**a)** Law of conservation of energy:

$\overline{){\mathbf{P}}{\mathbf{.}}{{\mathbf{E}}}_{{\mathbf{0}}}{\mathbf{+}}{\mathbf{K}}{\mathbf{.}}{{\mathbf{E}}}_{{\mathbf{0}}}{\mathbf{=}}{\mathbf{P}}{\mathbf{.}}{{\mathbf{E}}}_{{\mathbf{f}}}{\mathbf{+}}{\mathbf{K}}{\mathbf{.}}{{\mathbf{E}}}_{{\mathbf{f}}}}$

Kinetic energy

$\overline{){\mathbf{K}}{\mathbf{.}}{\mathbf{E}}{\mathbf{=}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{m}}{{\mathbf{v}}}^{{\mathbf{2}}}}$

$\begin{array}{rcl}\mathbf{m}\mathbf{g}\mathbf{h}& \mathbf{=}& \frac{\mathbf{1}}{\mathbf{2}}\mathbf{m}{{\mathbf{v}}_{\mathbf{f}}}^{\mathbf{2}}\end{array}$

For pendulum 1:

K.E_{1} = mgh = (4)(9.81)(30 × 10^{-2}) = 11.8 J

For pendulum 2:

K.E_{2} = mgh = (3)(9.81)(45 × 10^{-2}) = 13.2 J

For pendulum 3:

K.E_{3} = mgh = (2)(9.81)(30 × 10^{-2}) = 5.9 J

For pendulum 4:

Six pendulums of various masses **m** are released from various heights **h** above a tabletop, as shown in the figures below. All the pendulums have the same length and are mounted such that at the vertical position their lowest points are the height of the tabletop and just do not strike the tabletop when released. Assume that the size of each bob is negligible.

a) Rank each pendulum on the basis of the maximum kinetic energy it attains after release.

b) Rank each pendulum on the basis of its maximum speed. Rank from largest to smallest. To rank items as equivalent, overlap them.

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Energy in Pendulums concept. You can view video lessons to learn Energy in Pendulums. Or if you need more Energy in Pendulums practice, you can also practice Energy in Pendulums practice problems.

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Wickham's class at University of Guelph.