Can a Thief Escape a Building Using a Rope?

[brycenrg]

Homework Statement

A 75 kg thief wants to escape a building. He has a rope that supports 58kg how can he escape?

Homework Equations

f=ma

The Attempt at a Solution

75kg*g = W
58kg*g = T
T - W = 75kg*a
a = (t-w)/m
If he applies a acceleration upwards at 2.2 m/s^2 he would survive.
When i do the calculation I get a negative number, which would mean he would be applying a acceleration downwards which doesn't make sense. Why is that?
In my equation T is positive

 

[Mark44]

Homework Statement

A 75 kg thief wants to escape a building. He has a rope that supports 58kg how can he escape?

Homework Equations

f=ma

The Attempt at a Solution

75kg*g = W
58kg*g = T
T - W = 75kg*a
a = (t-w)/m
If he applies a acceleration upwards at 2.2 m/s^2 he would survive.
When i do the calculation I get a negative number, which would mean he would be applying a acceleration downwards which doesn't make sense. Why is that?
In my equation T is positive

Why would he want to climb upward to get out of a building? Shouldn't he lower himself down from the building?

 

[brycenrg]

Why would he want to climb upward to get out of a building? Shouldn't he lower himself down from the building?

That makes sense he has to accell downwards to go. But what it means is if he accels downwards more that 2.2 then the rope wouldn't support him right?

 

[Mark44]

That makes sense he has to accell downwards to go. But what it means is if he accels downwards more that 2.2 then the rope wouldn't support him right?

I think you are confused. If he was just hanging from the rope, with no acceleration, the rope would break, right? If he slid down the rope, just barely hanging onto it (which would burn his hands), he would be acclerating at just under $9.8 \frac m {sec^2}$. Would the rope break then?

 

[brycenrg]

I think you are confused. If he was just hanging from the rope, with no acceleration, the rope would break, right? If he slid down the rope, just barely hanging onto it (which would burn his hands), he would be acclerating at just under $9.8 \frac m {sec^2}$. Would the rope break then?

I am, I want to say if he used friction to slow him down to just = to T and under that force he would be ok. Which is under 2.2m/s^2.
But it seems like your saying he has to be going faster than gravity, which doesn't make sense to me

 

[Mark44]

I am, I want to say if he used friction to slow him down to just = to T and under that force he would be ok. Which is under 2.2m/s^2.
But it seems like your saying he has to be going faster than gravity, which doesn't make sense to me

Yes, it doesn't make sense, and that isn't what I was saying, either.

The acceleration due to gravity is acting downward. What is the tension on the rope if his downward acceleration, relative to the fixed rope, is less than 2.2 m/sec^2? What's the tension on the rope if his downward acceleration, again relative to the fixed rope, is more than 2.2 m/sec^2? You're getting bogged down in the minutiae of the problem and are missing the bigger picture.