PART 1: Standing on ledge about 1 meter off the ground, you step off knowing you

Question

PART 1: Standing on ledge about 1 meter off the ground, you step off knowing you can manage the impact. When you first start to fall downward, you have no initial velocity and your momentum is zero. However when you reach the ground you will be moving at gt m/s, where g is the acceleration of gravity and t is the time it takes to get to the ground, in this case roughly 4.4 m/s after 0.45 second. From the standpoint of an observer on the ground watching, you have momentum 4.4 times your mass in kg-m/s. From the standpoint of someone watching from afar and seeing both Earth and you, what is the total momentum of you and the Earth together?

a.     Zero. There is no outside force, so momentum is conserved. It starts and ends at zero.

b.     Twice your final momentum.

c.     Zero at the beginning and ending with your final momentum downward, the same as perceived by an observer on the Earth watching you.

d.     Zero at the beginning ending with your final momentum but upward, as you would perceive while falling.

PART 2: A common occurrence is to hear the siren of an approaching emergency vehicle and the change in its pitch (frequency) when the vehicle passes and moves away. If it is traveling at 80 km/hr and the speed of sound in cool dry air is 331 m/s, what frequency will we hear from the approaching vehicle if it emits 1200 Hz when at rest?

    a. 1490 Hz

    b. 1281 Hz

    c. 1119 Hz

    d. 1200 Hz

PART 3: If you take an ordinary plastic milk bottle that holds about 1 gallon or 3.8 liters of milk and remove the air from it, how much total force would be exerted by Earth's atmosphere on one side of the bottle?   

Hints: A liter is 1000 milliliters and 1 milliliter is 1 cm3. As a practicing physicist, assume that the bottle is a cube with volume a3 where "a" is the length of a side. Earth's atmospheric pressure is 14.7 lbs/in2 or 101 kPa.

   a. The side of the “cube” milk bottle is about 62cm, so the resulting air pressure gives a force of about 39000N. That’s 875 lbs.

   b. There is no force on the side of the bottle, only on the top or bottom.

   c. The side of the “cube” milk bottle is about 16cm, so the resulting air pressure gives a force of about 2600N. That’s 580 lbs.

   d. The weight of a column of air from Earth’s surface out to empty space is about 14.7 lbs for each square inch, or 101,00N for each square meter.

   e. The force of Earth’s atmosphere on the outside of the bottle is balanced by the force on the inside when the bottle is open, so there is no net force. If you remove the air inside, then the outside force crushes the bottle.

Explanation / Answer

part 2 )

using doppler effect when observer at rest and source is approaching towards observer

f' = f*(v/v-vs)

v = speed of sound = 331 m/s

vs = source speed = 80 km/hr = 22.22 m/s

f = 1200 Hz

f' = 1286 Hz =(B option )

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