Certainly! Let's solve this problem step by step.
### (a) Calculate the Blood's Weight
1. Determine the Density of Blood:
The density of blood is approximately [tex]\( 1050 \, \text{kg/m}^3 \)[/tex].
2. Calculate the Mass of the Blood:
The volume of blood in the man's body is [tex]\( 5.2 \times 10^{-3} \, \text{m}^3 \)[/tex].
To find the mass ([tex]\( m \)[/tex]) of the blood, we use the formula:
[tex]\[
\text{Mass} = \text{Density} \times \text{Volume}
\][/tex]
Substituting in the given values:
[tex]\[
m = 1050 \, \text{kg/m}^3 \times 5.2 \times 10^{-3} \, \text{m}^3 = 5.46 \, \text{kg}
\][/tex]
3. Calculate the Weight of the Blood:
Weight ([tex]\( W \)[/tex]) is the mass ([tex]\( m \)[/tex]) times the acceleration due to gravity ([tex]\( g \)[/tex]), which is approximately [tex]\( 9.81 \, \text{m/s}^2 \)[/tex]:
[tex]\[
W = m \times g
\][/tex]
Substituting in the calculated mass of the blood:
[tex]\[
W = 5.46 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 53.5626 \, \text{N}
\][/tex]
Therefore, the weight of the blood is approximately [tex]\( 53.56 \, \text{N} \)[/tex].
### (b) Expressing the Blood's Weight as a Percentage of the Body Weight
1. Given Body Weight:
The body weight of the man is given as [tex]\( 690 \, \text{N} \)[/tex].
2. Calculate the Percentage:
To find the percentage of the blood's weight relative to the body weight, we use the formula:
[tex]\[
\text{Percentage} = \left( \frac{\text{Blood's Weight}}{\text{Body Weight}} \right) \times 100
\][/tex]
Substituting in the given values:
[tex]\[
\text{Percentage} = \left( \frac{53.5626 \, \text{N}}{690 \, \text{N}} \right) \times 100 \approx 7.76\%
\][/tex]
Therefore, the blood's weight is approximately [tex]\( 53.56 \, \text{N} \)[/tex], and it constitutes about [tex]\( 7.76\% \)[/tex] of the man's body weight.
