Category: HC Verma Part 1: Mechanics

Problem Statement Solve the Newton’s Laws / mechanics problem: The coefficient of static friction between a block and an incline is 0.6. Find the angle of repose. Angle of repose $\theta_r = \arctan(\mu_s)$ Step 1: $\tan\theta_r = \mu_s = 0.6$. Step 2: $\theta_r = \arctan(0.6) \approx 31°$. $$\boxed{\theta_r = \arctan(0.6) \approx 31°}$$ Given Information Mass(es),…

Problem Statement Solve the Newton’s Laws / mechanics problem: A block is placed on a 25° incline. $\mu_s = 0.5$. Will the block slide? ($\tan 25° \approx 0.466$) Block slides if $\tan\theta > \mu_s$ Step 1: $\tan 25° \approx 0.466 Step 2: Since $\tan\theta $$\boxed{\text{Block does not slide (}\tan\theta Given Information Mass(es), forces, angles, and…

Problem Statement Solve the Newton’s Laws / mechanics problem: A 6 kg block on a surface ($\mu_k = 0.4$) is pushed by a 30 N force. Find the acceleration. ($g = 10$ m/s²) $F_{net} = F – f_k = F – \mu_k mg$; $a = F_{net}/m$ Step 1: $f_k = 0.4 \times 6 \times 10…

Problem Statement Solve the Newton’s Laws / mechanics problem: What is the minimum force needed to move a 10 kg block on a horizontal floor with $\mu_s = 0.5$? ($g = 10$ m/s²) Minimum force to initiate motion = $f_s^{max} = \mu_s mg$ Step 1: $F_{min} = \mu_s mg = 0.5 \times 10 \times 10…

Problem Statement Solve the Newton’s Laws / mechanics problem: A block of mass 5 kg rests on a horizontal surface. The coefficient of static friction is 0.4 and kinetic friction is 0.3. Find the maximum static friction force and the kinetic friction force. ($g = 10$ m/s²) $f_s^{max} = \mu_s N$; $f_k = \mu_k N$;…

Problem Statement Solve the Newton’s Laws / mechanics problem: A spring balance hangs from the ceiling of an elevator and supports a 5 kg mass. What does the spring balance read when the elevator (a) accelerates up at 2 m/s², (b) accelerates down at 2 m/s²? ($g = 10$ m/s²) Spring balance reads apparent weight…

Problem Statement Solve the Newton’s Laws / mechanics problem: Masses $m_1 = 6$ kg and $m_2 = 4$ kg are connected over a pulley. $m_2$ is on a frictionless 30° incline; $m_1$ hangs. Find the acceleration. ($g = 10$ m/s²) $a = (m_1 – m_2\sin30°)g/(m_1+m_2)$ Step 1: $a = (6 – 4\times0.5)(10)/(6+4) = (6-2)(10)/10 =…

Problem Statement Solve the Newton’s Laws / mechanics problem: A particle is in equilibrium under three forces: $\vec{F}_1 = 5\hat{i}$ N, $\vec{F}_2 = 3\hat{j}$ N, and $\vec{F}_3 = ?$. Find $\vec{F}_3$. Equilibrium: $\vec{F}_1+\vec{F}_2+\vec{F}_3 = 0$ Step 1: $\vec{F}_3 = -(\vec{F}_1+\vec{F}_2) = -(5\hat{i}+3\hat{j}) = -5\hat{i}-3\hat{j}$ N. Step 2: $|\vec{F}_3 Given Information Mass(es), forces, angles, and coefficients…

Problem Statement Solve the Newton’s Laws / mechanics problem: A block just starts sliding down an incline when the angle is 37°. Find the coefficient of static friction. At angle of friction: $\mu_s = \tan\theta_c$ Step 1: $\mu_s = \tan 37° = \sin37°/\cos37° = 0.6/0.8 = 0.75$. $$\boxed{\mu_s = 0.75}$$ Given Information Mass(es), forces, angles,…

Problem Statement Solve the kinematics problem: A 3 kg particle has position $x = (2t^3 – 3t^2 + 5)$ m. Find the net force at $t = 2$ s. $a = d^2x/dt^2$; $F = ma$ Step 1: $v = 6t^2 – 6t$; $a = 12t – 6$. Step 2: At $t = 2$: $a =…