High School

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 two decimal places, between you and the surface for you to be saved from the fire?

Answer :

Final Answer:

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

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.