A pendulum has a string with the length 1.2 m. You hold it at an angle of 22 degrees to the vertical and release it. The pendulum bob has a mass of 2.0 kg.
What is the potential energy before it is released?___J. What will be the velocity of the pendulum through the bottom of its swing? ___m/s.
Note:- Use g = 10 m/s^2. Use geometry to determine the height when released.
To calculate the potential energy before the pendulum is released, we need to determine the height of the bob when it is released.
The height can be determined as the vertical distance between the lowest point of the pendulum's swing and the initial position. This distance can be calculated using trigonometry.
The vertical component of the displacement can be given by:
Vertical displacement = Length of string * sin(angle)
Vertical displacement = 1.2 m * sin(22°)
Vertical displacement ≈ 0.4539 m
Therefore, the initial height of the bob is approximately 0.4539 m.
The potential energy can be calculated using the formula:
Potential energy = Mass * gravitational acceleration * height
Potential energy = 2.0 kg * 10 m/s^2 * 0.4539 m
Potential energy ≈ 9.078 J
The velocity of the pendulum at the bottom of its swing can be calculated using the principle of conservation of energy. At the bottom of its swing, all the potential energy is converted into kinetic energy.
Potential energy = Kinetic energy
Mass * gravitational acceleration * height = (1/2) * Mass * velocity^2
Simplifying the equation:
velocity^2 = 2 * gravitational acceleration * height
velocity^2 = 2 * 10 m/s^2 * 0.4539 m
velocity^2 ≈ 9.078 m^2/s^2
Taking the square root of both sides:
velocity ≈ 3.014 m/s
Therefore, the velocity of the pendulum at the bottom of its swing is approximately 3.014 m/s.