# Problem № 6 (10 points)

A cylinder with a mass of $M=1$ kg was placed on rails inclined at an angle $\alpha=30^{\circ}$ to the horizontal (the side view is shown in the figure). What is the minimum mass $m$ of the load that needs to be attached to the thread wound around the cylinder so that it starts rolling upwards? Slippage is absent.

![](https://cdn.mathpix.com/cropped/2024_05_06_7ac9c551b647ccda756fg-2.jpg?height=331&width=460&top_left_y=1248&top_left_x=821)

Answer: 1 kg

#
# Solution and evaluation criteria:

![](https://cdn.mathpix.com/cropped/2024_05_06_7ac9c551b647ccda756fg-2.jpg?height=474&width=463&top_left_y=1825&top_left_x=822)

The moment of forces relative to the point of contact of the cylinder with the plane: $m g($ ( $-R \sin \alpha)=M g R \sin \alpha$ (5 points) $m\left(1-\frac{1}{2}\right)=M \frac{1}{2}$

$m=M=1 \kappa 2$

(5 points)

#