Question

Suppose you find yourself in your friend's third floor apartment building when you smell smoke coming from outside the door. you open the door an see nothing but flames protruding from the hallway. Realizing that your only means of escape is through the window of the apartment, your freind agrees to donate many pairs of nylons which you tie together to form a makeshift rope. this nylon rope(no pun intended) can withstand a maximum tension of 500 N without breaking. you have a mass of 70Kg on this particular day.
a) why can't you slide down the rope at a near constant speeed?
b) What is the smallest prssible acceleration you must achieve in order to slide down the rope without it breaking? ans:2.9m/s square

Answer 1

(a) Because the tension in the rope would be larger than the maximum value allowed

When you are sliding down the slope, there are two forces acting on you:

- Your weight, $W=mg$, acting downward, where

m = 70 kg is your mass

g = 9.8 m/s^2 is the acceleration of gravity

- The tension in the rope, T, acting upward

Therefore, the equation of motion is

$T-mg=ma$

where a is the acceleration.

If you want to slide at constant speed, then the acceleration must be zero:

$a = 0$

And so the equation becomes

$T-mg=0$

This means that the tension in the rope must be:

$T=mg=(70 kg)(9.8 m/s^2)=686 N$

Which is larger than the maximum tension allowed in the rope (500 N), so the rope will break.

(b) $2.66 m/s^2$ downward

Again, we must refer to the equation of the forces:

$T-mg=ma$

In this case, we want the tension in the rope to be the maximum allowed value,

T = 500 N

the other data are

m = 70 kg is your mass

g = 9.8 m/s^2 is the acceleration of gravity

Substituting into the equation, we can find the corresponding value of acceleration:

$a=\frac{T-mg}{m}=\frac{500-(70)(9.8)}{70}=-2.66 m/s^2$

where the negative sign means the acceleration is downward.