When a 55 N stone is attached to a spring
scale and is submerged in water, the spring scale reads 30 N.
What is the density of the stone?
Answer in units of kg/m3.
apparent weight= 55N-densitywater*g*volumestone
30=55-densitywater*g*volumestone
solve for volume stone
volumestone= 25/(densitywater*g)
density of STone= massstone/volume
= (55/g)/(25/densitywater*g)=55/25 *densitywater
A book is placed on a horizontal wooden plane that is undergoing simple
harmonic motion with an amplitude of 1.0 m. The coefficient of friction
between the book and the horizontal wooden plane is given by = 0.5.
Determine the frequency of the horizontal wooden platform when the book
is about to slip from the horizontal wooden plane.
Well, it seems like that stone is really shy and likes to hide its true weight underwater. It's like a secret agent stone!
But fear not, we can still determine its density. The difference between the weight of the stone outside the water (55 N) and the reading on the spring scale inside the water (30 N) is the buoyant force acting on the stone. And this buoyant force is equal to the weight of the water displaced by the stone.
Let's calculate the weight of the water displaced:
Buoyant force = Weight of water displaced
Buoyant force = 55 N - 30 N
Buoyant force = 25 N
Now we need to divide this buoyant force by the acceleration due to gravity (approximately 9.8 m/s^2) to find the mass of the water displaced:
Mass = Buoyant force / Acceleration due to gravity
Mass = 25 N / 9.8 m/s^2
Mass ≈ 2.55 kg
Finally, let's find the volume of the water displaced by the stone. We know that the density of water is approximately 1000 kg/m^3. So:
Density = Mass / Volume
Volume = Mass / Density
Volume ≈ 2.55 kg / 1000 kg/m^3
Volume ≈ 0.00255 m^3
Since the density of the stone is the same as the density of the water displaced (because they're in equilibrium), we can say that the density of the stone is approximately:
Density = Mass / Volume
Density ≈ 2.55 kg / 0.00255 m^3
Density ≈ 1000 kg/m^3
So, the density of the stone is approximately 1000 kg/m^3. That stone might look innocent, but it certainly knows how to make a splash in the water!
To find the density of the stone, we can use Archimedes' principle, which states that the buoyant force experienced by an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
Here are the steps to find the density:
1. Calculate the weight of the stone in air:
The weight of the stone in air is given as 55 N.
2. Calculate the weight of the water displaced by the stone:
The spring scale reading when the stone is submerged in water is 30 N. This reading represents the buoyant force acting on the stone, which is equal to the weight of the water displaced by the stone.
Buoyant force = Weight of the water displaced
So, the weight of the water displaced by the stone is 30 N.
3. Calculate the apparent weight of the stone in water:
The apparent weight of the stone in water is the difference between its weight in air and the weight of the water displaced.
Apparent weight = Weight in air - Weight of water displaced
Therefore, the apparent weight of the stone in water is:
Apparent weight = 55 N - 30 N = 25 N
4. Use the relationship between the apparent weight and the buoyant force to find the density:
The apparent weight of an object submerged in a fluid is equal to the weight of the object minus the buoyant force on the object.
Apparent weight = Weight - Buoyant force
Rearranging the equation, we get:
Weight = Apparent weight + Buoyant force
Now, knowing the weight of the stone in air and the weight of the water displaced, we can substitute the values into the equation:
55 N = 25 N + 30 N
5. Solve for the density of the stone:
The density of an object can be calculated using the equation: Density = Mass/Volume. We can rearrange this equation to solve for the mass of the stone.
Weight = Mass x gravitational acceleration (g)
Rearranging the equation: Mass = Weight / g
We need to find the mass of the stone, so we can use the equation:
Mass of the stone = Weight of the stone in air / g
Assuming the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the mass of the stone:
Mass = 55 N / 9.8 m/s^2
6. Use the calculated mass to find the volume of the stone:
Since density = Mass / Volume, we can rearrange this equation to solve for the volume:
Volume = Mass / Density
Substituting the values we have:
Volume = (Mass of the stone) / (Density of the stone)
Note that the units of the mass are in kilograms (kg) and the units of volume are in cubic meters (m^3).
7. Finally, calculate the density of the stone:
Density = Mass / Volume
Substituting the values into the equation, we get:
Density = (Mass of the stone) / (Volume of the stone)
Now, calculate the density using the values obtained from the previous steps.
By following these steps, you will be able to find the density of the stone in units of kg/m³.