Would operation of heavy equipment in the front yard of a 50-year-old home make the foundation crack?

Not unless it would cause earthquake movement to your home. If equipment is causing your house to shake and pictures to fall off your walls, then it is considered the same effect as an earthquake and could have effect of your home's foundation. Also, if your 50 year old home is like many others of that age, it is build stronger than newer homes of today. If you are worried, hire a home inspector to come out and evaluate your foundation, the charge somewhere between $75 and $150 for a quick housecall.