A15N crate rests on an ramp , the maximum angle just before it slips is 25 degree with the horizantle , what the coefficient of static friction between the crate and ramp surfaces ?
To determine the coefficient of static friction between the crate and ramp surfaces, you need to use the maximum angle at which the crate just starts to slip. Here's how you can find it:
1. Identify the forces acting on the crate: In this case, we have the weight of the crate (mg) acting vertically downward, and the normal force (N) acting perpendicular to the ramp's surface.
2. Break down the weight force: The weight force can be resolved into two components: the force acting parallel to the ramp (mgsinθ) and the force acting perpendicular to the ramp (mgcosθ), where θ is the angle of the ramp.
3. Determine the maximum angle: The maximum angle just before the crate starts to slip is given as 25 degrees in the horizontal direction. This means that the force parallel to the ramp (mgsinθ) is equal to the maximum force of static friction (Ff).
4. Write the equilibrium condition: At the point of slipping, the crate is in equilibrium, meaning that the sum of all forces acting on it is zero. In this case, ∑F = 0. Therefore, we can write the equation mgsinθ = Ff.
5. Calculate the coefficient of static friction: Ff, the force of static friction, can be written as Ff = μsN, where μs is the coefficient of static friction. The normal force (N) is equal to mgcosθ. Substituting these values into the equation from step 4, we get mgsinθ = μsN = μsmgcosθ.
6. Simplify the equation and solve for the coefficient of static friction: Divide both sides of the equation by mg, which cancels each other out, and you get sinθ = μs*cosθ. Divide sinθ by cosθ to get tanθ, and you have tanθ = μs. Finally, take the arctan of both sides to find the coefficient of static friction, μs = arctan(θ).
Therefore, the coefficient of static friction between the crate and ramp surfaces is μs = arctan(25°). Using a scientific calculator, you can calculate the exact value of the coefficient of static friction.
ma=mgsinα-F(fr)=mgsinα-μN=
=mgsinα-μmgcosα
μ(stat.fr) => a=0
0= mgsinα-μmgcosα
μ=tanα