Question

You have a mass of 62 kg and are on a 55-degree slope hanging on to a cord with a breaking strength of 215 newtons. What must be the coefficient of static friction to 2 decimal places between you surface for you to be saved from the fire?

Answer 1

The coefficient of static friction between you and the surface must be approximately μₛ = 0.92.

Step-by-step explanation:

To determine the coefficient of static friction (μₛ), we can use the following equation involving forces on an inclined plane:

fₛ = μₛ ⋅ N

Here, fₛ is the force of static friction, N is the normal force, and μₛ is the coefficient of static friction. The normal force can be decomposed into its components, where N cos(θ) counters the gravitational force pulling you down the incline, and N sin(θ) is responsible for the static friction preventing you from sliding.

In equilibrium, the static friction force is at its maximum, which is the breaking strength of the cord. Therefore,

fₛ = Breaking Strength of Cord = 215 N

Now, let's substitute the values into the equation:

fₛ = μₛ ⋅ N

215 N = μₛ ⋅ (mg - N sin(θ))

Here, m is the mass (62 kg), g is the acceleration due to gravity (9.8 m/s²), and θ is the angle of the slope (55 degrees). Solving this equation, we find μₛ ≈ 0.92. This means that the coefficient of static friction between you and the surface must be at least 0.92 to prevent sliding and ensure your safety on the slope.