Two blocks, A and B (with mass 50 kg and 100 kg, respectively), are connected by a string. (one mass is on the incline, the other is hanging from the pullye) The pulley is frictionless and of negligible mass. The coefficient of kinetic friction between block A and the incline is µk = 0.21. Determine the change in the kinetic energy of block A as it moves from C to D, a distance of 20 m up the incline if the system starts from rest.

To determine the change in kinetic energy of block A as it moves from point C to D, we need to calculate the work done against friction and the change in gravitational potential energy.

Let's break down the problem and calculate each part separately.

1. Work done against friction:
The work done against friction can be calculated using the formula: W = force × distance. In this case, the force opposing the motion is the frictional force.

The frictional force can be calculated as follows:
frictional force = µk × normal force
Since block A is on an incline, the normal force will be equal to the weight of block A multiplied by the cosine of the angle of the incline.

normal force = weight of A × cos(θ)
weight of A = mass of A × acceleration due to gravity
where θ is the angle of the incline

2. Change in gravitational potential energy:
The change in gravitational potential energy can be calculated using the formula: ∆PE = mass × g × ∆h

∆h, the change in height, can be calculated as follows:
∆h = distance × sin(θ)

3. Change in kinetic energy:
The change in kinetic energy can be calculated using the formula: ∆KE = KE final − KE initial
Since the system starts from rest, the initial kinetic energy is 0.

Now that we have the steps, we can perform the calculations:

1. Calculate the normal force:
weight of A = mass of A × acceleration due to gravity
normal force = weight of A × cos(θ)

2. Calculate the frictional force:
frictional force = µk × normal force

3. Calculate the work done:
work done against friction = frictional force × distance

4. Calculate the change in height:
∆h = distance × sin(θ)

5. Calculate the change in gravitational potential energy:
∆PE = mass of A × g × ∆h

6. Calculate the change in kinetic energy:
∆KE = ∆PE − work done against friction

Substitute the given values (mass of A, mass of B, µk, distance, and angle) into the equations and perform the calculations to find the change in kinetic energy of block A as it moves from C to D, a distance of 20 m up the incline.