Question

Consider the following situation: An empty elevator with a mass m is being pulled up by a cable. If the elevator has a mass of 1,192 kg and is slowing down at a rate 2.47 m/s² while it is pulled up, what is the tension in the cable? Report your answer in SI units, rounded to a whole number

Please answer ASAP

Answer 1

we will fallow the sign convention that the values of   acceleration and force vectors which are directed downwards will have positive sign and vectors which are directed upward will have negative sign,

we have,

rate at which a elevator is slowing down while moving upward

that is velocity of the elevator ( directed upward ) is decreasing while it moving upward,

that is rate of change of velocity of the velocity ( directed upward ) is negative,

therefore, acceleration vector of of the elevator is directed downward,

so as per our convention acceleration of the elevator

we have,

mass of the empty elevator  

there are two forces acting on the elevator as,

1 ) tension    on the elevator directed upward, which tries to pull the elevator upward, and

2 ) gravitational force   on the elevator directed downward, which tries to pull the elevator downward

we have,

acceleration due to gravity   ( as per our convention positive sign because the acceleration due to gravity is directed downward )

gravitational force will be given as,

Let,

net force acting on the elevator, it will be given as,

_____________________________________ relation 1

and in terms of acceleration of the elevator it will be given as,

______________________________________ relation 2

So, equating relations 1 and 2 we get,

using ,   and    we get,

as per our convention negative sign indicates that the tension in the cable is directed upwards.

so, the tension in the cable is,

( expressed as a whole number rounded to a nearest a whole number )