Consider a pendulum swinging. Which type(s) of energy is/are associated with the pendulum in the following instances: i. the moment at which it completes one cycle, just before it begins to fall back towards the other end, ii. the moment that it is in the middle between the two ends, and iii. just before it reaches the end of one cycle (just before instant i.).1. i. potential and kinetic, ii. potential and kinetic, iii. kinetic2. i. potential, ii. potential and kinetic, iii. potential and kinetic3. i. potential, ii. kinetic, iii. potential and kinetic4. i. potential and kinetic, ii. kinetic iii. kinetic

The mechanical energy of a pendulum is the sum of two types of energy:

- The kinetic energy (KE), which is the energy associated to the motion of the pendulum, and which is given by

where m is the mass of the pendulum and v its speed;

- The potential energy (PE), which is the energy associated to the position of the pendulum, and which is given by

where g is the acceleration due to gravity and h the height of the pendulum, relative to its equilibrium position

The mechanical energy is the sum of these two values:

E = KE + PE

And neglecting air resistance, the pendulum is an isolated system, so the mechanical energy remains constant:

This means that the energy continuously converts from kinetic energy and potential energy, and viceversa.

In particular, at the following moments we have:

i. the moment at which it completes one cycle, just before it begins to fall back towards the other end --> potential

In fact, in this position the speed is zero, so the kinetic energy is zero.

ii. the moment that it is in the middle between the two ends --> kinetic

In fact, in this position the height of the pendulum is zero, so the potential energy is zero.

iii. just before it reaches the end of one cycle (just before instant i --> kinetic and potential

In fact, here the pendulum has not reached yet its maximum height: so, it is still in motion, therefore it still has kinetic energy and potential energy.