Question

Ferns spread spores instead of seeds, and some ferns eject the spores at surprisingly high speeds. One species accelerates 1.4 μg spores to a 4.5 m/s ejection speed in a time of 1.0 ms. What impulse is provided to the spores? What is the average force on a spore?

Answer 1

Answer:

Impulse is $6.3*10^{-9}\:N \cdot s$

The average force is $6.3*10^{-6} N$

Explanation:

When a mass $m$ undergoes a change in velocity $\Delta v$, its impulse $I$ is

$I =m\Delta v$

and if a force $F$ is acting for time $t$, then the impulse $I$ is given by

$I=F*t$

Now the mass of the spores in kg is

$m=1.4*10^{-6}g*\frac{10^{-3}kg}{g}=1.4*10^{-9}kg$

we calculate the impulse from the first formula:

$I =m\Delta v =(1.4*10^{-9}kg)(4.5\frac{m}{s} )=6.3*10^{-9}N\cdot s$

$\boxed{I=6.3*10^{-9}\:N \cdot s}$

Now that we have impulse, we calculate the average force on the spore from the second formula:

$F=\frac{I}{t} =\frac{6.3*10^{-9}}{1*10^{-3}s}=6.3*10^{-6} N$

$\boxed{F=6.3*10^{-6} N}$