A beaker weigh 0.4 N when empty nd 1.4 N when filled with water. what does it weigh when filled with brine of density 1.2 g/cm^3

Answer 1

To solve this problem, we first need to determine the weight of the water that fills the beaker. Given that the beaker weighs 0.4 N when empty and 1.4 N when filled with water, the weight of the water alone is:

\[ 1.4 \, \text{N} - 0.4 \, \text{N} = 1.0 \, \text{N} \]

Next, we use the relationship between weight, mass, and gravitational acceleration to find the mass of the water. The weight \( W \) is given by:

\[ W = m \cdot g \]

where \( m \) is the mass and \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \)).

Rearranging the equation to solve for mass \( m \):

\[ m = \frac{W}{g} = \frac{1.0 \, \text{N}}{9.8 \, \text{m/s}^2} \approx 0.102 \, \text{kg} \]

Since the density of water is \( 1.0 \, \text{g/cm}^3 \) (or \( 1000 \, \text{kg/m}^3 \)), and knowing the mass obtained, we can now find the volume \( V \) of the water:

\[ \text{Density} = \frac{ \text{Mass} }{ \text{Volume} } \]

\[ 1000 \, \text{kg/m}^3 = \frac{0.102 \, \text{kg}}{V} \]

Solving for \( V \):

\[ V = \frac{0.102 \, \text{kg}}{1000 \, \text{kg/m}^3} = 1.02 \times 10^{-4} \, \text{m}^3 = 102 \, \text{cm}^3 \]

This volume is the same for both water and brine, since the beaker is filled to the same level.

Now, given the density of brine is \( 1.2 \, \text{g/cm}^3 \) (or \( 1200 \, \text{kg/m}^3 \)), we calculate the mass of the brine needed to fill the same volume:

\[ \text{Density} = \frac{ \text{Mass} }{ \text{Volume} } \]

\[ 1200 \, \text{kg/m}^3 = \frac{m}{1.02 \times 10^{-4} \, \text{m}^3} \]

Solving for \( m \):

\[ m = 1200 \, \text{kg/m}^3 \times 1.02 \times 10^{-4} \, \text{m}^3 = 0.1224 \, \text{kg} \]

Converting this mass to weight:

\[ W = m \cdot g = 0.1224 \, \text{kg} \times 9.8 \, \text{m/s}^2 \approx 1.2 \, \text{N} \]

Finally, adding the weight of the empty beaker:

\[ \text{Total Weight} = \text{Weight of empty beaker} + \text{Weight of brine} \]

\[ \text{Total Weight} = 0.4 \, \text{N} + 1.2 \, \text{N} = 1.6 \, \text{N} \]

Thus, the beaker weighs 1.6 N when filled with brine of density \( 1.2 \, \text{g/cm}^3 \).