A scooter with a mass of 25kg on a horizontal plane that is inclined until at an angle of 3degrees.what is the minimum coefficient of static friction for the scooter not to slide?
To determine the minimum coefficient of static friction for the scooter not to slide on the inclined plane, we need to analyze the forces acting on the scooter.
1. Decompose the gravitational force: The gravitational force acting on the scooter can be divided into two components: the force perpendicular to the plane (mg * cosθ) and the force parallel to the plane (mg * sinθ), where m is the mass of the scooter and θ is the angle of inclination (3 degrees).
2. Find the force opposing motion: The force opposing motion is the force of static friction (fs). In this case, the minimum coefficient of static friction (µs) is required to prevent the scooter from sliding.
3. Determine the equation: Since the scooter is at the verge of sliding, the opposing force of friction will be at its maximum, given by fs = µs * (mg * cosθ).
4. Write the force equilibrium equation: The force of static friction must balance the component of gravitational force parallel to the plane. Thus, we have µs * (mg * cosθ) = mg * sinθ.
5. Solve for the coefficient of static friction: Rearrange the equation to solve for µs. Divide both sides of the equation by mg * cosθ: µs = (mg * sinθ) / (mg * cosθ).
6. Simplify the equation: Cancel out the mass (m) and simplify the trigonometric terms. Since mg appears on both sides, it cancels out, leaving: µs = tanθ.
7. Calculate the coefficient of static friction: Substitute the given angle of inclination (θ = 3 degrees) into the equation µs = tanθ to find µs = tan(3°).
Using a calculator, tan(3°) ≈ 0.0524
Therefore, the minimum coefficient of static friction for the scooter not to slide is approximately 0.0524.