the gravitational force exerted on a solid object is 5.00N.when the object is suspended from a spring scale and submerged completely in water the scale reads 3.50N. find the density of the object.
weightinwater=weight-densitywater*Volume
3.5=5-1E3kg/m^3*Volume
volume=1.5N/1000kg=.0015m^3=1.5liters
To find the density of the object, we can make use of Archimedes' principle, which states that the buoyant force exerted on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
1. First, we need to find the weight of the water displaced by the object. Since the scale reads 3.50N, this corresponds to the buoyant force acting on the object.
2. The buoyant force equals the weight of the water displaced, which can be expressed as:
Buoyant force = Weight of water displaced
Therefore, the weight of the water displaced is 3.50N.
3. Now, let's find the weight of the object in the air. We know that the gravitational force exerted on the object is 5.00N.
4. Since the object is submerged in water, it experiences two forces: the gravitational force downward and the buoyant force upward. These two forces add up to give the net force of 3.50N acting on the object.
Net force = Weight of the object - Buoyant force
3.50N = Weight of the object - 3.50N
5. Rearranging the equation, we can find the weight of the object in the air:
Weight of the object = 3.50N + 3.50N
Weight of the object = 7.00N
6. Now that we have the weight of the object, we can use the formula for density:
Density = Mass / Volume
However, it is important to note that the weight of an object can be expressed as:
Weight = Mass * gravitational acceleration
Therefore, we can substitute the weight into the formula:
Weight = Mass * gravitational acceleration
7.00N = Mass * 9.8 m/s^2 (approximating the acceleration due to gravity to be 9.8 m/s^2)
7. Solving for mass:
Mass = 7.00N / 9.8 m/s^2
Mass = 0.7143 kg (approx.)
8. Finally, using the formula for density:
Density = Mass / Volume
We do not have the value for volume, but we can rewrite the formula as:
Volume = Mass / Density
Volume = 0.7143 kg / Density
Rearranging the equation to solve for density:
Density = Mass / Volume
Density = 0.7143 kg / Volume
9. Unfortunately, we do not have the value for volume in this case, so we cannot calculate the exact density of the object without additional information or measurements.
Therefore, the density of the object cannot be determined with the given information.
To find the density of the object, we need to use the concept of buoyancy. Buoyancy is the upward force exerted by a fluid on an object immersed in it. In this case, the object is submerged in water, and we know the change in weight between when the object is outside the water and when it is submerged.
Step 1: Calculate the buoyant force.
The buoyant force is equal to the weight of the fluid displaced by the object. According to Archimedes' principle, this force is equal to the weight of the object that is submerged. So, the buoyant force is equal to 5.00 N - 3.50 N = 1.50 N.
Step 2: Calculate the weight of the fluid displaced.
The weight of the fluid displaced is equal to the buoyant force. Therefore, the weight of the fluid displaced is also 1.50 N.
Step 3: Calculate the volume of the object.
From Step 2, we know that the weight of the displaced fluid is equal to the buoyant force, which is given by the equation: buoyant force = weight of fluid displaced = ρ * V * g, where ρ is the density of the fluid (in this case, water), V is the volume of the fluid displaced, and g is the acceleration due to gravity.
Since the weight of the fluid displaced is equal to 1.50 N, and the acceleration due to gravity is approximately 9.8 m/s², we can rearrange the equation to solve for V: V = buoyant force / (ρ * g).
Step 4: Calculate the density of the object.
The density of the object is given by the equation: density of the object = mass of the object / volume of the object.
From Step 3, we have the volume of the object (V). Since we know the weight of the object (5.00 N), we can calculate the mass of the object using the formula: mass of the object = weight of the object / g.
Finally, we can substitute the mass and volume values into the density equation to find the density of the object.
Please note that in this explanation, we assume that the object is fully submerged in water without any other forces acting on it. Additionally, we assume that the spring scale remains accurate when submerged in water.