Physics question

Ph2A Win 2020 Homework Project No.3

Max Yuen

March 2020

Problem 1: It’s raining . . . Objects falling through the atmosphere will experience drag forces. In this exercise, you will discover why smoke and ash take a long time to settle, why clouds seem to float, why rain falls, etc. In this exercise, we will use the drag model and assume spherical particles so CD = 0.47. The density of air is 1.2kg/m3, approximately.

A) The diameter of a typical rain drop is on the order of 0.5mm to 8.0mm. Use the drag model to find out how long for a drop of water to fall 1 meter in the sky. The density of water is about 1.00g/cc (hint: compute the terminal velocity and use it to find out the time to fall 1 meter. Do this for 0.5mm, 1.0mm, 2.0mm)

B) When there’s a forest fire or a volcano erupts, a lot of small particles are thrusted into the atmosphere. These particles will reach terminal velocity rapidly and there are several categories. They are denoted as PM50, PM2.5, etc. The number after PM is the particle size in micrometers. PM2.5 means 2.5 micrometers or smaller. This is a dangerous category and can make people sick. Compute the time it takes for these particles to fall from an initial height of about 9km. The range of densities of the lighter particles is from 0.7g/cc to 2.45g/cc.

C) When a nuclear weapon detonates, the particles generated in the fall out can be as small as 10nm. How long will a sphere of Iodine-131 of diameter 10 nm, 100 nm, 1.0 micron, 20 microns stay in the air if the "air burst" put the particles at an initial height of 20km? What if you had strong winds that "carried" the particles say at 20mph in the horizontal direction. How much area would the ash cover? Assume the density of Iodine to be about 4.9g/cc.

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Problem 2: Sailboat You are sailing on the open sea, but you see an island in front of you. You’d like to explore it, but the wind is blowing directly from the island toward you! If you point your sails so that it catches the maximum wind force, you will be pushed away from the island. How can you get to the island?

HINT: Google search: Points of Sail. A diagram of a sailboat is shown below.

Sail

Mast

Boom

Boat

Wind

Heading Force

KeelRudder

Sail Jib

Mast

Boom Keel

Keel Force

Sail Force

Figure 1: Diagram showing a typical sailboat with various components. The jib and sail convert wind energy into a force that pushes the mast. The mast couples the force to the boat body. The keel is in the water and keeps the boat going along the long direction. The rudder helps steer the boat. The force diagram shows how the forces act to produce the heading force, which moves the ship forward.

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