Question

An elevator filled with passengers has a mass of 1,700 kilograms and accelerates upward from rest at a rate of 1 meters/seconds 2 for 1.8 seconds. Calculate the tension in the cable (in Newtons) supporting the elevator during this time.

Answer 1

The tension in the cable is 18371.9 newtons.

Step-by-step explanation:

Physically speaking, the tension can be calculated with the help of the Second Newton's Law. The upward acceleration means that magnitude of tension must be greater than weight of elevator, whose equation of equilibrium is described below:

`\Sigma F = T - m\cdot g = m \cdot a`

Where:

`T` - Tension in the cable, measured in newtons.

`m` - Mass of the elevator, measured in kilograms.

`g` - Gravity constant, measured in meters per square second.

`a` - Net acceleration of the elevator, measured in meters in square second.

Now, tension is cleared and resultant expression is also simplified:

`T = m \cdot (a + g)`

If
`m = 1700\,kg`,
`a = 1\,(m)/(s^(2))` and
`g = 9.807\,(m)/(s^(2))`, the tension in the cable is:

`T = (1700\,kg)\cdot \left(1\,(m)/(s^(2))+9.807\,(m)/(s^(2)) \right)`

`T = 18371.9\,N`

The tension in the cable is 18371.9 newtons.