# Tensions And Pulleys With Masses

The problem I am working on is:

"A block of mass m1 = 1.80 kg and a block of mass m2 = 6.30 kg are connected by a massless string over a pulley in the shape of a solid disk having radius R = 0.250 m and mass M = 10.0 kg. The fixed, wedge-shaped ramp makes an angle of θ = 30.0° as shown in the figure. The coefficient of kinetic friction is 0.360 for both blocks."

The provided diagram:

Determine the acceleration of the two blocks. (Enter the magnitude of the acceleration.)

Determine the tensions in the string on both sides of the pulley.

What I was wondering is why there are two different tension forces acting on the pulley? Could someone give me a descriptive answer? Also, does the mass of the pulley somehow affect the tension forces? Why exactly?

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Using the principle of virtual work, if you move the blocks a distance a, the inclined block is lowered by an amount equal to $a\sin(\theta)$, meaning that it gains energy $m_2 ga\sin(\theta)$. The total moving mass is $m_1 + m_2$, so that the acceleration is the same as for a mass $m_1 + m_2$ in 1 dimension with a force $m_2 g \sin(\theta)$, so that
$$a = {m_2 \over m_1 + m_2} g \sin\theta$$