Final answer:
The velocity of a pendulum at the lowest point of its arc is independent of its mass, based on the conservation of mechanical energy. In the scenario presented, a 2 kg metal ball would have a velocity at the lowest point of approximately 1.4 m/s, calculated using the formula v = √(2gh) where h is the height of the pendulum.
Step-by-step explanation:
When analyzing the motion of a pendulum, the velocity of a pendulum at its lowest point is independent of its mass. This concept is derived from the principle of conservation of mechanical energy. In the absence of air friction, the potential energy (PE) at the highest point of the swing is converted entirely into kinetic energy (KE) at the lowest point.
Let's calculate the velocity at the lowest point (point B) for a 2 kg metal ball. At the highest point A, the ball has potential energy equal to PE = mgh, where m is the mass, g is the acceleration due to gravity (9.81 m/s²), and h is the height above the lowest point of the swing. As the ball swings down to point B, this potential energy is converted to kinetic energy, KE = 0.5mv², where v is the velocity.
Setting the potential energy at A equal to the kinetic energy at B, we have mgh = 0.5mv². The mass m cancels out, and we can solve for v: v = √(2gh). Plugging in the values, for h = 10 cm = 0.1 m, we get v = √(2 * 9.81 m/s² * 0.1 m) ≈ 1.4 m/s. This demonstrates that the velocity at point B is independent of the mass and depends only on the height from which the pendulum is released.