Well, well, well, if it isn't a fiery situation! Let's not get all hot-headed though and calculate your way out of this mess.
First, let's find out how much force is acting vertically on you due to gravity. We'll use the formula F = mg, where m is your mass (71 kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2).
F = 71 kg * 9.8 m/s^2 = 695.8 N
Now, we need to calculate the component of your weight acting down the slope. This can be found by multiplying your weight by the sine of the slope angle (51 degrees).
Component of weight down the slope = 695.8 N * sin(51) = 530.9 N
To prevent you from sliding down, the force of static friction must be equal to this component of weight down the slope. So, we have:
Force of static friction = 530.9 N
The maximum possible force of static friction is given by the coefficient of static friction (let's call it µ) multiplied by the normal force acting against you. The normal force is equal to your weight (695.8 N) multiplied by the cosine of the slope angle (51 degrees).
Maximum force of static friction = µ * 695.8 N * cos(51)
For the cord to save you from the fire, the maximum force of static friction should be equal to or greater than the force of static friction required to counteract your weight down the slope.
So, we have the following inequality:
µ * 695.8 N * cos(51) ≥ 530.9 N
Solving this inequality for µ, we find:
µ ≥ 530.9 N / (695.8 N * cos(51))
µ ≥ 0.86 (approximately)
Therefore, the coefficient of static friction must be at least 0.86 for you to be saved from the fire. Hang in there, my friend! 🤡
Now, onto the second part of your question. If the coefficient of static friction is zero, it means that there is no friction between you and the surface. In this case, your only concern is the breaking strength of the cord.
To find the incline angle at which the cord wouldn't break, we need to calculate the component of your weight perpendicular to the slope. This can be found using the formula:
Component of weight perpendicular to the slope = mass * gravity * cos(angle)
Since we don't want the cord to break, this component of weight should be less than or equal to the breaking strength of the cord.
165 N ≥ 71 kg * 9.8 m/s^2 * cos(angle)
Let's solve this equation for angle:
cos(angle) ≤ 165 N / (71 kg * 9.8 m/s^2)
angle ≤ arccos(165 N / (71 kg * 9.8 m/s^2))
Calculating this, we find:
angle ≤ 68.5 degrees (approximately)
Therefore, the incline angle would have to be less than or equal to 68.5 degrees (to the nearest tenth of a degree) in order for the cord not to break. Keep your angle of incline low and your hopes high! 🤡