As a pendulum swings back and forth

a) at the lowest part of its swing, its energy is all kinetic.

b) at the end points of its swing, its energy is all potential.

c) kinetic energy is transformed into potential energy.

d) potential energy is transformed into kinetic energy. e) all of the above

E. All of the above.

Explanation:

These are the equations for potential (PE) and kinetic energy (KE):

PE = m · g · h

Where:

m = mass of the object.

g = acceleration due to gravity.

h = height.

KE = 1/2 · m · v²

Where:

m = mass.

v = speed.

At the end points of its swings, the pendulum is at its maximum height and its velocity is zero (for an instant). Then all the energy at these points is potential (answer B).

As the pendulum swings back from the end point it starts to lose height and acquires kinetic energy until it reaches the lowest part of the of its swing. At this point, all the potential energy was transformed into kinetic energy. The potential energy will be zero (because the height is zero) and due to energy conservation, the energy that once was potential energy has to be transformed into some kind of energy, in this case, into kinetic energy (we assume there is no air resistance, in which case some energy would be transformed into thermal energy as well, i.e., heat). (answer A and D).

After the lowest point, the pendulum acquires height (potential energy increases) and, due to the acceleration of gravity, it starts to lose velocity (kinetic energy decreases). Due to conservation of energy, the increase in potential energy must be equal to the decrease in kinetic energy. The kinetic energy is transformed into potential energy (answer C).

Then, the answer is E. All answers are correct.

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