Standard +0.3 This is a standard two-particle pulley system requiring resolution of forces on an incline, friction calculation, and Newton's second law applied to a connected system. While it involves multiple steps (finding sin α and cos α from tan α, resolving forces parallel to slope, applying F=ma to both particles), these are routine mechanics techniques with no novel insight required. Slightly easier than average due to straightforward setup and clear solution path.
5
\includegraphics[max width=\textwidth, alt={}, center]{099c81e0-a95a-4f98-801c-32d905ef7c7d-3_432_710_258_721}
Two particles of masses 5 kg and 10 kg are connected by a light inextensible string that passes over a fixed smooth pulley. The 5 kg particle is on a rough fixed slope which is at an angle of \(\alpha\) to the horizontal, where \(\tan \alpha = \frac { 3 } { 4 }\). The 10 kg particle hangs below the pulley (see diagram). The coefficient of friction between the slope and the 5 kg particle is \(\frac { 1 } { 2 }\). The particles are released from rest. Find the acceleration of the particles and the tension in the string.
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\includegraphics[max width=\textwidth, alt={}, center]{099c81e0-a95a-4f98-801c-32d905ef7c7d-3_432_710_258_721}
Two particles of masses 5 kg and 10 kg are connected by a light inextensible string that passes over a fixed smooth pulley. The 5 kg particle is on a rough fixed slope which is at an angle of $\alpha$ to the horizontal, where $\tan \alpha = \frac { 3 } { 4 }$. The 10 kg particle hangs below the pulley (see diagram). The coefficient of friction between the slope and the 5 kg particle is $\frac { 1 } { 2 }$. The particles are released from rest. Find the acceleration of the particles and the tension in the string.
\hfill \mbox{\textit{CAIE M1 2016 Q5 [7]}}