A 50.0-kg block and 100-kg block are connected by a string as in Figure P8.36. The pulley is frictionless and of negligible mass. The coefficient of kinetic friction between the 50-kg block and incline is 0.250. Determine the change in the kinetic energy of the 50-kg block as it moves from A to B, a distance of 20.0 m

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To determine the change in kinetic energy of the 50-kg block as it moves from A to B, we need to calculate the work done on the block by the friction force and the gravitational force.

First, let's calculate the work done by the gravitational force. The change in height between point A and B is zero as the block moves along the incline, so the work done by gravity is zero.

Next, let's calculate the work done by the friction force. The friction force can be calculated using the equation:

F_friction = μ * F_normal

where μ is the coefficient of kinetic friction and F_normal is the normal force.

The normal force can be calculated as:

F_normal = m * g * cos(θ)

where m is the mass of the block, g is the acceleration due to gravity, and θ is the angle of the incline.

Since the pulley is frictionless, the tension in the string is the same on both sides. Therefore, the force exerted on the 50-kg block by the string is equal to the weight difference between the two blocks. The weight can be calculated as:

F_weight = m * g

The net force acting on the block is then:

F_net = F_weight - F_friction

The work done by the friction force is calculated as:

W_friction = F_friction * d

where d is the distance traveled by the block (20.0 m in this case).

Finally, we can calculate the change in kinetic energy using the work-energy theorem:

ΔK.E. = W_net

where ΔK.E. is the change in kinetic energy.

By plugging in the values, we can calculate the answer.

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