Question

An object weighs 79.1 N in air. When it is suspended from a force scale and completely immersed in water the scale reads 21.8 N. Determine the density of the object. (b)When the object is immersed in oil, the force scale reads 48.4 N. Calculate the density of the oil.

Answer 1

To determine the density of the object, use Archimedes' principle. The density of the object is approximately 13.51 N/kg. Similarly, the density of the oil is approximately 25.28 N/kg.

Step-by-step explanation:

To determine the density of the object, we can use Archimedes' principle, which states that the buoyant force on an object is equal to the weight of the fluid it displaces.

First, we calculate the volume of the object:

The weight in air is 79.1 N. The weight in water is 21.8 N. The weight of the water displaced is 79.1 N - 21.8 N = 57.3 N.

Using the equation density = mass/volume, we can rearrange it to solve for volume:

Volume = mass/density = 57.3 N/9.8 m/s² = 5.85 kg.

Therefore, the density of the object is 79.1 N/5.85 kg ≈ 13.51 N/kg.

Similarly, we can calculate the density of the oil:

The weight in air is 79.1 N. The weight in oil is 48.4 N. The weight of the oil displaced is 79.1 N - 48.4 N = 30.7 N.

Using the equation density = mass/volume, we can rearrange it to solve for volume:

Volume = mass/density = 30.7 N/9.8 m/s² = 3.13 kg.

Therefore, the density of the oil is 79.1 N/3.13 kg ≈ 25.28 N/kg.

Answer 2

(a). The density of the object is 1382 kg/m³.

(b). The density of the oil is 536.4 kg/m³.

Step-by-step explanation:

Given that,

Weight in air = 79.1 N

Weight in water = 21.8 N

Weight in oil = 48.4 N

We need to calculate the volume of object

Using formula of buoyant force

`F_(b)=W_(air)=W_(water)`

`F_(b)=79.1-21.8`

`F_(b)=57.3\ N`

`F_(b)=\rho g h`

Put the value into the formula

`57.3=1000* V* 9.8`

`V=(57.3)/(1000*9.8)`

`V=5.84*10^(-3)\ m^3`

We need to calculate the density

Using formula of buoyant force

`F_(b)=\rho Vg`

`79.1=\rho*5.84*10^(-3)*9.8`

`\rho=(79.1)/(5.84*10^(-3)*9.8)`

`\rho=1382\ kg/m^3`

The density of the object is 1382 kg/m³.

(b). We need to calculate the volume of object

Using formula of buoyant force

`F_(b)=W_(air)=W_(oil)`

`F_(b)=79.1-48.4`

`F_(b)=30.7\ N`

We need to calculate the density

Using formula of buoyant force

`F_(b)=\rho_(oil) Vg`

`30.7=\rho_(oil)*5.84*10^(-3)*9.8`

`\rho_(oil)=(30.7)/(5.84*10^(-3)*9.8)`

`\rho=536.4\ kg/m^3`

The density of the oil is 536.4 kg/m³.

Hence, This is the required solution.