Question

A 2-meter-long pendulum, is set in motion, at 1.2 m/s, when the pendulum arm is at an angle of 25° from the vertical. Find the speed of the pendulum when it reaches the bottom of its swing.

Answer 1

ANSWER: Approximately 2.17 m/s.

EXPLANATION: Using the equations of motion for a pendulum, you can calculate the velocity of the pendulum at the bottom of its swing as follows:

v = √(gL(1 - cos(θ)))

Where:
v is the velocity of the pendulum at the bottom of its swing

g is the acceleration due to gravity (9.8 m/s^2)

L is the length of the pendulum (2 meters)

θ is the angle of the pendulum at the top of its swing (25°)

Substituting these values into the equation gives:

v = √(9.8 * 2 * (1 - cos(25°)))

Solving this equation gives a velocity of approximately 2.17 m/s. This is the speed of the pendulum at the bottom of its swing.