stationary, the work done according to the laws of physics is zero. This follows from the fact that work is the product of force on an object and the distance moved by the object in the direction of the force.

When we lift an object, the ligaments that make up our muscles are stretched or compressed by it. This has to be accommodated for by cellular activity in many cells to stop our body parts from getting permanently deformed. The process requires the use of chemical energy.

The generation of energy by cells can be through anaerobic or aerobic process, both of which produce by-products which have to be expelled regularly. Their presence causes pain; it can be considered as a way of our body reminding us to stop and take a break.

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