You have a mass of 69 kg and are on a 47 degree slope hanging on to a cord with a breaking strength of 160 newtons. What must be the coefficient of static friction to 2 decimal places between you and the surface for you to be saved from the fire?
Wt. = m*g = 69kg * 9.8N/kg = 676.2 N.
F1 = 676.2*sin47 = 494.54 N. = Force parallel to the slope.
F2 = 676.2*cos47 = 461.2 N. = Force perpendicular to the slope.
160-Fs = = m*a
160-u*F2 = m*0 = 0
u*461.2 = 160
u = 0.35 = Coefficient of static friction.
Actually, Henry is incorrect. The acceleration is NOT equal to 0. The acceleration is F1/m thus, the equation he wrote (160 - Fs = m • a) should have m • a = F1.
Final equation:
Ft - uF2 = F1
160 - u(461.2) = 494.54
u = .725
To determine the coefficient of static friction needed to save you from the fire, we can break down the problem into several steps.
Step 1: Determine the component of your weight parallel to the slope.
To find this, we need to calculate the gravitational force acting on you. The formula to calculate gravitational force is:
F_gravity = mass * g
where mass is your mass and g is the acceleration due to gravity (approximately 9.8 m/s^2). So, plugging in the values:
F_gravity = 69 kg * 9.8 m/s^2 = 676.2 N
Next, we need to determine the component of this force parallel to the slope. This can be done using the formula:
F_parallel = F_gravity * sin(theta)
where theta is the angle of the slope (47 degrees in this case). Plugging in the values:
F_parallel = 676.2 N * sin(47 degrees) ≈ 464.93 N
Step 2: Determine the breaking force of the cord.
The breaking force of the cord is given as 160 newtons.
Step 3: Calculate the maximum static friction force.
The maximum static friction force is equal to the force exerted parallel to the slope without causing motion.
Maximum static friction force = F_parallel
Step 4: Determine the coefficient of static friction.
The coefficient of static friction (µ) can be found using the formula:
µ = (Maximum static friction force) / (Breaking force of the cord)
µ = F_parallel / 160 N
Plugging in the values:
µ = 464.93 N / 160 N ≈ 2.91
Therefore, the coefficient of static friction needed for you to be saved from the fire is approximately 2.91.