Category: HC Verma Part 1: Mechanics

Problem Statement Solve the Newton’s Laws / mechanics problem: Sand falls at 0.5 kg/s onto a belt moving at 2 m/s. Find the force needed to maintain constant belt speed. (Hint: use momentum principle.) Force = rate of momentum change = $(dm/dt) \times v$ Step 1: $F = v \times (dm/dt) = 2 \times 0.5…

Problem Statement Solve the Newton’s Laws / mechanics problem: In an Atwood machine, $m_1 = 5$ kg (on rough table, $\mu_k = 0.2$) and $m_2 = 3$ kg (hanging). Find whether the system moves. ($g = 10$ m/s²) Check if $m_2g > f_k = \mu_k m_1 g$ Step 1: $m_2 g = 30$ N; $f_k…

Problem Statement A block is placed on a conveyor belt moving at 5 m/s (leftward). $\mu_k = 0.4$, $g = 10$ m/s². Initially block is stationary. Find time until block matches belt speed. Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical Concepts…

Problem Statement Solve the Newton’s Laws / mechanics problem: A 0.5 kg block moves on a circular track of radius 2 m at constant speed 4 m/s. The track is horizontal. Find the friction force (centripetal). ($g = 10$ m/s²) Centripetal force = $mv^2/r$ (provided by friction) Step 1: $f = mv^2/r = 0.5 \times…

Problem Statement Solve the Newton’s Laws / mechanics problem: A block is projected up a rough 30° incline ($\mu_k = 0.3$) at 10 m/s. Find the deceleration and how far it goes. ($g = 10$ m/s²) Going up: both gravity component and friction act down: $a = g(\sin\theta + \mu_k\cos\theta)$ Step 1: $a = 10(\sin30°…

Problem Statement Solve the Newton’s Laws / mechanics problem: A 4 kg block rests on a 6 kg block. The 6 kg block is on a frictionless surface. All surfaces have $\mu_k = 0.3$. A force $F = 20$ N acts on the 6 kg block. Find the accelerations. ($g = 10$ m/s²) Check if…

Problem Statement A car on a road with $\mu_s = 0.6$ needs to stop urgently. Find the maximum deceleration without the wheels skidding. ($g = 10$ 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 draws on…

Problem Statement Solve the Newton’s Laws / mechanics problem: Two masses $m_1 = 5$ kg (on table, $\mu_k = 0.2$) and $m_2 = 3$ kg (hanging) are connected by a string. Find the acceleration and tension. ($g = 10$ m/s²) $m_2 g – \mu_k m_1 g = (m_1+m_2)a$ Step 1: $a = (m_2 – \mu_k…

Problem Statement Solve the rotational mechanics problem: Explain why friction is necessary for a cylinder to roll without slipping down an incline, and in what direction friction acts. Rolling without slipping requires friction; friction provides torque that causes rolling Step 1: Gravity component along incline = $mg\sin\theta$ (down slope). Step 2: With Given Information Mass…

Problem Statement Solve the Newton’s Laws / mechanics problem: A 3 kg block on a 37° rough incline ($\mu_k = 0.25$) is pulled up by a force $F = 30$ N along the incline. Find the acceleration. ($g = 10$ m/s², $\sin37°=0.6$, $\cos37°=0.8$) $F – mg\sin\theta – \mu_k mg\cos\theta = ma$ Step 1: $mg\sin37° =…