Category: HC Verma Part 1: Mechanics

Problem Statement Solve the Newton’s Laws / mechanics problem: A pendulum is hung in a car. When the car accelerates at 5 m/s² forward, find the angle the pendulum makes with the vertical. ($g = 10$ m/s²) In car’s frame: pseudo force $ma$ backward; $\tan\theta = a/g$ Step 1: $\tan\theta = a/g = 5/10 =…

Problem Statement A 3 kg block rests on a 7 kg block which is on a frictionless table. Friction between blocks: $\mu_s = 0.5$. A force is applied on the bottom block. Find the maximum force so that both blocks move together. ($g = 10$ m/s²) Given Information All quantities, constants, and constraints stated in…

Problem Statement Solve the kinematics problem: Two equal masses $m$ are connected by a string. One hangs, one sits on a frictionless surface. Find the acceleration and tension. $a = m_2 g/(m_1+m_2)$; with $m_1 = m_2 = m$: $a = g/2$; $T = mg/2$ Step 1: $a = mg/(m+m) = g/2$. Step 2: $T =…

Problem Statement Solve the Newton’s Laws / mechanics problem: A block of mass 3 kg rests on a horizontal surface. A horizontal force of 20 N is applied. If the block does not move, find the friction force. What is the normal force? Static friction = applied force (when not moving); $N = mg$ Step…

Problem Statement Solve the Newton’s Laws / mechanics problem: A uniform string of mass 0.3 kg and length 1 m hangs from a ceiling. Find the tension at the midpoint. Tension at a point supports the weight of string below that point Step 1: Mass per unit length = 0.3 kg/m. Step 2: Length below…

Problem Statement Solve the Newton’s Laws / mechanics problem: A 5 kg body on a smooth 37° incline is held at rest by a force $F$ parallel to the incline. Find $F$ and the normal force. ($g = 10$ m/s², $\sin37°=0.6$, $\cos37°=0.8$) Along incline: $F = mg\sin\theta$; perpendicular: $N = mg\cos\theta$ Step 1: $F =…

Problem Statement Solve the Newton’s Laws / mechanics problem: Three blocks of mass 1 kg, 2 kg, 3 kg are connected by strings on a frictionless surface. A force $F = 12$ N pulls the 3 kg block. Find the tension in each string segment. $a = F/(m_1+m_2+m_3)$; tension at each junction Step 1: $a…

Problem Statement Solve the momentum/collision problem: State Newton’s second law in terms of momentum. Show it reduces to $F = ma$ when mass is constant. $\vec{F} = d\vec{p}/dt$ Step 1: $\vec{F} = \dfrac{d\vec{p}}{dt} = \dfrac{d(m\vec{v})}{dt}$. Step 2: If $m$ is constant: $= m\dfrac{d\vec{v}}{dt} = m\vec{a}$. ∎ $$\boxed{\vec{F} = \frac{d\vec{p}}{dt} = Given Information Masses $m_1$, $m_2$…

Problem Statement Solve the Newton’s Laws / mechanics problem: A 2 kg block sits on a 5 kg block which is on a frictionless table. A force $F = 28$ N is applied on the bottom block. The coefficient of static friction between blocks is 0.4. Find the acceleration and check if the top block…

Problem Statement Solve the momentum/collision problem: A 0.5 kg ball moving at 20 m/s is brought to rest in 0.02 s by a catcher’s mitt. Find the average force exerted. $F \cdot \Delta t = \Delta p$ Step 1: $\Delta p = m(v_f – v_i) = 0.5(0 – 20) = -10$ kg m/s. Step 2:…