IDNLearn.com: Your reliable source for finding precise answers. Discover comprehensive answers to your questions from our community of experienced professionals.
Sagot :
To determine the weight of the water displaced by a block of iron with given dimensions, follow these steps:
1. Calculate the Volume of the Iron Block:
The volume ([tex]\( V \)[/tex]) of a rectangular block is found by multiplying its length ([tex]\( l \)[/tex]), width ([tex]\( w \)[/tex]), and height ([tex]\( h \)[/tex]) together.
[tex]\[ V = l \times w \times h \][/tex]
Given:
[tex]\[ l = 3.00 \, \text{cm}, \quad w = 3.00 \, \text{cm}, \quad h = 3.00 \, \text{cm} \][/tex]
[tex]\[ V = 3.00 \times 3.00 \times 3.00 = 27.00 \, \text{cm}^3 \][/tex]
2. Determine the Mass of the Displaced Water:
Since the iron block will displace an equal volume of water, we need to calculate the mass of this water. The mass ([tex]\( m \)[/tex]) is found by multiplying the volume by the density ([tex]\( \rho \)[/tex]) of water.
Given the density of water:
[tex]\[ \rho = 1.00 \, \text{g/cm}^3 \][/tex]
[tex]\[ m = V \times \rho = 27.00 \, \text{cm}^3 \times 1.00 \, \text{g/cm}^3 = 27.00 \, \text{g} \][/tex]
3. Convert the Mass to Kilograms:
The mass must be converted to kilograms to use the formula for weight. There are 1000 grams in a kilogram.
[tex]\[ m_{\text{kg}} = \frac{m}{1000} = \frac{27.00 \, \text{g}}{1000} = 0.027 \, \text{kg} \][/tex]
4. Calculate the Weight of the Displaced Water:
The weight ([tex]\( W \)[/tex]) of the water displaced can be calculated using the formula [tex]\( W = m \times g \)[/tex], where [tex]\( g \)[/tex] is the acceleration due to gravity.
Given [tex]\( g = 9.80 \, \text{m/s}^2 \)[/tex]:
[tex]\[ W = m_{\text{kg}} \times g = 0.027 \, \text{kg} \times 9.80 \, \text{m/s}^2 = 0.2646 \, \text{N} \][/tex]
Hence, the weight of the water displaced by the block of iron is [tex]\( 0.2646 \, \text{N} \)[/tex], which approximates to [tex]\( 0.265 \, \text{N} \)[/tex].
1. Calculate the Volume of the Iron Block:
The volume ([tex]\( V \)[/tex]) of a rectangular block is found by multiplying its length ([tex]\( l \)[/tex]), width ([tex]\( w \)[/tex]), and height ([tex]\( h \)[/tex]) together.
[tex]\[ V = l \times w \times h \][/tex]
Given:
[tex]\[ l = 3.00 \, \text{cm}, \quad w = 3.00 \, \text{cm}, \quad h = 3.00 \, \text{cm} \][/tex]
[tex]\[ V = 3.00 \times 3.00 \times 3.00 = 27.00 \, \text{cm}^3 \][/tex]
2. Determine the Mass of the Displaced Water:
Since the iron block will displace an equal volume of water, we need to calculate the mass of this water. The mass ([tex]\( m \)[/tex]) is found by multiplying the volume by the density ([tex]\( \rho \)[/tex]) of water.
Given the density of water:
[tex]\[ \rho = 1.00 \, \text{g/cm}^3 \][/tex]
[tex]\[ m = V \times \rho = 27.00 \, \text{cm}^3 \times 1.00 \, \text{g/cm}^3 = 27.00 \, \text{g} \][/tex]
3. Convert the Mass to Kilograms:
The mass must be converted to kilograms to use the formula for weight. There are 1000 grams in a kilogram.
[tex]\[ m_{\text{kg}} = \frac{m}{1000} = \frac{27.00 \, \text{g}}{1000} = 0.027 \, \text{kg} \][/tex]
4. Calculate the Weight of the Displaced Water:
The weight ([tex]\( W \)[/tex]) of the water displaced can be calculated using the formula [tex]\( W = m \times g \)[/tex], where [tex]\( g \)[/tex] is the acceleration due to gravity.
Given [tex]\( g = 9.80 \, \text{m/s}^2 \)[/tex]:
[tex]\[ W = m_{\text{kg}} \times g = 0.027 \, \text{kg} \times 9.80 \, \text{m/s}^2 = 0.2646 \, \text{N} \][/tex]
Hence, the weight of the water displaced by the block of iron is [tex]\( 0.2646 \, \text{N} \)[/tex], which approximates to [tex]\( 0.265 \, \text{N} \)[/tex].
Thank you for using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. IDNLearn.com has the solutions to your questions. Thanks for stopping by, and come back for more insightful information.