Question 1: Define terminal velocity and explain the physical principles that determine its value.

Answer: Terminal velocity is the constant speed achieved by a falling object when the downward force of gravity is balanced by the upward drag force, resulting in no further acceleration.

Question 2: List the key forces acting on an object falling through a fluid as it approaches terminal velocity.

Answer: The main forces are gravity (weight) pulling downward and drag (air resistance or fluid friction) acting upward.

Question 1: Calculate the terminal velocity of a sphere with a mass of 0.5 kg and a radius of 0.05 m falling through air. Assume the drag coefficient (Cd) is 0.5, the density of air (ρ) is 1.2 kg/m³, and the acceleration due to gravity (g) is 9.8 m/s². Use the formula: Vt = √(2mg / (ρ A Cd)) where A = π r².

Answer: Approximately 9.4 m/s

Question 1: Describe a simple experimental setup to investigate the terminal velocity of a small object falling through a viscous liquid. Include the key variables you would control and measure, as well as safety precautions.

Answer: An experiment can be set up by dropping objects of known size and mass into a transparent container filled with viscous liquid like glycerol. Variables to control include object size, mass, and liquid viscosity. Measure the fall time over a set distance to determine terminal velocity. Safety precautions include wearing goggles, handling chemicals carefully, and ensuring the container is stable to prevent spills.

Question 1: A student measures the fall speed of a feather and a small metal ball in air. The feather reaches a constant speed of 0.5 m/s after falling 2 meters, while the metal ball reaches 9 m/s after falling 3 meters. Explain why the metal ball has a higher terminal velocity and what factors influence these differences.

Answer: The metal ball has a higher terminal velocity because it has a greater mass and a smaller surface area relative to its mass, resulting in less relative drag. Factors influencing terminal velocity include mass, surface area, shape, and fluid density.

Question 1: Describe at least two real-world applications where understanding terminal velocity is important and explain their significance.

Answer: In parachuting, knowing terminal velocity helps ensure safe landing speeds by designing parachutes that increase drag. In the design of industrial hoppers, understanding how particles reach terminal velocity allows for better control of material flow and prevents blockages.

Question 1: Explain why objects with different shapes but the same mass can have different terminal velocities.

Answer: Different shapes affect the drag force experienced during fall; a streamlined shape experiences less drag and thus reaches a higher terminal velocity compared to a shape with more surface area or irregularities.