Question

Same as previous example: you have a block of mass m=25 kg sitting on a flat, frictionless surface that makes an angle of θ with the horizontal. Only now there is friction. μₖ =0.4,μₖ =0.21.

a) If the ramp is slowly tilted from horizontal to larger and larger angles, at what angle will the block begin to slip?

Answer 1

The angle at which the block will begin to slip on an inclined plane can be calculated using the equation θ = tan-1(μk)

Step-by-step explanation:

When an object is on an inclined plane, the force of gravity can be broken down into two components: one parallel to the plane and one perpendicular to the plane. The maximum angle at which the block will begin to slip can be determined when the force of friction is equal to the parallel component of the weight of the block.

The formula to calculate the force of friction is given by f'k = μkmg, where μk is the coefficient of kinetic friction, m is the mass of the block, and g is the acceleration due to gravity. The formula to calculate the parallel component of the weight is given by Fp = mg sin(θ), where θ is the angle of the inclined plane.

Setting the force of friction equal to the parallel component of the weight and solving for θ, we get μk = tan(θ). Rearranging the equation, we find that the angle at which the block will begin to slip is given by θ = tan-1(μk).