🔭 physics

1. **Problem statement:** Calculate the kinetic energy of a dart hitting a target at a speed of 4.39 m/s, then find the height from which the dart must be dropped to reach that ene

1. The problem is to calculate the power $P_2$ dissipated by a resistor $R_2$ given the output voltage $V_{out}$ and the resistance $R_2$. 2. The formula for power dissipated by a

1. **Problem statement:** A pulley has two rims with radii $R_1$ (inner) and $R_2$ (outer). Two blocks with masses $m_1$ and $m_2$ hang from strings wrapped around these rims. The

1. **Problem statement:** A rectangular block of mass $m$, width $w$, and height $h$ is hinged at its lower right corner on a tabletop. A force $F$ is applied perpendicular to the

1. **State the problem:** The intensity of a sound wave, $I$, is doubled. We need to find the difference in sound level, $\Delta L$, measured in Decibels (dB). 2. **Formula used:**

1. **State the problem:** We have a mass-spring system with mass $m=4$ kg and spring constant $k=100$ N/m. The mass is displaced by $0.2$ m from equilibrium and released from rest.

1. **State the problem:** Calculate the net electrostatic force on charge $q_1 = 2\,\mu C$ located at a vertex of an equilateral triangle with side length $0.1$ m, due to charges $

1. **State the problem:** We need to find the branch currents $I_1$, $I_2$, $I_3$, and $I_4$ in the given circuit using Kirchhoff's Current Law (KCL).

1. **Problem statement:** We need to find the velocity with which a bullet strikes the ground, assuming it reaches terminal velocity before impact. 2. **Key concept:** Terminal vel

1. **Problem statement:** We have a falling object with velocity $v(t)$ under constant gravitational acceleration $g=10$ m/s², described by the differential equation $v' = -10$. Th

1. **Stating the problem:** We want to evaluate or understand the integral expression for the vector field \( \vec{E} \) given by

1. **Problem statement:** A small rock is thrown vertically upward with an initial speed of 18.0 m/s from the edge of a building 3000 cm tall. We want to find the speed of the rock

1. **State the problem:** A glider starts descending from rest with a constant acceleration of $2\,m/s^2$ for the first 15 seconds, then continues with zero acceleration for the ne

1. **State the problem:** Investigate the relationship between net force, mass, and acceleration using the experimental setup with a trolley, pulley, and hanging masses. 2. **Varia

1. **State the problem:** Investigate the relationship between net force, mass, and acceleration using an experimental setup with a trolley, pulley, and hanging masses. 2. **Variab

1. **State the problem:** Convert an acceleration of 5.70 meters per second squared to miles per minute squared. 2. **Formula and conversion factors:**

1. **State the problem:** Given the displacement function $s(t) = t^3 - 6t^2 - 36t$, find the maximum speed and maximum velocity in the first 7 seconds of motion. 2. **Recall formu

1. **Problem statement:** A uniform slender rod of length 3 m and mass 18 kg is pinned at one end and released from rest at 30° below the horizontal. We need to find the initial an

1. **State the problem:** A bullet of mass 10g (0.01 kg) is fired at 100 m/s into a wooden block of mass 190g (0.19 kg) suspended by a string. The bullet embeds in the block, and w

1. **State the problem:** An object Z has a kinetic energy of 800 J at point X and moves horizontally to point Y, experiencing a constant opposing force of 100 N over a distance of

1. **Problem statement:** Two forces of magnitudes 3N and 4N act perpendicular to each other on a 2kg object initially at rest. Find the kinetic energy after 20 seconds. 2. **Step