A pendulum is released from some height. When it reaches the bottom of its swing, its speed is 2.5 m/s. What is the initial height of the pendulum?
To find the initial height of the pendulum, we can use the principle of conservation of mechanical energy. At the highest point of the swing, the pendulum will have maximum potential energy (due to its height) and zero kinetic energy. At the bottom of the swing, it will have zero potential energy and maximum kinetic energy. Since energy is conserved, we can equate the initial potential energy (mgh) to the final kinetic energy (1/2 mv^2).
Let's assume the mass of the pendulum is "m," the acceleration due to gravity is "g," and the final velocity is 2.5 m/s.
We can write the equation as:
mgh = (1/2)mv^2
Since "m" is common on both sides of the equation, we can cancel it out:
gh = (1/2)v^2
Now, we can solve for "h," the initial height of the pendulum.
h = (1/2)v^2/g
Plugging in the values:
v = 2.5 m/s
g = 9.8 m/s² (approximate value)
h = (1/2)(2.5)^2 / 9.8
h ≈ 0.318 meters
Therefore, the initial height of the pendulum is approximately 0.318 meters.