A block at rest. The coefficients of static and kinetic friction are .75(Static) and .64(Kinetic). The acceleration of gravity is 9.8m/s^2 and the mass is 46kg. I've solved for the frictional force which is, 252.0841609N. Though what is the largest angle which the incline can have so the mass does not slide down the incline?
TanTheta=mu*g
To find the largest angle at which the mass does not slide down the incline, we need to consider the forces acting on the block.
The main forces involved are the force due to gravity (mg) acting vertically downward and the frictional force (Ff) acting parallel to the incline in the opposite direction of motion.
Since the block is at rest, the force of static friction is equal to the force exerted by the gravitational force component parallel to the incline. We can calculate this force using the formula:
Ff(static) = μ(static) * N
where μ(static) is the coefficient of static friction and N is the normal force acting perpendicular to the incline.
The normal force (N) can be calculated using:
N = mg * cos(θ)
where m is the mass of the block and θ is the angle of the incline measured from the horizontal.
Substituting the expression for N into the formula for Ff(static), we get:
Ff(static) = μ(static) * mg * cos(θ)
Now, we can substitute the given values into the equation:
Ff(static) = (0.75) * (46 kg) * (9.8 m/s^2) * cos(θ)
Given that the calculated frictional force is 252.0841609 N, we can set this equation equal to the frictional force:
252.0841609 N = (0.75) * (46 kg) * (9.8 m/s^2) * cos(θ)
Now, we can solve for θ. First, divide both sides by (0.75) * (46 kg) * (9.8 m/s^2):
cos(θ) = 252.0841609 N / [(0.75) * (46 kg) * (9.8 m/s^2)]
cos(θ) ≈ 0.777
To find the largest angle, take the inverse cosine (arccos) of both sides:
θ ≈ arccos(0.777)
Using a calculator, the largest angle is approximately 39.5 degrees.
Therefore, the largest angle at which the mass does not slide down the incline is approximately 39.5 degrees.