As you watch a storm approach, you wonder about the formation of hailstones. You

Question

As you watch a storm approach, you wonder about the formation of hailstones. You recently heard on the Weather Channel that, while the altitude may vary considerably, hailstones sometimes originate around 500 m above the ground. You wonder whether air resistance has a noticeable effect on the speed of a falling hailstone, and perform a calculation to compare the speed the hailstone would achieve without air resistance to your everyday experiences. If the two differ, explain what has happened to the initial potential energy of the system.

Known:

Unknown:

Strategy:

Solution:

Explanation / Answer

In general the potential energy converts to kinetic energy as the
object gains speed while falling.
PE = KE
mgh = ½mv²
gh = ½v²
v² = 2gh
v = (2gh)

This is when the objects starts from rest, if the object has an initial
speed the equation for final speed takes the form:
mgh = ½mVf² - ½mVi²
mgh = ½m(Vf²-Vi²)
Vf = (Vi²+2gh)

v = (2*9.8*500) = 99 m/s = 360 km/hr

Yes they differ, if a hailstone has an impact speed of 360 km/hr
it's going to plunge right through the ground, which obvioulsy doesn't
happen.

In the case with ignoring air resistance all initial PE has been converted
to KE.

In the case with air resistance, the speed will be lower so some of the
initial PE converts to KE, but some is also lost to air friction, mainly as
heat being dissipated from the object while heating up the air around
it as it dives through it.

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