The gravitational force exerted on a solid object is 5.15 N as measured when the object is suspended from a spring scale. When the suspended object is submerged in water, the scale reads 4.00 N. Find the density of the object.
The buoyancy force in water is 1.15 N.
1.15 N = V*g*1000 kg/m^3
5.15 N = V*g*(density)
Combine the two above equations to get
density/1000 = 5.15/1.15 = 4.48
density = 4480 kg/m^3
= 4.48 g/cm^3
The answer is wrong, and I am not sure why
Nvm it is correct! Thank you!
To find the density of the object, we can make use of Archimedes' principle and the concept of buoyancy.
1. Archimedes' principle states that when an object is submerged in a fluid, it experiences an upward buoyant force equal to the weight of the fluid it displaces.
2. We can calculate the buoyant force using the difference in the gravitational force of the object in air and in water. The difference in the scale readings (5.15 N - 4.00 N) gives us the weight of the water displaced by the object.
3. Next, we need to find the weight of the water displaced. We know that the density of water is approximately 1000 kg/m³ and the acceleration due to gravity is 9.8 m/s². Using the formula weight = mass x gravity, we can find the weight of the water displaced.
4. Now that we have the weight of the water displaced and the buoyant force, we can equate them. The buoyant force is equal to the weight of the water displaced (density of water x volume of the object submerged x gravity), and this force is equal to the difference in scale readings (5.15 N - 4.00 N).
5. Rearrange the equation to solve for the volume of the object submerged: density of water x volume of the object submerged x gravity = 5.15 N - 4.00 N.
6. Once we have found the volume of the object submerged, we can calculate its density. The density can be calculated using the formula density = mass/volume.
By following these steps, we can find the density of the object.