Question

A pendulum with a 1.0-kg weight is set in motion from a position 0.04 m above the lowest point on the path of the weight. What is the kinetic energy of the pendulum at the lowest point?

Answer 1

The kinetic energy of the pendulum at the lowest point is 0.393 joules.

Step-by-step explanation:

Under the assumption that effects from non-conservative forces can be neglected, the maximum kinetic energy of the pendulum (lowest point) (
`K_(2)`), measured in joules, is equivalent to the maximum gravitational potential energy (highest point) (
`U_(g,1)`), measured in joules, by th Principle of Energy Conservation:

`U_(g,1) = K_(2)` (1)

By the definition of potential gravitational energy and under the assumption that the height of the lowest point is zero, we conclude that the kinetic energy of the pendulum is:

`K_(2) = m\cdot g\cdot y_(2)` (1b)

Where:

`m` - Mass of the weight of the pendulum, measured in kilograms.

`g` - Gravitational acceleration, measured in meters per square second.

`y_(2)` - Height of the pendulum at highest point, measured in meters.

If we know that
`m = 1\,kg`,
`g = 9.807\,(m)/(s^(2))` and
`y_(2) = 0.04\,m`, then the kinetic energy of pendulum at the lowest point:

`K_(2) = (1\,kg)\cdot \left(9.807\,(m)/(s^(2)) \right)\cdot (0.04\,m)`

`K_(2) = 0.393\,J`

The kinetic energy of the pendulum at the lowest point is 0.393 joules.