Question

An elevator cab is pulled directly upward by a single cable. The elevator cab and its single occupant have a mass of 2300 kg. When that occupant drops a coin, its acceleration relative to the cab is 6.80 m/s² downward. What is the tension in the cable?

Answer 1

15.64 KN

Step-by-step explanation:

mass of the elevator cab with a single occupant= 2300 kg

acceleration relative to the cab
`a_(ce)`= 6.80 m/s^2

acceleration of the coin relative to the cab in the opposite direction of motion of cab so we can consider it as a= -6.80 m/s^2

The acceleration of elevator cab relative to the ground
`a_(cg)`

now we can say that

`a_(ce) +a_(eg) =a_(cg)`

=-6.80+ a_{eg}= -9.8

[tex]a_{eg}=-9.8+6.80=-3.8

The forces that act on elevator cab are tension and gravitational, applying newtons second law

T- mg= ma_{eg}

Then the tension in the cable is

T= 2300(-3.8)+2300×9.8= 15640 N= 15.64 KN

therefore tension in the string will be 15.64 KN