Please show every step of the solutions! Thanks so much in advance! Problem 1. W

Question

Please show every step of the solutions! Thanks so much in advance!

Problem 1. What is the total mass of the Earth?s atmosphere? How does this compare to the mass of the Earth? Problem 2. A partially evacuated chamber is used in a physics experiment. It has a small door (of area 0.01 m^2) that can be pulled open. If a force of F = 750 N or greater F is required to open the door, determine the air pressure inside the chamber. You can certainly assume that the air outside the chamber is at atmospheric pressure. Problem 3. Does a ship float higher in the Great Lakes or in the ocean? Explain your answer. Problem 4. An empty metal soap dish barely floats in the water. A bar of ivory soap also floats in the water. However, when the bar of soap is attached to the dish, the combination sinks. Explain. Problem 5. How would you determine the density of an irregularly shaped rock? Problem 6. A helium filled balloon is tied to a 2 m long uniform string of mass 0.05 kg. The balloon is spherical with a radius of 0.4 m. when released it lifts a length h of the string off of the ground. Find the length h given that the balloon has a mass of 0.25 kg.

Explanation / Answer

1)Mass of atmosphere=5.3*10^18 kg

Mass of earth=5.97*10^24 kg

2)Let the pressure inside be P.

Balancing forces,

P*0.01+750=101325*0.01

P=26325Pa

3) In the ocean since the ocean has salts and therefore has a higher density. Therefore, by archimede's principle, the ship floats higher in ocean.

4)While both float independently, the combination sinks because the combined volume is same while the combined mass is much more than individual mass. Therefore, the maximum buoyant force generated is the same but the force of gravity acting downward is more for the combination which sinks as a result.

5)Take a beaker of water and weight it on a scale.

Now dip the rock in it and weigh again. The difference can be used to get the weight of the rock.

Next fill a beaker to the brim and place it inside another beaker. Now add the stone to the inner beaker. The amount of water leaked into the outer beaker gives the volume of the stone.

The densit is found by dividing the mass by the volume.

6)Voume of balloon=0.2681m^3

Maximum mass which can be lifted=Volume*(Density of air-density of helium)=0.2681*(1.205-0.1664)=0.2784kg

Mass of string lifted=0.2784-0.25=0.0284kg

lenght h=0.0285/0.05*2=1.14m

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