A pendulum bob of mass m swinging from the end of a light string of length L = 1.89 m. The bob has speed of v0 = 9.42 m/s when the string makes an angle θ0 = 33.9° with the vertical. What is the speed (in m/s) of the bob when it is at its lowest point?

the speed of the bob is increased by the change in height

h = 1.89 m [1 - cos(33.9º)]

1/2 m v0^2 + m g h = 1/2 m v^2 ... v^2 = v0^2 + 2 g h

To find the speed of the bob at its lowest point, we can use the principle of conservation of mechanical energy.

The mechanical energy of the system is conserved, which means that the sum of the kinetic energy and potential energy remains constant throughout the motion.

At the highest point, the bob's speed is given as v0 = 9.42 m/s. At this point, the potential energy is maximum (zero kinetic energy) and the kinetic energy is minimum (zero potential energy).

At the lowest point, the bob's potential energy is zero (as it is at the bottom of its swing), and all of its mechanical energy is converted into kinetic energy. Therefore, the kinetic energy at the lowest point is maximum.

The formula for kinetic energy of an object is given by:
Kinetic energy (K) = (1/2) * m * v^2

Since we know the mass of the bob, m, we can find the kinetic energy at the lowest point. Then we can solve for the velocity, v.

To find the kinetic energy at the highest point, we'll use the given speed (v0) and the appropriate formula.

1. Find the kinetic energy at highest point:
K0 = (1/2) * m * v0^2

2. Find the velocity at the lowest point using the principle of conservation of mechanical energy:
K0 = K
(1/2) * m * v0^2 = (1/2) * m * v^2
v^2 = v0^2

3. Take the square root of both sides to find the velocity at the lowest point:
v = v0

Hence, the speed of the bob at its lowest point is 9.42 m/s.