Find the speed, v, of a pendulum at the bottom of its swing (B), given that it has mass m and initial height at A is h (the difference in height from B to A). Your answer will be in terms of g as well.
Included is a drawing of a pendulum at its maximum height (A), and at its minimum height (the middle) (B), and once again at its maximum height, on the other side (C).
PLEASE HELPPP:(
To find the speed of a pendulum at the bottom of its swing, we can use the principle of conservation of mechanical energy.
Let's consider the initial height of the pendulum at point A. The potential energy at A is given by mgh, where m is the mass of the pendulum, g is the acceleration due to gravity, and h is the height difference between points A and B. At this point, the kinetic energy of the pendulum is zero since it is momentarily at rest.
When the pendulum reaches point B, at the bottom of its swing, its potential energy is zero since it is at its lowest point. The entire potential energy at point A is converted into kinetic energy at point B.
The equation for the conservation of mechanical energy is:
Potential energy at A = Kinetic energy at B
mgh = (1/2)mv^2
Where v is the velocity or speed of the pendulum at point B.
Simplifying the equation, we have:
gh = (1/2)v^2
To find the speed v, we can isolate it by multiplying both sides of the equation by 2 and taking the square root:
v = √(2gh)
Therefore, the speed of the pendulum at the bottom of its swing (point B) is given by v = √(2gh), where g is the acceleration due to gravity and h is the height difference between points A and B.
potential energy at top (stopped) = kinetic energy at bottom
m g h = (1/2) m v^2
v = sqrt (2 g h)