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Remember the formula used to calculate the gravitational potential energy of a mass given its mass and height above an arbitrary zero level is
PEgravity = mgh
When a pendulum is pulled back from equilibrium through an angle θ, its height is calculated with the formula
h = L - L cos θ
where θ is the angular displacement
The formula used to calculate the kinetic energy of a massive particle is
KE = ½ mv2
In the absence of non-conservative forces, such as friction or applied, external forces, the mechanical energy in a system is conserved. That is
During the swing of a simple pendulum, when does the bob possess maximum PE?
PE is maximum at the endpoints (maximum amplitude)
During the swing of a simple pendulum, when does the bob possess maximum KE?
KE is maximum at equilibrium (bottom position)
During the swing of a simple pendulum, what is the magnitude of the bob's maximum velocity?
Another way of looking at conservation of energy is with the following energy diagram. As you can see,
- the "purple" curve represents the pendulum bob's KE which during each cycle begins with an initial value of zero, increases to a maximum value, and then returns to zero
- the "green" curve represents the PE of the bob which begins each cycle at a maximum value, then becomes zero as the bob passes through its equilibrium position, and returns to its maximum value
- the "brown" line represents the total energy of the pendulum bob that always remains constant
If a pendulum is initially released at an angle of 37º, at what angle will its PE and the KE be equal?
25.9º
Refer to the following information for the next question.
At any intermediate position during the oscillation, the pendulum bob would have both PE and KE.
PEmax = PEintermediate + KEintermediate = KEmax
If the pendulum was released at point A, derive an expression for the pendulum's instantaneous velocity at point B, an intermediate position in its swing.
See the related lesson on vertical circles if you are asked to calculate the tension of the string during the pendulum's oscillation. Remember that a pendulum is merely the bottom half of a vertical circle! These conservation of energy methods are the easiest way to determine an object's speed so that tensions can be calculated.
What else can I help you with?
Will law of energy conservation apply to simple pendulum?
Yes, the law of energy conservation applies to a simple pendulum. The total mechanical energy (kinetic energy + potential energy) of the pendulum remains constant as it swings back and forth, assuming no external forces are acting on it. Therefore, energy is conserved in the system.
Point of oscillation of simple pendulum?
The point of oscillation of a simple pendulum is the equilibrium position where the pendulum comes to rest when there is no external force acting on it. It is the bottom-most point of the pendulum's swing where the potential energy is at a minimum and the kinetic energy is at a maximum. This point marks the center of the pendulum's oscillation movement.
What simple machine is a pendulum?
A pendulum is a type of simple machine called a lever. It consists of a rod with a weight (bob) at one end and a pivot point at the other. The swinging motion of the pendulum results from the transfer of gravitational potential energy to kinetic energy.
What is fiction how does it affect the swing of a pendulum?
A swinging pendulum follows a simple physical path that is described as simple harmonic motion. A frictionless pendulum would swing forever. Friction generates heat which radiates away energy from the system. Therefore friction will cause the pendulum to slow and stop as all the energy gets removed from the S.H.M. If you rig up a way to replace the lost energy, then the pendulum will continue to swing. This is the method used in a pendulum clock. The energy put into the wind up spring will replace the energy lost due to friction until the spring winds down. The key point is "energy is conserved" which means you cannot create or destroy it. You can only move it from one place to another or convert it into something else.
Why a compound pendulum is called equivalent simple pendulum?
Compound pendulum is a physical pendulum whereas a simple pendulum is ideal pendulum. The difference is that in simple pendulum centre of mass and centre of oscillation are at the same distance.
Will law of energy conservation apply to simple pendulum?
Yes, the law of energy conservation applies to a simple pendulum. The total mechanical energy (kinetic energy + potential energy) of the pendulum remains constant as it swings back and forth, assuming no external forces are acting on it. Therefore, energy is conserved in the system.
What happen to simple pendulum at lowest point of its swing?
At the lowest point of its swing, a simple pendulum's velocity is at its maximum, and its potential energy is at its minimum. The kinetic energy is at its highest since the pendulum has the highest speed.
Point of oscillation of simple pendulum?
The point of oscillation of a simple pendulum is the equilibrium position where the pendulum comes to rest when there is no external force acting on it. It is the bottom-most point of the pendulum's swing where the potential energy is at a minimum and the kinetic energy is at a maximum. This point marks the center of the pendulum's oscillation movement.
Investigate whether a simple pendulum will swing continuously in air.Explain your finding?
A simple pendulum will definitely not swing continuously in air. The pendulum would lose energy to its surroundings in overcoming air resistance.
Why a simple pendulum will not swing continuously in air?
Because of the air resistance which causes the pendulum to gradually lose energy.
What simple machine is a pendulum?
A pendulum is a type of simple machine called a lever. It consists of a rod with a weight (bob) at one end and a pivot point at the other. The swinging motion of the pendulum results from the transfer of gravitational potential energy to kinetic energy.
What is fiction how does it affect the swing of a pendulum?
A swinging pendulum follows a simple physical path that is described as simple harmonic motion. A frictionless pendulum would swing forever. Friction generates heat which radiates away energy from the system. Therefore friction will cause the pendulum to slow and stop as all the energy gets removed from the S.H.M. If you rig up a way to replace the lost energy, then the pendulum will continue to swing. This is the method used in a pendulum clock. The energy put into the wind up spring will replace the energy lost due to friction until the spring winds down. The key point is "energy is conserved" which means you cannot create or destroy it. You can only move it from one place to another or convert it into something else.
Is oscillation of compound pendulum or simple pendulum is perfectly simple harmonic motion?
A simple pendulum exhibits simple harmonic motion
Why a compound pendulum is called equivalent simple pendulum?
Compound pendulum is a physical pendulum whereas a simple pendulum is ideal pendulum. The difference is that in simple pendulum centre of mass and centre of oscillation are at the same distance.
When metamorphic rock melts and turns into lava is matter conserved?
Yes, this is a simple physical change and matter is always conserved in these. In fact, matter is always conserved except in nuclear reactions where the sum of matter and energy is conserved.
Why a compound pendulum is called an equivalent simple pendulum?
A compound pendulum is called an equivalent simple pendulum because its motion can be approximated as that of a simple pendulum with the same period. This simplification allows for easier analysis and calculation of its behavior.
Give three applications of simple pendulum in your daily life?
applications of simple pendulum
