Pick a topic on the left, open a problem and check the solution hint by hint.
An oil drop of mass $m = 2.4 \cdot 10^{-15}$ kg is in equilibrium between the horizontal plates of a parallel-plate capacitor. The distance between the plates is $d = 1$ cm, the voltage is $U = 500$ V, and the upper plate is positively charged (see the figure). Find the charge of the drop,…
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…
Two capacitors of capacitances $C_1 = 2$ µF and $C_2 = 3$ µF are connected in series to a voltage source $U = 100$ V (see the circuit). Find the capacitance of the combination, the charge on each capacitor and the voltage across each of them. The capacitors were uncharged before the connection.
A resistor $R_1 = 4$ Ω is connected in series with two resistors $R_2 = 6$ Ω and $R_3 = 3$ Ω connected in parallel (see the circuit). A voltage $U = 24$ V is applied to the ends of the whole section. Find the current in each resistor and the voltage across $R_1$.
A point source of light is at the bottom of a vessel, at a depth $h = 3$ m below the surface of a liquid with refractive index $n = 1.25$ (see the figure). A bright circle is seen on the surface of the liquid, outside of which no light leaves the liquid into the air. Find the radius $R$ of this…
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 monatomic ideal gas performs the cycle $1 \to 2 \to 3 \to 4 \to 1$ shown on the $p$–$V$ graph (see the figure): $1 \to 2$ is isochoric heating, $2 \to 3$ isobaric expansion, $3 \to 4$ isochoric cooling, $4 \to 1$ isobaric compression. On the graph the pressure is given in units of $10^5$ Pa and…
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…