Energy is the capacity to do work. So if I have energy I can do work. But if a rock has 100J from falling down a building to push a pillar into the ground, it might not have enough energy to have any work done to push it in. So what happens to that 100Js? Ignoring air resistance. Since energy can neither be destroyed or created so I'm unsure where energy that isn't used has gone. I'm theorizing that heat and sound is produced from the impact and that's the energy dissipated but I'm not completely sure about it. I'm unsure if the friction of the pillar constitutes into this. But then again work done against friction also requires a distance which is 0 when the pillar doesn't move. Thanks for the help! :)
yup, you are right. upon impact(assume rock+pillar stick together ie. perfectly inelastic collision, momentum conserved, kinetic energy not conserved, lost as heat and sound). also, work done against friction between the sides of the pillar against the ground(as your pillar gains momentum and hence velocity).
You would use Newton's second law. The same rock from before is traveling down with a magnitude and direction of mass * acceleration. sumF=ma, W=FdcosT W=dmacosT, substituting. for some arbitrary acceleration, the work done is given by the equation.. If you want to use percentages, divide this number by the necessary work to achieve an optimal result, and multiply by 100. This method will however lead to some level of uncertainty constrained by the assumption that some optimal amount of work is the minimum amount of work needed in a system.