Imagine a particle of mass m, constrained to move along the x-axis, subject to some specified force F(x, t). The program of classical mechanics is to deter- mine the position of the particle at any given time: x(t). Once we know that, we can figure out the velocity (\( v=\frac{dx}{dt}\) ), the momentum (p = mv), the kinetic energy ( \( T=\frac{1}{2}mv^2 \) ), or any other dynamical variable of interest. And how do we go about determining x(t)? We apply Newton's second law: F = ma. (For conservative systems the only kind we shall consider, and, fortunately, the only kind that occur at the microscopic level---the force can be expressed as the derivative of a potential energy function, \( F=-\frac{\partial V}{\partial x} \) , and Newton's law reads \( m\frac{d^2x}{dt^2}=-\frac{\partial V}{\partial x} \) .) This, together with appropriate initial conditions (typically the position and velocity at t 0), determines x(t). Quantum mechanics approaches this same problem quite differentl...
Contoh Soal dan Pembahasan Asas Black - Soal Nomor 1. Suhu tiga macam cairan bermassa sama A, B, dan C berturut-turut adalah 10°C, 20°C, dan 30°C. A dan B dicampur suhunya menjadi 16°C, sedangkan B dan C dicampur suhunya menjadi 24°C. Jika A dan C dicampur, suhunya menjadi .... A. 10°C B. 15°C C. 20°C D. 25°C E. 30°C Pembahasan : Cairan A dan cairan B : \begin{align*} Q_{serap} &= Q_{lepas} \\ m\cdot c_A\cdot \Delta T &= m\cdot c_B\cdot \Delta T \\ c_A\cdot (16-10) &= c_B \cdot (20-16) \\ 6c_A &= 4c_B \\ 3c_A &= 2c_B \end{align*} Cairan B dan cairan C : \begin{align*} Q_{serap} &= Q_{lepas} \\ m\cdot c_B\cdot \Delta T &= m\cdot c_C\cdot \Delta T \\ c_B\cdot (24-20) &= c_C \cdot (30-24) \\ 4c_B &= 6c_C \\ 2c_B &= 3c_C \end{align*}