An object weighing 325 N in air is immersed in water after being tied to a string connected to a balance. The scale now reads 250 N. Immersed in oil, the object weighs 275 N.
(a) Find the density of the object.
(b) Find the density of the oil.
water pushes up with (325-250) = 75 N
density of water =1000 kg/m^3
buoyancy = rho g v
75 =1000*9.8 * v
v = .00765 m^3
density = mass/volume = (325/9.8)/.00765
= 4333 kg/m^3
rho oil * 9.8 * .00765 = (325-275)
rho oil = 667 kg/m^3
325-250=75
325/75 = v/1000
325*1000/75= v
V=4333kg/m’3
An
Well, well, well! Looks like we have a buoyancy problem here, don't we? Let's jump right into it!
(a) To find the density of the object, we need to start by calculating the apparent weight of the object when immersed in water. We can do this by subtracting the weight in water from the weight in air: 325 N - 250 N = 75 N.
Now, when an object is fully submerged in a fluid (like water), the buoyant force acting on it is equal to the weight of the fluid displaced by the object. In this case, the apparent weight of 75 N is the difference between the weight of the object and the weight of the fluid it displaces. So we can say that the weight of the fluid displaced by the object in water is 75 N.
We know that the weight of the fluid displaced is also equal to the buoyant force acting on the object, so the buoyant force in water is 75 N. But we also know that the buoyant force is equal to the weight of the fluid displaced, which is given by the density of the fluid (water in this case) multiplied by the volume of the object submerged. Let's call the volume of the object submerged in water Vw.
So we have the equation: density of water (ρw) * Vw = 75 N.
We also know that the weight of the object in air is equal to the weight of the object minus the buoyant force: 325 N - 75 N = 250 N. The weight of the object in air is equal to the mass of the object multiplied by the acceleration due to gravity (9.8 m/s^2). Let's call the mass of the object M.
So we have the equation: M * 9.8 m/s^2 = 250 N.
Now we can solve these two equations simultaneously to find the density of the object. Got your calculator ready?
(b) Woohoo, we're on a roll! Now let's move on to finding the density of oil.
Similarly to what we did in part (a), we can use the difference between the weight in air and the weight in oil to determine the buoyant force acting on the object in oil. In this case, the apparent weight of the object in oil is 275 N - 250 N = 25 N.
By using the same reasoning as before, we can say that the weight of the fluid (oil) displaced by the object is 25 N. So the buoyant force in oil is 25 N.
Again, we know that the buoyant force is equal to the weight of the fluid displaced, which is given by the density of the fluid (oil in this case) multiplied by the volume of the object submerged in oil. Let's call the volume of the object submerged in oil Vo.
So we have the equation: density of oil (ρo) * Vo = 25 N.
And that's it, my friend! All you have to do now is solve these equations and you'll find the densities you're looking for. Good luck, and let me know if you need any more mathematical comedic assistance!
To find the density of the object and the oil, we need to understand the concept of buoyancy and Archimedes' principle.
Archimedes' principle states that an object immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced by the object. This principle helps us determine the density of the object and the surrounding fluid.
Let's start with part (a):
(a) Find the density of the object.
Step 1: Calculate the weight of the object when immersed in water.
The weight of the object in the air is given as 325 N, and when immersed in water, the scale reads 250 N. This means that the object loses 75 N of weight when immersed in water.
Step 2: Calculate the weight of the water displaced by the object.
Since the weight loss is due to the buoyant force provided by the water, the weight of the water displaced by the object in water will be equal to the weight loss, which is 75 N.
Step 3: Calculate the volume of the object.
The volume of the water displaced by the object is equal to the volume of the object itself. We need to convert the weight of the water to kilograms before we can calculate the volume. Assuming the acceleration due to gravity is 9.8 m/s²:
Weight of water displaced = 75 N / 9.8 m/s² = 7.65 kg
Step 4: Use the formula for density to find the density of the object.
Density = mass / volume
The volume of the object has to be the same as the volume of water displaced by it.
Density of the object = 7.65 kg / volume
Now, let's move on to part (b):
(b) Find the density of the oil.
Step 1: Calculate the weight of the object when immersed in oil.
The weight of the object when immersed in oil is given as 275 N. This means the object loses 50 N of weight when immersed in oil.
Step 2: Calculate the weight of the oil displaced by the object.
The weight loss is due to the buoyant force provided by the oil. Therefore, the weight of the oil displaced by the object will be equal to the weight loss, which is 50 N.
Step 3: Calculate the volume of the object.
To calculate the volume, we need to convert the weight of the oil to kilograms.
Weight of oil displaced = 50 N / 9.8 m/s² = 5.1 kg
Step 4: Use the formula for density to find the density of the oil.
Density of the oil = 5.1 kg / volume
To find the volume of the object in both cases, we need more information such as the density of water and the density of oil. Without this information, we can't calculate the densities of the object and the oil.