High School

An elevator has a mass of 3000 kg. If the upward tension in the supporting cable is 42000 N, how far does it rise in 2 seconds, assuming it begins at rest?

Answer :

Answer: 8.4 m

Explanation: I have no idea how I came to this conclusion but it is right

The elevator rises at a distance of 8.38 meters in 2 seconds, assuming it starts at rest.

Given:

Mass of the elevator: 3000 kg

Upward tension in the cable: 42000 N

Time: 2 seconds

Initial velocity: 0 m/s

Using Newton's second law:

Force = mass × acceleration

Tension - Weight = mass × acceleration

Weight (mg) = 3000 × 9.81

Weight (mg) = 29430 N

The acceleration is:

Acceleration (a) = (Tension - Weight) / mass

Acceleration (a) = (42000 - 29430) / 3000

Acceleration (a) = 4.19 m/s²

The kinematic equation for displacement:

Distance = Initial velocity × Time + 0.5 × Acceleration × Time²

Distance = (0) × (2 ) + 0.5 × (4.19 ) × (2)²

Distance = 0 + 0.5 × 4.19 × 4²

Distance = 0 + 8.38 m

So, the elevator rises at a distance of approximately 8.38 meters in 2 seconds, assuming it starts at rest.

To know more about displacement and distance:

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