I was taking my dogs for a walk yesterday evening when this question occurred to me.

The two dogs were pretty enthusiastic about the walk and wanted to run on ahead, so the leads were taut and they were sort of gently pulling me along. But they're quite small so I could easily control the speed at which we walked. At this stage they were presumably using more energy than that required to simply walk at that same speed given the resistance I was providing.

Suddenly, a cat spotted us and ran away. The dogs, upon seeing this, tried to give chase, running and pulling the leads with all their might. But I held onto the leads and continued walking at the same speed as before. So the result was two dogs frantically trying to pull and run but not going any faster.

So my question is: Are the dogs doing any more work (or using any more energy) when trying to chase the cat than when they were gently tugging along? Intuitively I think yes, (especially given the gasping and panting coming out of both of them) but I can't figure out why: they are moving at the same speed and pulling the same weight (i.e. me) as before....