Physics (Physics of Matter) Homework

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PHYS 101, section B01, Spring 2020

Homework 4 (Week 4: Ch.4 Ostdiek 8e) (Homework)

INSTRUCTOR

Stephen Mahan Liberty University

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A ship on a large river approaches a bridge, and the captain notices that the ship is about a foot too tall to fit under the bridge. A crew member suggests pumping water from the river into an empty tank on the ship. Would this help?

Yes

No

Why or why not?

It would help because pumping water from the river into the ship lowers the river height.

It would not help because the water is still part of the ship–river system, whether the water is in the river or in a tank on the ship.

It would not help because pumping water into the ship makes the ship less dense, causing it to displace less water and ride higher in the water.

It would help because pumping water into the ship makes the ship more dense, causing it to displace more water and ride lower in the water.

Pistons are fitted to two cylindrical chambers connected through a horizontal tube to form a hydraulic system. The piston chambers and the connecting tube are filled with an incompressible fluid. The cross-sectional areas of piston 1 and piston 2 are A

and A , respectively. A force F is exerted on piston 1. Rank the resultant force F on piston 2 that results from the combinations

of F , A , and A given from greatest to smallest. If any of the combinations yield the same force, give them the same ranking.

(Use only ">" or "=" symbols. Do not include any parentheses around the letters or symbols.)

a.

b.

c.

d.

e.

f.

1

2 1 2

1 1 2

F = 5.0 N; A = 1.1 m ; and A = 2.2 m1 1 2

2 2

F = 2.5 N; A = 1.1 m ; and A = 0.55 m1 1 2

2 2

F = 2.5 N; A = 2.2 m ; and A = 4.4 m1 1 2

2 2

F = 5.0 N; A = 0.55 m ; and A = 2.2 m1 1 2

2 2

F = 5.0 N; A = 0.55 m ; and A = 1.1 m1 1 2

2 2

F = 2.5 N; A = 2.2 m ; and A = 1.1 m1 1 2

2 2

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A bicycle tire pump has a piston with area 0.42 in . If a person exerts a force of 24 lb on the piston while inflating a tire, what pressure does this produce on the air in the pump?

psi

2

A large truck tire is inflated to a gauge pressure of 66 psi. The total area of one sidewall of the tire is 1,340 in . What is the net outward force (in lb) on the sidewall because of the air pressure? (Enter the magnitude.)

lb

2

A viewing window on the side of a large tank at a public aquarium measures 49 in. by 59 in. The average gauge pressure from the water is 4 psi. What is the total outward force on the window?

lb

The total mass of the hydrogen gas in the Hindenburg zeppelin was 18,000 kg. What volume did the hydrogen occupy? (Assume that the temperature of the hydrogen was 0°C and that it was at a pressure of 1 atm.)

m

3

A large balloon used to sample the upper atmosphere is filled with 390 m of hydrogen. What is the mass of the hydrogen (in kg)?

kg

3

Find the gauge pressure (in psi) at the bottom of a freshwater swimming pool that is 16.1 ft deep.

psi

The depth of the Pacific Ocean in the Mariana Trench is 36,198 ft. What is the gauge pressure at this depth?

psi

An ebony log with volume 11.8 ft is submerged in water. What is the buoyant force on it (in lb)? (Enter the magnitude.)

lb

3

An empty storage tank has a volume of 6,520 ft . What is the buoyant force exerted on it by the air? (Assume the air is at 0°C and 1 atm.)

lb

3

A modern-day zeppelin holds 8,800 m of helium. Compute its maximum payload at sea level. (Assume the helium and air to be at 0°C and 1 atm.)

N

3

A boat (with a flat bottom) and its cargo weigh 5,200 N. The area of the boat's bottom is 6 m . How far below the surface of the water is the boat's bottom when it is floating in water?

m

2

A scale reads 390 N when a piece of copper is hanging from it. What does it read (in N) when it is lowered so that the copper is submerged in water?

N

A rectangular block of ice with dimensions 2 m by 2 m by 0.3 m floats on water. A person weighing 845 N wants to stand on the ice. Would the ice sink below the surface of the water?

Yes

No

A dentist's chair with a person in it weighs 1850 N. The output plunger of a hydraulic system starts to lift the chair when the dental assistant's foot exerts a force of 46 N on the input piston. Neglecting any difference in the heights of the piston and the plunger, what is the ratio of the area of the plunger to the area of the piston?

= A

A plunger

piston

The wing of an airplane has an average cross-sectional area of 11 m and experiences a lift force of 93,000 N. What is the average difference in the air pressure between the top and bottom of the wing?

N/m

2

2

Air flows through a heating duct with a square cross-section with 9-inch sides at a speed of 5.5 ft/s. Just before reaching an outlet in the floor of a room, the duct widens to assume a square cross-section with sides equal to 13 inches. Compute the speed of the air flowing into the room (in ft/s), assuming that we can treat the air as an incompressible fluid.

ft/s

How are the concepts of pressure, force, and area related to the function of snowshoes as a person stands at rest on the snow?

The wide area of the snowshoes allows the snowshoes to provide a larger force than the person's weight as the person stands on the snow; this supports the person.

Since the snowshoes have a relatively large area, they reduce the force that the person's feet apply to the snow.

Snowshoes distribute a person's weight (a force) over a larger area; this reduces the pressure from the snowshoes on the snow.

Is it possible to measure altitude with a barometer?

Yes. As the altitude increases, the air pressure decreases, so a lower barometer reading indicates a higher altitude.

No. Air pressure is constant at all elevations, so a barometer measuring air pressure is not able to give information about altitude.

Yes. As the altitude increases, the air pressure also increases, so a higher barometer reading indicates a higher altitude.

Various objects in our daily lives are attached to windows, refrigerators, bathroom walls, and other surfaces using suction cups. How does a suction cup work?

The pressure from the atmosphere is greater than the pressure inside the suction cup. This difference causes the suction cup to be pressed against the surface it is attached to.

Suction cups only work if they make use of some form of chemical adhesive. Air pressure alone cannot produce strong enough forces to hold a suction cup in place.

The air molecules inside a suction cup pull the suction cup toward the surface it is attached to, holding it in place.

Use the following table to determine which of the other materials from the list would float if placed in a container of ethyl alcohol. Select all correct answers.

Substance Density (kg/m )

concrete 2,500

ethyl alcohol 791

ice 917

juniper wood 560

lead 11,340

silver 10,500

concrete

ice

juniper wood

lead

silver

None of the above materials would float; they are all solids and would sink in a liquid.

3

A person does the back float in a freshwater lake and later does the same in the ocean. In which case is more of the person's body above the water line?

The person will float with more of her body above water in the ocean.

The person will float with more of her body above water in freshwater.

Since both situations involve the person floating in a solution that is primarily water, there will not be a difference between the two cases.

A metal bowl with a weight of 1.05 N is placed in a larger kitchen container filled with soybean oil. How much soybean oil must the bowl displace in order to float? For reference, the mass density of soybean oil is about 917 g/liter and its weight density is about 8.99 N/liter. Please give your answer in liters.

liters

While an airplane is in flight, the pressure along the top of the wing is lower than the pressure along the bottom of the wing, providing a lift force. How does the speed of the air going past the top of the wing compare to the speed of the air going past the bottom of the wing?

The speed of the air going past the top of the wing is greater than the speed of the air passing the bottom of the wing.

Since the wings are attached to the plane they are both moving through the air at the same speed and the air moving above or below the wings is passing the wing at the same speed.

The speed of the air is greater when passing the bottom of the wing than it is when passing the top of the wing.

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