A Silver bowl has a mass of 1.78kg. It is shaped like a cylinder and has a diameter of 35.0 cm and a height of 8.00cm. It is placed in water. Find (a)the volume of water it displaces, (b) The buoyant force exerted on it by the water, and(c)how deeply it sinks into the water.
(1) The volume of the displaced water is 1.78 kg divided by the density of water, 1000 kg/m^3.
That is 1.78*10^-3 m^3 or 1780 cm^3
(2) The buoyant force (in Newtons) is 1.78 kg * 9.8 m/s^2
(3) How deeply it floats depends upon its position in the water. Is the cylinder axis parallel or perpendicular to the water surface?
Comparing the displaced water volume to the cylinder volume will tell you the fraction that is under water.
This cylinder is in the left front coernr it is the float switch. It should not leak there unless the tub is cracked. Most likely the the coernr baffels are what is leaking. They are super easy to replace. The simply pull out and you can press the new ones right in. If you had left a model number I could of given you the part numbers. There is a left and right one, replace both at the same time for best proformance. Good luck. Was this answer helpful?
To find the answers, we can follow these steps:
Step 1: Calculate the volume of the silver bowl.
Step 2: Determine the volume of water it displaces.
Step 3: Calculate the buoyant force exerted on the bowl by the water.
Step 4: Find out how deeply the bowl sinks into the water.
Let's calculate each step:
Step 1: Calculate the volume of the silver bowl
The shape of the bowl is a cylinder, so we can use the formula for the volume of a cylinder:
Volume = π * r^2 * h
where r is the radius of the cylinder (half of the diameter) and h is the height of the cylinder.
Given:
Diameter (d) = 35.0 cm
Height (h) = 8.00 cm
First, we need to find the radius (r) by dividing the diameter by 2:
r = d/2 = 35.0 cm / 2 = 17.5 cm
Now we can calculate the volume:
Volume of the silver bowl = π * r^2 * h
Volume = 3.14 * (17.5 cm)^2 * 8.00 cm
Step 2: Determine the volume of water it displaces
The volume of water displaced is equal to the volume of the silver bowl.
Step 3: Calculate the buoyant force exerted on the bowl by the water
The buoyant force is equal to the weight of the water displaced by the object. Since we know the mass of the bowl, we can use Archimedes' Principle to find the buoyant force:
Buoyant force = Weight of the water displaced = mass of the water displaced * acceleration due to gravity
To calculate the weight of the water displaced, we need the density of water. The density of water is approximately 1000 kg/m^3.
Now, we can determine the mass of the water displaced:
Mass of the water displaced = density of water * volume of water displaced
Step 4: Find out how deeply the bowl sinks into the water
The depth to which the bowl sinks into the water depends on the buoyant force and the weight of the bowl.
(a) To find the volume of water displaced, perform the calculation in Step 1.
(b) To find the buoyant force exerted on the bowl, calculate the mass of the water displaced in Step 3 and then use Archimedes' Principle.
(c) The depth to which the bowl sinks into the water can be calculated by comparing the weight of the bowl with the buoyant force. If they are equal, the bowl will remain at the same level as the water. If the weight of the bowl exceeds the buoyant force, it will sink deeper into the water.
Note: To get the final results, you need to perform the calculations using the specific values provided in the problem statement.
To solve this problem, we need to understand the concepts of volume, density, and buoyancy.
(a) The volume of water displaced by the silver bowl is equal to the volume of the bowl itself. Since the silver bowl is shaped like a cylinder, we can use the formula for the volume of a cylinder:
Volume = π * r^2 * h
where π is a constant approximately equal to 3.14159, r is the radius of the cylinder, and h is the height of the cylinder.
First, let's find the radius of the silver bowl. The diameter is given as 35.0 cm, so the radius (r) is half of the diameter:
r = 35.0 cm / 2 = 17.5 cm
Now we can substitute the values into the formula:
Volume = 3.14159 * (17.5 cm)^2 * 8.00 cm
Make sure to convert the units to meters to maintain consistency in the calculation. The result will be in cubic meters.
(b) The buoyant force exerted on an object submerged in a fluid is equal to the weight of the fluid displaced by the object. This can be calculated using Archimedes' principle:
Buoyant force = density of fluid * gravity * volume of fluid displaced
In this case, the fluid is water, so we need to know the density of water. The density of water at room temperature is approximately 1000 kg/m^3.
Buoyant force = (density of water) * gravity * volume of water displaced
where gravity is the acceleration due to gravity, approximately 9.8 m/s^2.
(c) The depth to which an object sinks into a fluid is determined by the equilibrium between the weight of the object and the buoyant force acting upon it. The object will sink until these forces are balanced:
Weight of the object = Buoyant force
To find the depth to which the silver bowl sinks into the water, we can use the equation:
Depth = Weight of the object / (density of water * gravity * area of the base of the object)
where the weight of the object is equal to its mass multiplied by the acceleration due to gravity.
Now let's calculate the answers to each part of the question.
(a) The volume of water displaced by the silver bowl is given by the formula:
Volume = 3.14159 * (0.175 m)^2 * 0.08 m
Calculate the result.
(b) The buoyant force exerted on the silver bowl is given by the formula:
Buoyant force = 1000 kg/m^3 * 9.8 m/s^2 * (volume of water displaced)
Substitute the value of the volume of water displaced and calculate the result.
(c) The depth to which the silver bowl sinks into the water is given by the formula:
Depth = (1.78 kg * 9.8 m/s^2) / (1000 kg/m^3 * 9.8 m/s^2 * (π * (0.175 m)^2))
Calculate the result.
Remember to use the appropriate units and convert them if necessary to maintain consistency throughout the calculations.