I was reading a textbook example. The question stated that ‘a person of mass $72 \; kg$ stands in a lift of mass $540 \; kg$. the lift is supported by a cable that can be modeled as light and in-extensible. Draw a diagram showing all the forces acting on the lift.’, and the diagram shown had tension force of the cable, the equal and opposite reaction force, and also the downward weight. However, I was confused about the weight which shown as $540 \cdot g$, i.e. $540 \times 9.8 \; N$, but why is this? Why is it not $(540+72) \cdot 9.8 N$ because isn’t the person’s mass also acting on the lift?
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The system is the lift and so you must count all forces acting on the lift which are:
- gravitational attraction of the Earth downwards, $540g$,
- normal contact force due to man standing on lift downwards, $70g$
- tension force due to cable upwards, $540g+70g$.
The assumption is that the lift and man are at rest or are moving with constant velocity.
