An object is solid throughout. When the object is completely submerged in ethyl alcohol, its apparent weight is 15.8 N. When completely submerged in water, its apparent weight is 13.0 N. What is the volume of the object?
Would I start by doing 15.8 - 13?
No, to find the volume of the object, you would use the principle of buoyancy. The apparent weight of an object submerged in a fluid is equal to the weight of the displaced fluid.
To find the volume of the object, you can use the equation:
apparent weight in fluid = weight of object - weight of displaced fluid
Given:
Apparent weight in ethyl alcohol = 15.8 N
Apparent weight in water = 13.0 N
Since the object is solid throughout, its weight does not change, only the weight of the displaced fluid changes.
First, find the weight of the object using the equation:
Weight of object = Apparent weight in ethyl alcohol + Weight of displaced ethyl alcohol
Then, find the weight of the displaced water using the equation:
Weight of displaced ethyl alcohol = Weight of object - Apparent weight in water
Finally, use the principle of buoyancy:
Weight of displaced water = density of water * volume of object * acceleration due to gravity
By rearranging the equation, you can solve for the volume of the object:
Volume of object = (Weight of displaced water) / (density of water * acceleration due to gravity)
Using the given information, you can substitute the values into the equations to find the volume of the object.
To find the volume of the object, we need to use the concept of buoyancy and Archimedes' principle. The difference in apparent weight when the object is submerged in different fluids can help us find the volume.
The apparent weight of an object submerged in a fluid is equal to the actual weight of the object minus the buoyant force acting on it. The buoyant force is equal to the weight of the fluid displaced by the object.
Let's start by finding the buoyant force in ethyl alcohol and water.
Buoyant force in ethyl alcohol:
Apparent weight in ethyl alcohol = 15.8 N
Actual weight of the object = ?
Buoyant force in ethyl alcohol = Actual weight - Apparent weight = Actual weight - 15.8 N
Buoyant force in water:
Apparent weight in water = 13.0 N
Actual weight of the object = ?
Buoyant force in water = Actual weight - Apparent weight = Actual weight - 13.0 N
Now, to find the volume of the object, we need to compare the buoyant forces in ethyl alcohol and water.
Since the object is solid throughout, its volume will remain constant. Therefore, the buoyant forces in ethyl alcohol and water will be equal.
Set up the equation:
Buoyant force in ethyl alcohol = Buoyant force in water
Actual weight - 15.8 N = Actual weight - 13.0 N
Now, subtract Actual weight from both sides:
-15.8 N = -13.0 N
Simplify:
-15.8 + 13.0 = 0
2.8 N = 0
However, this implies that the object has no weight, which is not possible. Thus, there might be a mistake in the given information or calculations steps.
Please double-check the information provided or re-evaluate the calculations to ensure accuracy.
You can start there, but there is a lot more to do
True weight (in air) = W
ethyl alcohol density = 790 kg/m^3
(You have to look that up)
Water density = 1000 kg/m^3
You have to solve for two unknowns, Weight W and Volume V. You have two equations to work with:
15.8 N = W - 790*9.8*V
13.0 N = W - 1000*9.8*V
NOW do the subtraction
2.8 N = 210*9.8 V
V = 1.36*10^-3 m^3
= 1.36 liters
W = 26.33 N