Final answer:
The velocity of the pendulum's ball is not constant; it varies due to the conversion of potential energy into kinetic energy and vice versa. The velocity at the bottom of the swing is independent of the ball's mass. It can be calculated using the conservation of mechanical energy formula, where the mass cancels out.
Step-by-step explanation:
The velocity of the ball is not constant as it swings back and forth. When you pull the ball to one side and release it, the pendulum will experience a change in velocity as it moves through its arc. This is because the gravitational force acting on the pendulum converts potential energy into kinetic energy, and vice versa, as it swings.
Showing that the velocity of the ball is independent of its mass involves understanding that the change in kinetic energy only depends on the height from which the ball was released, not the mass of the ball itself. When the ball swings down to point B from point A, the potential energy lost is converted into kinetic energy.
Using the equation for gravitational potential energy (PE = mgh) and kinetic energy (KE = 0.5mv^2), and setting PE equal to KE because energy is conserved, the mass (m) cancels out. Therefore, the velocity at point B does not depend on the mass of the ball.
To calculate the velocity of the ball at point B, you can use the conservation of mechanical energy. Potential energy at point A converts to kinetic energy at point B: mgh = 0.5mv^2. Again, the mass cancels out, leaving gh = 0.5v^2. Solving for the velocity, v = √(2gh). If the height (h) at point A is 10 cm, then g is 9.8 m/s^2, the velocity (v) at point B can be calculated.