Category: HC Verma Part 1: Mechanics

Problem Statement Solve the Newton’s Laws / mechanics problem: A 2 kg block moving at 6 m/s on a frictionless surface hits a spring ($k = 400$ N/m). Find the maximum compression of the spring. Energy conservation: $\frac{1}{2}mv^2 = \frac{1}{2}kx^2$ Step 1: $x = v\sqrt{m/k} = 6\sqrt{2/400} = 6\sqrt{0.005} = 6 \times 0.0707 = 0.424$…

Problem Statement Solve the momentum/collision problem: A force $F = (3t^2 + 2)$ N acts on a 1 kg particle for $t = 0$ to $t = 2$ s. Find the change in momentum. $\Delta p = \int_0^t F\,dt$ (impulse) Step 1: $\Delta p = \displaystyle\int_0^2 (3t^2+2)\,dt = [t^3+2t]_0^2 = (8+4) – 0 = 12$…

Problem Statement Solve the Newton’s Laws / mechanics problem: A 4 kg block on a table ($\mu_k = 0.25$) is connected by a string to a 2 kg hanging mass. Find the acceleration and tension. ($g = 10$ m/s²) $m_2g – \mu_k m_1 g = (m_1+m_2)a$ Step 1: $a = (m_2 – \mu_k m_1)g/(m_1+m_2) =…

Problem Statement Solve the Newton’s Laws / mechanics problem: A 2 kg block on a 30° incline has $\mu_k = 0.2$. Find the acceleration when sliding down. ($g = 10$ m/s²) $a = g(\sin\theta – \mu_k\cos\theta)$ Step 1: $a = 10(\sin30° – 0.2\cos30°) = 10(0.5 – 0.2 \times 0.866) = 10(0.5 – 0.173) = 10(0.327)…

Problem Statement A block of mass 2 kg is on a cart that accelerates at 3 m/s² to the right. The block is connected to the cart wall by a spring. Find the spring’s compression/extension. ($k = 500$ N/m) Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as…

Problem Statement Solve the Newton’s Laws / mechanics problem: A force $\vec{F} = 3\hat{i} + 4\hat{j}$ N acts on a 2 kg particle. Find the acceleration vector and its magnitude. $\vec{a} = \vec{F}/m$ Step 1: $\vec{a} = (3\hat{i}+4\hat{j})/2 = 1.5\hat{i}+2\hat{j}$ m/s². Step 2: $|\vec{a}| = \sqrt{2.25+4} = \sqrt{6.25} = 2.5$ m/s². $$\boxed{\vec{a} = 1.5\hat{i}+2 Given…

Problem Statement In an Atwood machine, $m_1 = 4$ kg and $m_2 = 6$ kg. Find the tension, acceleration, and the pressure on the pulley. ($g = 10$ m/s²) Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical Concepts & Formulas This problem…

Problem Statement Solve the gravitation problem: A satellite orbits Earth at radius $r = 7 \times 10^6$ m. Find the orbital speed. ($g = 9.8$ m/s² at Earth’s surface, $R_E = 6.4 \times 10^6$ m) $v = \sqrt{GM_E/r}$; use $GM_E = gR_E^2$ Step 1: $GM_E = gR_E^2 = 9.8 \times (6.4\times10^6)^2 = 9.8 \times 4.096\times10^{13}…

Problem Statement Solve the Newton’s Laws / mechanics problem: A car of mass 1000 kg goes over a bump of radius 20 m at 10 m/s. Find the force exerted by the car on the road at the top of the bump. ($g = 10$ m/s²) At top: $mg – N = mv^2/r$ (centripetal); by…

Problem Statement A coin placed 0.1 m from the center of a turntable. If $\mu_s = 0.5$, find the maximum angular velocity before the coin slides. ($g = 10$ m/s²) Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical Concepts & Formulas This…