🔭 physics

1. **Problem statement:** We want to derive the formula for kinetic energy in terms of charge $q$, mass $m$, velocity $v$, and potential difference $U$. 2. **Given:** The kinetic e

1. **Problem statement:** A 3.0 kg block on a horizontal surface is connected by a rope over a frictionless pulley to a 5.0 kg ball hanging vertically. The coefficient of friction

1. **Stating the problem:** Find the maximum height of the arrow given by the height function $$h(t) = -16t^2 + 80t + 25$$ where $h$ is height in feet and $t$ is time in seconds.

1. **State the problem:** We have a cannon ball launched with an initial velocity of 56 feet per second. Its height after $t$ seconds is given by the equation:

1. **State the problem:** We have the height equation of an object thrown upward: $$h = -16t^2 + 157t + 3$$

1. **State the problem:** A 62 kg person is in an elevator moving upward at a constant speed of 4.0 m/s for 5.0 s. We need to find the work done by the normal force on the person.

1. **State the problem:** Calculate the electrostatic force between a +5.0 C charge and a +9.0 C charge separated by 4 m using Coulomb's Law. 2. **Formula:** Coulomb's Law is given

1. **Stating the problem:** We have a thermometer showing a temperature between -10°C and -20°C, closer to -10°C, approximately at -13°C. 2. **Understanding the thermometer scale:*

1. The problem asks: What temperature does the thermometer show? 2. Since the problem does not provide any numerical data or image, we cannot determine the temperature value.

1. **State the problem:** We have two radioactive samples with given amounts over time. Sample 1 starts at 800 mg and decreases to 400 mg after 1 month. Sample 2 starts at 1000 mg

1. **Problem statement:** We want to find the work function $\phi$ and its uncertainty $\Delta \phi$ from the equation $$E = h \nu - \phi$$ given the measured values with uncertain

1. **Problem Statement:** Understand the kinetic theory of gases and interpret changes in an ideal gas on a pressure-volume (P-V) diagram. 2. **Concepts and Formulas:** The kinetic

1. **State the problem:** Amy's toy rocket is launched straight up, and its height over time is modeled by a downward-opening parabola. We need to find when the rocket is on the gr

1. **Problem Statement:** Two planes, a Cessna and a Boeing 747, are flying toward the same intersection point at the same altitude. The Cessna is 100 miles north of the intersecti

1. The question "what is the power?" is ambiguous without context. 2. In physics, power is defined as the rate at which work is done or energy is transferred.

1. **مسئله را می‌نویسیم.** یک تکه یخ با جرم $400-42=358\,g$ را داخل آبِ $0^\circ C$ می‌اندازیم. پس از برقراری تعادل، جرم یخ باقی‌مانده $410\,g$ می‌شود. دمای اولیه یخ را می‌خواهیم.

1. **صورت مسئله:** یک گرمکن می‌تواند دمای جرم $m$ از آب را در $30$ ثانیه، بدون تغییر حالت، به اندازه $60^\circ C$ بالا ببرد.

1. The problem asks to state another term for "quantity of motion." The answer is momentum. 2. The two factors used to determine the momentum of an object are mass and velocity.

1. **State the problem:** We need to solve the equation given by Kirchhoff's voltage law for the current $I$ in a series circuit: $$7.8I + 8.2I - 12.8 = 0$$

1. **Problem statement:** We have a series circuit with total resistance $R_{total} = 25\ \Omega$ and voltage drop across the battery $V = 6.0\ \text{V}$. We need to find: (a) The

1. **State the problem:** We are given the position function of a ball rolling down an inclined plane as $$s(t) = 2t^3 + 3t^2 + 4$$ where $s(t)$ is the distance in cm and $t$ is th