What speed does a pendulum bob reach at its lowest point if it has a mass of 0.750 kg and is released from an angle of 60.0°?

To determine the speed of the pendulum bob at its lowest point, we can use the principle of conservation of mechanical energy. At the highest point, when the bob is released from a 60.0° angle, it has maximum potential energy and minimal kinetic energy. At the lowest point of its swing, the potential energy is converted into kinetic energy, meaning the total mechanical energy remains constant throughout the motion.

First, we need to calculate the height from which the bob is released. The height can be calculated using the length of the pendulum and the angle. Assuming the length of the pendulum is ( L ), the height ( h ) can be expressed as:

[ h = L - L \cos(\theta) = L(1 - \cos(\theta)) ]

For ( \theta = 60° ), we have:

[ \cos(60°) = 0.5 ]

[ h = L(1 - 0.5) = L(0.5) ]

Thus, the bob descends from a height of ( 0.5L ).

The gravitational potential energy ( U ) at the height ( h ) is given by:

[ U = mgh \