Question

g A person exploring a deep cave system becomes injured and needs to be rescued. The fastest way to get them is to pull them straight up out of the cave through a small opening just overhead, using a motor-driven cable. The lift is performed in three stages, each of them 10 m in height (total of 30 meters to extract the person). In the first stage, the person is accelerated to a speed of 5 m/s. They are then lifted at constant speed of 5 m/s, then in the last stage they are slowly decelerated to zero speed. If the person weighs 80 kg, how much work is done in each stage

Answer 1

1. W = 8848 J

2. W = 7848 J

3. W = 6848 J

Step-by-step explanation:

The work (W) can be found using the following equation:

`W = E_(k) + E_(p)`

Where: E(k) is the kinetic energy and E(p) is the potential energy

Now let's find the work for every stage.

Stage 1:

`W = E_(k) + E_(p) = (1)/(2)mv^(2) + mgh`

Where: m is the mass, g is the gravity, h is the height, v is the speed

`W = (1)/(2)mv^(2) + mgh = (1)/(2)80 kg*(5 m/s)^(2) + 80 kg*9.81 m/s^(2)*10 m = 8848 J`

Stage 2:

`W = E_(k) + E_(p) = 0 + E_(p)`

The kinetic energy is equal to zero because the acceleration is constant.

`W = E_(p) = mgh = 80 kg*9.81 m/s^(2)*10 m = 7848 J`

Stage 3:

`W = E_(k) + E_(p) = (1)/(2)mv^(2) + mgh = -(1)/(2)80 kg*(5 m/s)^(2) + 80 kg*9.81 m/s^(2)*10 m = 6848 J`

I hope it helps you!