1 Answer

Golden rule of mechanics: do not let friction deceive you, follow Newton's three laws. It is nothing more than one of our forces of interest. More importantly, friction is a force, just as much as a human force is.

"When work is done by an object it loses energy" Completely true. Work is done by the object when the net force acting on an object is opposite (or partially opposite) the object's motion. Suppose a car in in a testing zone, and compresses a spring as it comes to rest. The car did work on the spring, and the car lost energy, because its speed decreased. The spring gained energy, because the car did work on it compressing it from its unstressed length.

Now, let's talk about the real situation when car stops. You apply the brakes, which will apply an extra friction force to the wheels. By doing so, your car does mechanical work which is converted to frictional heat. Kinetic energy is converted to thermal energy as your car stops. You may argue that the object didn't technically loose energy, because the thermal energy is still in the car. However, eventually, this energy will escape via heat transfer modes to the surroundings.

"and when work is done on an object it gains energy?" Completely true, unless the energy comes from within the object (such as a car or human). When work is done on an object, the net force is aligned (or partially aligned) with the direction of motion and it increases speed. This occurs if an external human pushes the object, or if the object uses its own energy to have the environment induce propulsion.

If the net work done on an object is zero, the object will remain at a constant speed. This will happen if the net force is zero, or if the net force is perpendicular to the direction of motion, in which case, the object will change direction, but not speed.

As for the situations in the body of the question, think about the above statements, and pay attention to the word "net" which means total. Think about all forces acting on an object as being equally important, rather than classifying as "driving force" or "counter force".