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A small block lies on a horizontal disk at a distance $r = 0.2$ m from the axis of rotation (see the figure). The coefficient of friction between the block and the disk is $\mu = 0.5$. The disk is spun up slowly. At what angular velocity $\omega$ will the block start to slip? Find the corresponding…
The figure shows the graph of the velocity of a car versus time (velocity in m/s, time in seconds). Find the acceleration of the car on each stage of the motion, the distance travelled and the average speed over the whole motion.
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 block of mass $m = 0.5$ kg is pressed against a light spring of stiffness $k = 200$ N/m compressed by $x = 10$ cm; the block is not attached to the spring. The spring is released and the block moves along a horizontal floor with a coefficient of friction $\mu = 0.2$ (see the figure). Find the…
A block slides without friction down a hill of height $h = 2$ m and then, passing smoothly onto a horizontal stretch, slides along it until it stops. The coefficient of friction on the horizontal stretch is $\mu = 0.25$ (see the figure). Find the speed of the block at the foot of the hill and the…
A person of mass $m = 70$ kg stands on the floor of an elevator cabin. The elevator moves with an acceleration $a = 2$ m/s² directed: 1) upward; 2) downward (see the figure). Find the weight of the person in each case. Take $g = 10$ m/s².
Two blocks of masses $m_1 = 2$ kg and $m_2 = 3$ kg are joined by a light inextensible thread and lie on a smooth horizontal table. A horizontal force $F = 20$ N is applied to block $m_2$ (see the figure). Find the acceleration of the blocks and the tension in the thread.
A block of mass $m = 10$ kg lies on a horizontal table. It is pulled by a force $F = 50$ N directed at an angle $\alpha = 30°$ above the horizontal (see the figure). The coefficient of friction between the block and the table is $\mu = 0.2$. Find the acceleration of the block. Take $g = 10$ m/s².
A ball of mass $m = 0.1$ kg hangs on a thread of length $l = 1$ m and moves uniformly in a circle in a horizontal plane. The thread makes an angle $\alpha = 60°$ with the vertical (see the figure). Find the tension $T$ in the thread and the period $\tau$ of the ball's revolution. Take $g = 10$ m/s².