PHYS CH. 7 Fluid Mechanics
How does the buoyant force on a fully submerged object compare with the weight of water displaced
According to Archimedes' principle, the buoyant force of a fully submerged object in water will be exactly equal to the weight of water that is displaced
Before boarding an airplane, you buy a bag of chips (or any item packaged in an airtight bag) and while in flight, you notice that the bag is puffed up. Explain why this occurs
As you increase in altitude, atmospheric pressure decreases. The pressure inside the closed package was originally the same as the pressure at a lower altitude. As atmospheric pressure decreases the pressure inside the closed container is greater than the pressure outside and this causes the bag to puff up.
Would the water level in a canal lock go up or down if a battleship in the lock were to sink?
Following the same reason as above, if a battleship was originally floating in a lock it must displace a weight of water that is equal to the weight of the battleship. Since water is less dense than iron (material of the battleship), a larger volume of water must be displaced to account for the mass of the battleship. The ship is made to displace a larger amount of water. Now, when the battleship sinks, the volume of water displaced is equal to the volume of the battleship. Since the object is sinking, the buoyant force must be less than the weight of the object and thus less water is displaced when the battleship sinks. If less water is displaced, then the water level in the lock would go down.
How does the volume of a completely submerged object compare with the volume of water displaced?
For a completely submerged object, the volume of water displaced will be equal to the volume of the object
If a 1-L container is immersed halfway in water, what is the volume of water displaced? What is the buoyant force on the container?
If the container is halfway immersed then the amount of volume of the container under the water is ½ L. This means the ½ L of water is displaced. It turns out that the density of water can be written as ρwater = 1 kg / L and thus we can solve for the mass of water in a volume of ½ L. ( )( ) 1 2 1 0.5 ρ = = = kg L m V L kg The weight of this amount of water is w = mg = (0.5 kg)(10 m/s2) = 5 N According to Archimedes' principle, the buoyant force is equal to the weight of the fluid displaced and thus it is 5 N.
How much force is necessary to push a nearly weightless but rigid 1-L carton beneath the surface of water?
In order to push a 1-L carton "weightless" carton below the surface of water, we must displace 1-L of water. When the 1-L of water is displaced an upward buoyant force equal to the weight of the fluid displaced will act on the carton. We would have to apply a force equal to the upward buoyant force in order to immerse the object in the water. The weight of this amount of water is w = mg = (1 kg)(10 m/s2) = 10 N According to Archimedes' principle, the buoyant force is equal to the weight of the fluid displaced and thus it is 10 N. Thus, we would need to apply a downward force equal to 10 N in order to completely immerse the 1-L carton. The fact that is weightless is just to let us know that there is no force from gravity that is helping to submerge the object.
If liquid pressure were the same at all depths, would there be a buoyant force on an object submerged in the liquid? Explain.
No, the buoyant force is a direct result of a difference in pressure between the bottom of the object and top of the object. (See question # 6 above in first section)
How does the pressure exerted by a liquid change with depth in the liquid? How does the pressure exerted by a liquid change as the density of the liquid changes?
Pressure increases with depth. As the density of the liquid increases, the pressure exerted by the liquid also increases. The pressure below the surface of salt water is greater than the pressure below fresh water since salt water is more dense that fresh water.
Distinguish between force and pressure.
Pressure is the amount of force exerted per unit area. Force has direction and is a vector quantity. Pressure is a scalar quantity meaning that we just talk about the size of the pressure and not the direction.
The relative densities of water, ice, and alcohol are 1.0 g/cm3, 0.9 g/cm3, and 0.8 g/cm3 respectively. Ice cubes float in water but will they float higher or lower in a mixed alcoholic drink (which in general consist of alcohol and some water substance)? What can you say about a cocktail in which the ice cubes lie submerged at the bottom of the glass
Since ice is less dense than water but is denser than alcohol, if water and alcohol are mixed the density of the mixture will be less than the density of water. This means that ice will float lower in in the mixture of water and alcohol. As the density of the liquid decreases, the object will have to displace more liquid in order to remain floating. If the ice sinks, this means that there is more alcohol in the mixture as compared to water. If it was an even mixture the density would likely be 0.9 g/cm3 but if there is more alcohol than water then the density would be less than the density of the ice and the ice would sink.
In a deep dive, a whale is appreciably compressed by the pressure of the surrounding water. What happens to the whale's density
Since the whale is compressed, its volume has decreased. Density is inversely proportional to volume and thus as the volume decreases the density increases.
Which do you suppose exerts more pressure on the ground, an elephant or a woman standing on spike heels? (Which will be more likely to make dents in a linoleum floor?)
Since the women's weight is distributed on a very small area, the woman likely exerts more pressure on the ground. The elephant weighs more but has large foot pads to distribution the weight over a larger area.
What is the difference between being immersed and being submerged?
Submerged refers to something that sinks will immersed refers to placing something below the surface of fluid. If an object is immersed, something might be holding it under the fluid but if the object is released it might float to the surface or sink.
State Archimedes' principle
The buoyant force acting on an object is equal to the weight of the fluid that is displaced.
A ship sailing from the ocean into a freshwater harbor sinks slightly deeper into the water. Does the buoyant force on it change? If so, does is increase or decrease?
The buoyant force acting on the ship does not change. When an object floats the buoyant force acting on the object must equal the weight of the object. Since the weight of the object didn't change the buoyant force remains the same. Now fresh water is less dense than salt water. So, when the ship enters fresh water, more water must be displaced to equal the weight of the object. Think about the fact that if something is less dense then it is less compact. Fresh water is less compact as compare to salt water. In order to get the same mass of fresh water as compared to salt water you must have a larger volume.
Why does buoyant force act upward on an object submerged in water?
The buoyant force comes from the difference in pressure at the bottom of the object as compared to the top of the object. Since the pressure is greater at a greater depth, the pressure at the bottom of the object is greater than the pressure at the top of the object. Pressure = Force/Area and thus there is a greater force on the bottom of the object directed upward as compared to the force acting on the top of the object acting downward.
Does the buoyant force on a fully submerged object depend on the weight of the object or on the weight of the fluid displaced by the object? Does the force depend on the weight of the object or on its volume? Explain.
The buoyant force on a fully submerged object depends on the weight of the fluid that is displaced by the object. The weight of the fluid displaced will be affected by the volume of the object. Thus the buoyant force depends on the volume of the object. Two objects with the same mass but different volumes will displace different amounts of fluid and thus will experience different buoyant forces.
Why is it inaccurate to say that heavy objects sink and that light objects float? Give exaggerated examples to support your answer.
The density of the object relative to the density of the fluid is what determines whether or not an object will float. An exaggerated example would be a penny sinks and yet a large log will float. The log obviously has a larger mass than the penny but it also has a smaller density.
Discounting the pressure of the atmosphere, if you swim twice as deep in water, how much more water pressure is exerted on your ears? If you swim in salt water, will the pressure be greater than in fresh water at the same depth? Why or why not?
The liquid pressure increase with depth and is proportional to how far below the surface you go. Thus, if you double the distance below the surface, the pressure on your ears would be doubled. (PLiquid = ρfluid g h). If you swim in salt water which is more dense, the pressure on your ears will be greater at the same depth since the liquid pressure also depends directly on the density of the fluid.
Stand on a bathroom scale and read your weight. When you lift one foot up so you're standing on one foot, does the reading change? Does a scale read force or pressure
The scale will read the same value if you lift up one foot. The scale reads force not pressure. When you lift up one foot, less area is in contact with the scale and thus the pressure on the scale has increased but the force is still the same.
Compared to an empty ship, would a ship loaded with a cargo of Styrofoam sink deeper into water or rise in water? Explain.
The ship loaded with Styrofoam will sink deeper in the water. The buoyant force of a floating object is equal to the weight of the object. Since the loaded ship weighs more, the buoyant force must be greater and thus more water must be displaced.
When you are sun bathing and wading on a stony beach, why do the stones hurt your feet less when you get in deep water?
The stones hurt your feet less in deeper water. This is likely due to the fact that as you go deeper in the water, your body displaces more water and thus there is greater upward buoyant force acting on your body. You are not pushing down as hard on the rocks at in the deeper water due to the larger upward buoyant force.
What happens to the volume of a loaf of bread that is squeezed? What happens to the mass? What happens to the density?
The volume decreases. The mass remains the same. The density increases
How does water pressure one meter below the surface of a small pond compare to water pressure on meter below the surface of a huge lake?
The water pressure would be same in both cases because you are measuring the pressure in both cases at the same depth. The amount of water in the "container" doesn't affect the pressure only the depth below the surface.
A barge filled with scrap iron is in a canal lock. If the iron is thrown overboard, does the water level at the side of the lock rise, fall, or remain unchanged? Explain
This is a bit more difficult. In general scrap iron will sink if place in the water. When it is on the barge, the barge is displacing enough volume of water to allow the scrap metal to float. Since iron is more dense than water, this means that the barge ship is displacing a volume of water that is greater than the iron in order to allow the iron to float on the barge. Once the iron is thrown into the water, the water displaced by the iron is less because now the only the volume of the iron is displaced. This means that the water level will actual drop when the iron is thrown in. Less water is displaced when the iron sinks as compared to when it was floating on the barge
What weight of water is displaced by a 100-ton floating ship? What is the buoyant force that acts on the ship
When an object floats it is in equilibrium and the downward force of gravity (weight of the object) is exactly equal to the upward buoyant force. Thus the buoyant force acting on a 100-ton floating ship is 100-tons. According to Archimedes' principle, the buoyant force is equal to the weight of the fluid displaced and thus the weight of the water displaced will also be 100-tons
A half-filled bucket of water is on a spring scale. Will the reading on the scale increase or remain the same if a fish is placed in the bucket? (Will your answer be different if the bucket is initially filled to the brim when the fish is placed in the bucket?)
When the fish is placed in the half-filled bucket of water, the reading of scale will increase by a factor of the fish's weight. If the bucket was filled to the top, when the fished is placed in the water some of the water will spill out. The amount of water that will spill out is exactly equal to the volume of the fish. Now we assume that the fish is denser than water, which means that the weight of the water that spills out will be less than the weight of the fish. (Both the fish and spilled water have the same volume but the fish is more compact and thus has a greater weight). The scale would still read an increase but it would not be as great as when the bucket was only filled half way. It would read a difference between the weight of the fish and weight of the water that spilled out.
Why do you suppose that airplane windows are smaller than bus windows?
When traveling in a bus, atmospheric pressure changes very little as you go up and down hills. The pressure inside the bus and outside the bus is easy to equalize. As a plane increases its altitude, the pressure decreases significantly. The pressure inside the airplane must be kept relatively constant since passengers can only withstand slight changes in atmospheric pressure. This means that the pressure inside the plane is very larger compared to outside the plane at high altitudes. The windows on the plane will experience a force based on the difference in pressure between inside and outside the plane as well as the area of the window. By making the window area smaller, the force on the window is less.
