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A uniform ladder of mass $m = 10$ kg and length $L$ leans against a smooth vertical wall and a rough floor, making an angle $\alpha = 60°$ with the floor (see the figure). Find the reaction force $N_w$ of the wall and the friction force acting on the ladder from the floor, as well as the minimum…
A load of mass $m = 5$ kg hangs on two light threads attached to the ceiling. The threads make angles $\alpha = 37°$ and $\beta = 53°$ with the horizontal (see the figure). Find the tensions $T_1$ and $T_2$ in the threads. Take $g = 10$ m/s², $\sin 37° = \cos 53° = 0.6$, $\cos 37° = \sin 53° = 0.8$.
A uniform beam of mass $M = 20$ kg and length $L = 6$ m rests with its ends on two supports $A$ and $B$. A load of mass $m = 60$ kg hangs from the beam at a distance $a = 2$ m from support $A$ (see the figure). Find the support reactions $N_A$ and $N_B$. Take $g = 10$ m/s².
A ball of mass $m = 0.2$ kg hangs on a light thread. Under a horizontal force $F$ the ball is in equilibrium and the thread is deflected from the vertical by an angle $\alpha = 37°$ (see the figure). Find the force $F$ and the tension $T$ in the thread. Take $g = 10$ m/s², $\sin 37° = 0.6$, …