A raindrop of mass 3.35 × 10^-5 kg falls vertically at a constant speed under the influence of gravity and air resistance. As it falls 100-in, what is work (lone on the raindrop) (a) by the gravitational force and (b) by air resistance?

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Amal JeevaLv10

20 Oct 2020

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When a raindrop falls, it increases in size and so it's mass at time t is a function of t, namely, m(t). The rate of growth of the mass is km(t) for some positive constant k. When we apply Newton’s Law of Motion to the raindrop, we get (mv)′ = gm, where v is the velocity of the raindrop (directed downward) and g is the acceleration due to gravity. The terminal velocity of the raindrop is

Find an expression for the terminal velocity in terms of g and k.

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Consider a very small raindrop slowly falling down in quiet air.Because of the dropâs
small size and low speed, the air resistence to its fall is viscousrather than turbulent.
Consequently, the resistive force is depends linearly on the dropâsvelocity,
~R= -b~v, (1)
where b is a constant which depends on the size and shape of thedrop and the airâs viscosity but does not depend on the dropâsweight of what itâs made of.
Suppose a raindrop of weight mg =0.077 Âµg Ã 9.8 m/s2 reachesterminal speed
vt = 0.088 m/s high above the ground. What is the numeric value ofthe coefficient b in eq. (1) for the air resistence to this dropâsmotion?
Answer in units of kg/s.

2)Now consider a plastic pellet of the same size and shape as theraindrop but of a higher density ? p = 3.48Ãdensityofwater. If wedrop it in the middle of the same cloud that produced the raindrop,what would be its terminal velocity vtp?
Answer in units of m/s.

A 0.14-kg pinecone falls 16m on the ground, where it lands with a speed of 13 m/s.
A) What speed would the pinecone have landed if there had been no air resistance?
B) How much work was done on the pinecone by air resistance?
C) What was the avg. air resistance exerted on the pinecone?