Finding tension in a cable of a accelerating lift

[Sleve123]

A lift has mass 800 kg. It is moving upwards and has an accerleration
of -0.1 ms-2. The lift is supported by a single cable.

What is the tension in the cable?

I get T = -7760 N (I'm taking up as negative), just checking what anybody else gets

F = ma

T + mg = -(-0.1)m

T = 800(0.1 - 9.8) = -7760 N

 

[tiny-tim]

Welcome to PF!

Hi Sleve123! Welcome to PF!

T + mg = -(-0.1)m

T = 800(0.1 - 9.8) = -7760 N

Assuming ths is one of Mr Otis's new-fangled lifts , with the cable above the lift …

shouldn't T be opposite to mg? ​

(and negative tension would be compression)

 

[Sleve123]

Hi Sleve123! Welcome to PF!


Assuming ths is one of Mr Otis's new-fangled lifts , with the cable above the lift …

shouldn't T be opposite to mg? ​

(and negative tension would be compression)

I think what I've done is work out the force applied to the lift to produce that outcome.

In my equation:

T + mg = -(-0.1)m

The value of T could be positve or negative.

Doesn't the negative value just tell me that the force applied on the lift from the tension in the wire is in the up direction (because I took up as negative), not down.

 

[tiny-tim]

The value of T could be positve or negative.

No, tension can only be positive.

(plus, the question itself asks "What is the tension in the cable?", and you can't give a negative answer to that)

Doesn't the negative value just tell me that the force applied on the lift from the tension in the wire is in the up direction (because I took up as negative), not down.

That's extremely confusing, and almost bound to lead to mistakes

In an exam, even if you get the correct answer, the examiner will probably think it was just luck.

Try it again, with T positive. ​

 

[Sleve123]

So:

mg - T = -(-0.1)m

T = m(g - 0.1)

T = 800 x 9.7 = +7760N

 

[tiny-tim]

So:

mg - T = -(-0.1)m

T = m(g - 0.1)

T = 800 x 9.7 = +7760N

Yup!

(though, again, you seem determined to make things complicated …

the question gives an upward acceleration, so wouldn't it be safer to go with upward directions, avoid the double-negative, and write T - mg = -0.1m ?)

 

[Sleve123]

Thanks, as long as I'm right. I'll make it simpler for myself next time.