A $10 \text{ kg}$ block rests on a smooth (frictionless) plane inclined at $30^\circ$ to the horizontal. If the block is released from rest, determine its acceleration down the plane and the normal force exerted by the plane.

Determine the banking angle $\theta$ required for a road with a radius of curvature of $200 \text{ m}$ so that a car traveling at $25 \text{ m/s}$ does not rely on friction to stay on the road.

Two blocks, A ($m_A = 10 \text{ kg}$) and B ($m_B = 15 \text{ kg}$), are connected by a single light inextensible cable passing over two smooth pulleys. Block A rests on a horizontal frictionless surface, and Block B is suspended vertically. Determine the acceleration of each block and the tension in the cable when released from rest.

A person of mass $m$ stands on a scale inside an elevator. The reading on the scale represents the normal force exerted by the scale on the person, which is their "apparent weight." Analyze the apparent weight of the person when the elevator is accelerating upwards, accelerating downwards, moving at a constant velocity, or in free fall.

A skydiver jumps from a plane and falls towards the earth. Initially, the only significant force acting on them is gravity. However, as their velocity increases, the aerodynamic drag force (air resistance) becomes significant. Analyze how their acceleration changes over time and define the concept of terminal velocity based on Newton's Second Law.