Maximum static friction force = μs * N = 0.6 * (5 kg * 9.8 m/s²) = 29.4 N, approximately 30 N.

Once the applied force exceeds the maximum static frictional force, the block will start moving.

The maximum angle for static friction is given by tan(θ) = μs. Here, θ = tan⁻¹(0.5) which is approximately 26.57 degrees, so the block can remain at rest at angles less than this.

The block will not slide if the component of gravitational force down the incline is less than or equal to the maximum static friction force, leading to θ = tan⁻¹(μs).

The presence of kinetic friction opposes the motion, thus decreasing the acceleration of the block compared to a frictionless incline.

Maximum static frictional force (Fs) = μs * N = μs * mg = 0.5 * 10 kg * 9.8 m/s² = 49 N, approximately 50 N.

Frictional force (f_k) = μ_k * N = μ_k * mg = 0.3 * 10 kg * 9.8 m/s² = 29.4 N, approximately 30 N.

Frictional force (Ff) = μk * N = μk * mg = 0.3 * (5 kg * 10 m/s²) = 15 N.

Maximum static frictional force (Fs) = μs * N = μs * mg = 0.4 * (5 kg * 10 m/s²) = 20 N.

Net force = mg sin(30) - μmg cos(30). Acceleration a = (mg sin(30) - μmg cos(30))/m = g(sin(30) - μ cos(30)). Substituting g = 10 m/s² gives a = 10(0.5 - 0.2 * √3/2) = 4.9 m/s².

Frictional force = μk * N = 0.4 * 100 N = 40 N. Net force = applied force - frictional force = 50 N - 40 N = 10 N.

Net force = applied force - frictional force. Frictional force = μ_k * N = 0.4 * 10 kg * 9.8 m/s² = 39.2 N. Net force = 50 N - 39.2 N = 10.8 N. Acceleration = F/m = 10.8 N / 10 kg = 1.08 m/s², approximately 1 m/s².

Frictional force = μk * N = 0.3 * 100 N = 30 N. Net force = applied force - frictional force = 50 N - 30 N = 20 N.

The centripetal force required is provided by friction: F = mv^2/r. The frictional force is μmg. Setting them equal gives μ = v^2/(rg). Here, μ = (20^2)/(100*9.8) ≈ 0.4.

If the box does not move, the net force acting on it is zero, meaning the applied force equals the frictional force.

Applying a force at an angle reduces the normal force because part of the applied force acts vertically upward, counteracting the weight of the block.

As the angle increases, the component of gravitational force parallel to the plane increases, which can lead to a decrease in static friction until it reaches its maximum value.

As the angle increases, the component of gravitational force parallel to the plane increases, which can lead to a decrease in static friction until it reaches its maximum value.

The maximum frictional force occurs when an object is at rest, just before it starts to slide, which is characterized by static friction.

The coefficient of static friction (μs) is given by μs = F/N, where F is the force and N is the normal force. Here, μs = 20 N / 50 N = 0.4.

Frictional force is directly proportional to the normal force. Increasing the normal force increases the frictional force.

Increasing surface roughness generally increases the coefficient of friction due to greater interlocking between the surfaces.

Frictional force = μ * N = 0.2 * 200 N = 40 N. Work done = frictional force * distance = 40 N * 5 m = 200 J.

Work done against friction = frictional force * distance = (μk * m * g) * d = (0.4 * 5 kg * 9.8 m/s²) * 10 m = 196 J, approximately 40 J.

The coefficient of friction is independent of the surface area in contact; it depends on the materials and their surface roughness.

The coefficient of kinetic friction is generally independent of the speed of sliding, while it depends on surface roughness, normal force, and material.

Kinetic friction is independent of the contact area and depends only on the normal force and the coefficient of kinetic friction.