An object of mass 50 g floats in a liquid of density 2.5 g/ml. When the object is placed in a liquid of density 2.0 g/ml, it sinks to the bottom of the container. What is the force that the object exerts on the bottom of the container?
[g = 10m/s^2 = 10N/kg]
Its density must be 2.5g/cc., so its volume must be (50/2.5) = 20cc.
Mass = 50g., = 0.050kg.
(.050 x 9.8) = weight of 0.49N.
When sunken in the 2g/ml. fluid, it will displace 20cc. of it.
The fluid's mass will be (20 x 2) = 40g., = 0.040kg.
(.040 x 9.8) = 0.392N.
Force on bottom = (0.49 - 0.392) = 0.098N.
Well, well, well... looks like we have a sinking situation here! So, let me get this straight... The object changes its behavior like a chameleon when the liquid density changes. Fascinating!
Since the object floats in the first liquid and sinks to the bottom of the second one, it means that the second liquid is denser. The force that the object exerts on the bottom of the container is equal to the weight of the object.
To find the force, we need to calculate the weight of the object in the second liquid.
The mass of the object is 50 g, which translates to 0.05 kg (50 g/1000 = 0.05 kg).
In the first liquid, the buoyant force acting on the object is equal to the weight of the liquid displaced. Using the density and the volume of the liquid, we can calculate the buoyant force.
Buoyant Force = Density of Liquid x Volume of Liquid Displaced x Gravity
In the case of the first liquid, the buoyant force equals the weight of the object, hence why it floats.
Now, in the second liquid, the object sinks. This means that the weight of the object is greater than the buoyant force acting on it.
To find the force that the object exerts on the bottom of the container, we simply calculate the weight of the object in the second liquid.
Since the density of the second liquid is 2.0 g/ml, and the object's mass is 50 g, the volume of the object is 50 g / 2.0 g/ml = 25 ml.
The weight of the object in the second liquid is calculated using the formula:
Weight = Mass x Gravity
Weight = 0.05 kg x 10 m/s^2
Calculating the value gives us the force that the object exerts on the bottom of the container. Go on, crunch those numbers, my friend!
To find the force that the object exerts on the bottom of the container, we can use the buoyancy force formula:
Buoyancy force = Volume of the object * Density of the liquid * Acceleration due to gravity
First, let's determine the volume of the object:
Mass of the object = 50 g = 0.05 kg
Density of the liquid it floats in = 2.5 g/ml = 2.5 kg/L
Since density is mass/volume, we can rearrange the formula to solve for volume:
Volume of the object = Mass of the object / Density of the liquid it floats in
= 0.05 kg / 2.5 kg/L
= 0.02 L
Now let's calculate the buoyancy force when the object is placed in a liquid of density 2.0 g/ml:
Density of the liquid it sinks in = 2.0 g/ml = 2.0 kg/L
Buoyancy force = Volume of the object * Density of the liquid * Acceleration due to gravity
= 0.02 L * 2.0 kg/L * 10 N/kg
= 0.4 N
Therefore, the object exerts a force of 0.4 Newtons (N) on the bottom of the container.
To find the force that the object exerts on the bottom of the container, we need to consider the buoyant force and the weight of the object.
The buoyant force is the force exerted by a fluid on an object immersed in it, and it acts in the upward direction. It can be calculated using Archimedes' principle, which states that the buoyant force is equal to the weight of the fluid displaced by the object.
1. First, we need to determine the volume of the object in both liquids.
In the first liquid with a density of 2.5 g/ml:
Mass of the object = 50 g
Density of the liquid = 2.5 g/ml
Using the formula density = mass/volume, we can rearrange it to find the volume:
Volume in the first liquid = Mass of the object / Density of the liquid
Volume in the first liquid = 50 g / 2.5 g/ml = 20 ml
In the second liquid with a density of 2.0 g/ml:
Volume in the second liquid = Mass of the object / Density of the liquid
Volume in the second liquid = 50 g / 2.0 g/ml = 25 ml
2. Next, let's calculate the buoyant force in each liquid.
Buoyant force in the first liquid:
Buoyant force = Weight of the liquid displaced
Weight of the liquid displaced = Density of the liquid * Volume in the first liquid * Gravitational acceleration
Buoyant force in the first liquid = 2.5 g/ml * 20 ml * 10 N/kg = 500 N
Buoyant force in the second liquid:
Buoyant force = Weight of the liquid displaced
Weight of the liquid displaced = Density of the liquid * Volume in the second liquid * Gravitational acceleration
Buoyant force in the second liquid = 2.0 g/ml * 25 ml * 10 N/kg = 500 N
3. Finally, we can find the force that the object exerts on the bottom of the container.
Force exerted by the object = Weight of the object - Buoyant force in the second liquid
Weight of the object = Mass of the object * Gravitational acceleration = 50 g * 10 N/kg = 500 N
Force exerted by the object = 500 N - 500 N = 0 N
Therefore, the force that the object exerts on the bottom of the container is 0 N.