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What is the net force on a 1000 kg elevator that is falling freely with acceleration 9.8 m/s²?

Answer

For free fall, the net force is $F_{net}=ma$. With $m=1000\,\text{kg}$ and $a=9.8\,\text{m/s}^2$, $F_{net}=1000\times 9.8=9800\,\text{N}$ downward. (In free fall, gravity is the only force, so this is also the elevator’s weight $mg$.)

Explanation

What “falling freely” tells you

If the elevator is falling freely (free fall), there is no support force from a cable or the shaft walls. That means the only significant force acting on it is gravity.

Applying Newton’s second law

Newton’s second law says the net force is

$$F_{net}=ma$$

Here,

  • $m = 1000\,\text{kg}$
  • $a = g = 9.8\,\text{m/s}^2$ downward

So,

$$F_{net}=1000\times 9.8=9800\,\text{N}$$

Direction: downward.

What about tension or normal force?

In free fall, the contact/support forces are $0$ (or negligible). So the net force equals the gravitational force:

$$F_g = mg = 9800\,\text{N} \text{ downward}$$

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