Energy Of A Pendulum Gizmo

Energy in a Pendulum

In a simple pendulum with no friction, mechanical energy is conserved. Total mechanical energy is a combination of kinetic energy and gravitational potential energy. Every bit the pendulum swings back and forth, there is a constant exchange between kinetic free energy and gravitational potential energy.

Potential Energy

The potential energy of the pendulum can be modeled off of the basic equation

PE = mgh

where g is the acceleration due to gravity and h is the top. We often employ this equation to model objects in free autumn.

However, the pendulum is constrained by the rod or string and is not in free autumn. Thus nosotros must express the height in terms of θ, the angle and L, the length of the pendulum. Thus h = 50(1 – COS θ)

When θ = 90 ° the pendulum is at its highest point. The COS 90 ° = 0, and h = L(ane-0) = Fifty, and PE = mgL(1 – COS θ) = mgL

When the pendulum is at its lowest point, θ = 0 ° COS 0 ° = one and h = 50 (ane-ane) = 0, and PE = mgL(1 –1) = 0

At all points in-between the potential energy can be described using PE = mgL(1 – COS θ)

Kinetic Free energy

Ignoring friction and other not-conservative forces, we find that in a simple pendulum, mechanical energy is conserved. The kinetic free energy would be KE= ½mv² ,where m is the mass of the pendulum, and five is the speed of the pendulum.

At its highest point (Point A) the pendulum is momentarily motionless. All of the free energy in the pendulum is gravitational potential energy and there is no kinetic energy. At the lowest point (Indicate D) the pendulum has its greatest speed. All of the free energy in the pendulum is kinetic energy and there is no gravitational potential energy. Still, the full energy is constant every bit a office of time. Yous can detect this in the post-obit BU Physlet on energy in a pendulum.

Simple Pendulum in four positions

If in that location is friction, nosotros have a damped pendulum which exhibits damped harmonic motion. All of the mechanical free energy somewhen becomes other forms of energy such equally heat or audio.

Mass and the Menstruation

Your investigations should accept plant that mass does not affect the catamenia of a pendulum. One reason to explain this is using conservation of energy.

If we examine the equations for conservation of energy in a pendulum system nosotros find that mass cancels out of the equations.

KE_i + PE_i= KE_f+PE_f

[½mv² + mgL(1-COSq) ]_i = [½mvⁱⁱ + mgL(1-COSq) ]_f

In that location is a straight relationship between the angle θ and the velocity. Because of this, the mass does non bear upon the beliefs of the pendulum and does non alter the period of the pendulum.