Category: HC Verma Part 1: Mechanics

Problem Statement A road is banked at angle $\theta$ for speed $v$. Derive the formula for $\tan\theta$. Find $\theta$ for $v = 20$ m/s and $r = 200$ m. ($g = 10$ m/s²) Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical Concepts…

Problem Statement A ball of mass 0.1 kg is whirled in a horizontal circle of radius 0.5 m at 2 rev/s. Find the centripetal force. 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 fundamental physical…

Problem Statement A 4 kg block is pressed against a rough wall ($\mu_s = 0.5$) by a horizontal force $F$. Find the minimum $F$ to prevent the block from sliding. ($g = 10$ m/s²) Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical…

Problem Statement Solve the Newton’s Laws / mechanics problem: A 4 kg block is pressed against a smooth wall by a horizontal force $F = 40$ N. What is the normal force from the wall and the friction from the wall? ($g = 10$ m/s²) Normal from wall = $F$ (horizontal equilibrium); friction from wall…

Problem Statement A 0.5 kg ball on a string of length 1 m makes a conical pendulum with half-angle 30°. Find the tension and period. ($g = 10$ 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 A 2 kg ball slides down a smooth curved surface to the bottom where the radius of curvature is 0.5 m. If the speed at the bottom is 4 m/s, find the normal force. ($g = 10$ m/s²) Given Information All quantities, constants, and constraints stated in the problem above Physical constants used…

Problem Statement A car moves over a hill of radius $r = 50$ m at the top. Find the maximum speed at which it just maintains contact. ($g = 10$ 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…

Problem Statement A 5 kg block hangs from a string (max tension 60 N). An additional 1 kg mass is placed on it suddenly. Will the string break? ($g = 10$ m/s²) Given Information All quantities, constants, and constraints stated in the problem above Physical constants used as needed (see Concepts section) Physical Concepts &…

Problem Statement A 5 kg block starts from rest and is acted on by a constant force of 10 N on a frictionless surface. How far does it travel in 4 s? 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 2 kg block is between two springs (constants $k_1 = 100$ N/m and $k_2 = 150$ N/m) and the springs are compressed equally. Find the acceleration when released from rest. If both springs compressed by $x$: net force = $(k_1+k_2)x$ (both push same direction? No…