The mass of block A is 4 kg, the mass of block B is 3 kg, and the angle of the ramp is θ = 30°. The rope moves over the pulley without slipping. The coefficient of kinetic friction between the block A and the ramp is 0.15. The pulley can be modeled as a uniformly dense cylinder with a mass of 4 kg and a radius of 10 cm. What is the magnitude of the tension (in N) in the rope between block B and the pulley?

Explanation:

We need to use the Newton's second law.

Block A

(1)

Block B

(2)    

Pulley

Here we need to use Newton's law related to the torque.

(3)

I is the momentum of inertia of a cylinder (I=(1/2)mr²)

α is the angular acceleration (a/R)

Let's combine 1 and 2 to find T(B)-T(A)

(4)

From 3 we have:

(5)

We can equal (4) and (5)

Therefore, using (2) we can find the tension in the rope between block B:

I hope it helps you!

the one with the highest speed