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

Answer:

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

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 $m = 1\,kg$, $g = 9.807\,\frac{m}{s^{2}}$ and $y_{2} = 0.04\,m$, then the kinetic energy of pendulum at the lowest point:

$K_{2} = (1\,kg)\cdot \left(9.807\,\frac{m}{s^{2}} \right)\cdot (0.04\,m)$

$K_{2} = 0.393\,J$

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