Question

wo blocks sit on two different inclined planes that form a scalene triangle. They are connected to each other by a light-weight string that runs over an ideal pulley. 80.0 kg 80.0kg 53.130 30.0° Assuming zero friction between each block and the surfaces they slide on, what will be the magnitude of the acceleration of the system?

Answer 1

a = 1.47 m/s²

Step-by-step explanation:

As it can be seen in the attached image, we have two forces acting in the direction along the slides, that are the components of the force of gravity along both slides (to the right the one acting on the mass on the right plane, to the left the one acting on the other mass)

We can choose as our system to both masses, so, in this way, the tensions in the strings joining the masses to the pulley are internal, and don't show up in the equation for the acceleration of both blocks.

Taking the ideal pulley as redirecting the force on the mass on the left, we can say that the component of Fg towards the left, opposes to the one on the mass of the right slide.

So, we can apply Newton's 2nd Law to one axis along the slide, choosing as positive the right direction, as follows:

m₂*g* sin (53.13) - m₁*g*sin (30º) = (m₁+m₂)*a

Replacing by the masses and solving for a:

a = (80 kg*9.8 m/s²*0.8) - (80 kg*9.8m/s²*0.5) / 160 kg

⇒ a = 80 kg*9.8 m/s²*0.3 / 160kg = 235.2 kg*m/s² / 160 kg = 1.47 m/s²