Masses on Slopes#

Two masses \(m_1=\) 12 \(\rm{kg}\) and \(m_2=\) 3 \(\rm{kg}\) are connected by a light rope which passes over a light, low friction pulley between low friction slopes of \(30^\circ\) and \(10^\circ\) as shown in the figure. Approximating the masses of the rope and pulley to be negligible and the friction of both the slopes and the pulley to be negligible, find the acceleration of mass \(m_2\) up the slope.

There is a triangle with a block on each of its slopes, and a pulley at the top vertex. The right slope is at 10 degrees with the horizontal with the block labelled m sub 1 on it. The left slope is at 30 degrees with the horizontal with the block labelled m sub 2 on it. The two blocks are connected by a rope that passes over the pulley at the top.

Part 1#

Show your work to find the acceleration by drawing free body diagrams, axes and acceleration vectors, and write Newton’s second law equations in components independently for both masses. Upload the image as a pdf, and title it “part1.pdf”.

Answer Section#

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Part 2#

The acceleration of \(m_2\) is:

Answer Section#

Please enter in a numeric value in \(\rm{\frac{m}{s^2}}\).

Attribution#

Problem is licensed under the CC-BY-NC-SA 4.0 license.
The Creative Commons 4.0 license requiring attribution-BY, non-commercial-NC, and share-alike-SA license.