Question

Mosses don't spread by dispersing seeds; they disperse tiny spores. The spores are so small that they will stay aloft and move with the wind, but getting them to be windborne requires the moss to shoot the spores upward. Some species do this by using a spore-containing capsule that dries out and shrinks. The pressure of the air trapped inside the capsule increases. At a certain point, the capsule pops, and a stream of spores is ejected upward at 3.6 m/s, reaching an ultimate height of 20 cm.A)What fraction of the initial kinetic energy is converted to the final potential energy?Express your answer numerically.UfKi =B)What happens to the "lost" energy?Choose the correct answerIt has been transformed into thermal energy of the spores and surrounding air.It has been transformed into thermal energy of the spores and potential energy of surrounding air.It has been transformed into potential energy of the spores and kinetic energy of surrounding air.It has been transformed into potential energy of the spores and surrounding air.

Answer 1

A) 0.3

The initial kinetic energy of the stream of spores is

$K_i = \frac{1}{2}mv^2$

where m is the mass of the spores and v = 3.6 m/s is their initial speed.

The final gravitational potential energy (at the point of maximum height) of the spores is

$U_f = mgh$

where g=9.8 m/s^2 is the acceleration due to gravity and h = 20 cm = 0.20 m is the maximum height.

Therefore, the fraction of kinetic energy converted to final potential energy is

$\frac{U_f}{K_i}=\frac{mgh}{\frac{1}{2}mv^2}=\frac{2gh}{v^2}=\frac{2(9.8 m/s^2)(0.20 m)}{(3.6 m/s)^2}=0.30$

So, about 30% of the initial kinetic energy is converted into potential energy.

B) It has been transformed into thermal energy of the spores and surrounding air

In fact, because of the presence of the air resistance during the motion of the spores, some of the mechanical energy of the spores is "wasted" and converted into thermal energy (heat) of the spores and the surrounding air. Without the air resistance, the mechanical energy would be conserved, and the final potential energy of the spore would be equal to the initial kinetic energy.