What effect does acceleration have on an object, such as your body, that is made up of many loosely connected parts?

The acceleration will effect individually on all the parts and organs of the body.

Explanation:

When the body feels accelerations in the air lift condition, each and every parts and organs of the body will be pushing each other due to the acceleration and push caused by the seat we are sitting to our muscles.

There will be transfer of pushing energy from the seat caused by acceleration to the muscles and then to each and every organs because the organs and remaining parts will feel directly pulled by the gravitational force and acceleration at same time but in different directions.

So the weight of the parts and organs will become large when airlift or when we are accelerated to upward direction.

During free fall they will become less weight as then only gravitational force will be acting on them and not any other forces.