So I have some confusion here, I am sure I knew this at some point. Let's say an object of 10 kg is dropped from a height of 10 m. When it reaches the ground, the work done on the object should be the force ($mg$) x distance or 10 kg x 9.8 m/s/s x 10 m. That gives 980 joules of work done on the object by gravity.
But the object did not gain 980 joules of mechanical energy. It lost 980 joules of GPE and gained 980 joules of kinetic energy (up to the point of it reaching ground level).
Using the change in GPE and KE, it looks like no work was done on the object because the loss in GPE equals the gain in KE.
So
a) am I right that no net work was done on the car by sum of all forces?
b) is the work done by gravity equal to force time distance, or is it equal to the change in mechanical energy of the object which is zero?
Best Answer
The confusion here comes from the fact that your choice of system is not clearly defined.
If the system is the earth plus the object, then there is no external force, and therefore no change in total energy. The potential energy of the system is transfered into kinetic energy. No external work done, and external work is what adds or removes energy of the system.
If the system is the object, then gravity does external work on the system, adding energy, increasing its kinetic energy. Potential energy is not defined for a single object. There is no potential energy with this choice of system. Potential energy is always defined for pairs of interacting objects. With this system, there is work done.