(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, , 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
where a is the acceleration.
If you want to slide at constant speed, then the acceleration must be zero:
And so the equation becomes
This means that the tension in the rope must be:
Which is larger than the maximum tension allowed in the rope (500 N), so the rope will break.
(b) downward
Again, we must refer to the equation of the forces:
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:
where the negative sign means the acceleration is downward.