- #1

AN630078

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- Homework Statement
- Hello, I have found a mechanics problem concerning an elevator accelerating downwards. I have tried to comprehensively answer the question but I find that I usually struggle with these questions, particularly whether acceleration is positive or negative etc.

A man of mass 70kg is travelling in a lift of mass 500kg (excluding the mass of the man) which is suspended from a vertical cable and is moving downwards with an acceleration of 1.5ms^-1. Take g=9.8ms^-2.

Find the force exerted on the man by the lift and the tension in the cable.

- Relevant Equations
- ΣF=ma

The acceleration of the elevator is downwards and therefore negative.

The overall acceleration of the man is downward with the the direction of the elevator meaning that ma is negative.

The external forces acting on the man are the force of gravity acting downwards (-W=-mg) and the supporting Normal Force FN applied upward on the man by the elevator.

So ΣF= -ma= -mg+FN

FN =mg - ma

The force acting on the man=70*9.8-70*-1.5

Force=791 N

(Is it correct to denote the acceleration as negative in this calculation i.e. -1.5ms^-1?)

To find the tension in the cable;

Force= ma is in direction of motion i.e. downwards. Also mg is being applied in the downward direction. The direction of tension is always along the string and away from the body i.e. here in the upward direction.

Balancing the forces:

T=mg+ma

T=m(g+a)

Would the mass be mass of man+mass of elevator = 70kg+500kg=570kg

Then; T=570(9.8*-1.5)

T=-8379 N

I apologise clearly I am rather confused here, I am trying to improve my understanding of mechanics problems I just struggle to visualise them to understand them fully. I have drawn free body diagram for this scenario to help me picture what is happening but I am still struggling a little. I would be very grateful of any help

The overall acceleration of the man is downward with the the direction of the elevator meaning that ma is negative.

The external forces acting on the man are the force of gravity acting downwards (-W=-mg) and the supporting Normal Force FN applied upward on the man by the elevator.

So ΣF= -ma= -mg+FN

FN =mg - ma

The force acting on the man=70*9.8-70*-1.5

Force=791 N

(Is it correct to denote the acceleration as negative in this calculation i.e. -1.5ms^-1?)

To find the tension in the cable;

Force= ma is in direction of motion i.e. downwards. Also mg is being applied in the downward direction. The direction of tension is always along the string and away from the body i.e. here in the upward direction.

Balancing the forces:

T=mg+ma

T=m(g+a)

Would the mass be mass of man+mass of elevator = 70kg+500kg=570kg

Then; T=570(9.8*-1.5)

T=-8379 N

I apologise clearly I am rather confused here, I am trying to improve my understanding of mechanics problems I just struggle to visualise them to understand them fully. I have drawn free body diagram for this scenario to help me picture what is happening but I am still struggling a little. I would be very grateful of any help