An elevator cab of mass `m=500` kg is descending with speed `v_(i)=4.0m//s` when its supporting cable begins to slip, allowing it to fall with constant acceleration `vec(a)=vec(g)//5`.
During the fall through a distance `d=12` m, what is the work `W_(g)` done on the cab by the gravitational force `vec(F)_(g)`?

Explanation

To find the work done on the elevator cab by the gravitational force during its fall, we can follow these steps:

### Step 1: Identify the given values
- Mass of the elevator cab, \( m = 500 \, \text{kg} \)
- Initial speed, \( v_i = 4.0 \, \text{m/s} \) (not directly needed for work calculation)
- Acceleration, \( a = \frac{g}{5} \) where \( g = 9.8 \, \text{m/s}^2 \)
- Distance fallen, \( d = 12 \, \text{m} \)

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