1. A typical virus is a packet of protein and DNA or RNA and can be spherical in shape. The influenza A virus is a spherical virus that has a diameter of 85nm. If the volume of saliva coughed on to you by a friend with the flu is .010cm^3 and 10^-9 of that volume consists of viral particles, how many influenza viruses have just landed on you?
2. Keplar's Law of planetary motion says that the square of the period of a planet(T^2) is proportional to the cube of the distance of the planet from the sun (r^3). Mars is about twice as far from the sun as venus. How does the period of mars compare with the period of venus?
1. To find the number of influenza viruses that have landed on you, we need to calculate the volume of viral particles in the saliva.
Given:
Diameter of the influenza A virus = 85 nm
First, we need to calculate the volume of the virus using the formula for the volume of a sphere:
Volume of a sphere = (4/3) * π * (radius)^3
Since the virus is spherical, the radius is half of the diameter:
Radius of the influenza A virus = 85 nm / 2 = 42.5 nm
Now, let's convert the radius to cubic centimeters (cm^3) since the volume of the saliva is given in cm^3:
1 nm = 10^-7 cm
Radius in cm = 42.5 nm * 10^-7 cm/nm = 4.25 * 10^-6 cm
Volume of the influenza A virus = (4/3) * π * (4.25 * 10^-6 cm)^3
Now, let's calculate the volume of the saliva coughed onto you:
Volume of saliva = 0.01 cm^3
Since 10^-9 of that volume consists of viral particles, we can calculate the volume of viral particles:
Volume of viral particles = (10^-9) * 0.01 cm^3
Now, we can find the number of influenza viruses using the ratio of volumes:
Number of influenza viruses = Volume of viral particles / Volume of the influenza A virus
2. Keplar's Law of planetary motion states that the square of the period of a planet (T^2) is proportional to the cube of the distance of the planet from the sun (r^3).
Given:
Distance of Mars from the sun = 2 * Distance of Venus from the sun
Let's assume the period of Venus is T, and the distance of Venus from the sun is r.
According to Keplar's Law, we have the following relation:
(T_v)^2 / (r_v)^3 = (T_m)^2 / (r_m)^3
Since Mars is about twice as far from the sun as Venus, r_m = 2 * r_v.
Substituting the values, we have:
(T_v)^2 / (r_v)^3 = (T_m)^2 / (2 * r_v)^3
Simplifying the equation:
(T_v)^2 / (r_v)^3 = (T_m)^2 / 8 * (r_v)^3
Cross multiplying:
(T_v)^2 * 8 * (r_v)^3 = (T_m)^2 * (r_v)^3
Cancelling out (r_v)^3 on both sides:
(T_v)^2 * 8 = (T_m)^2
Therefore, the square of the period of Mars is 8 times the square of the period of Venus.
1. To determine the number of influenza viruses that have landed on you, we need to calculate the volume of viral particles and then divide it by the volume of a single virus.
Let's break down the steps:
Step 1: Calculate the volume of viral particles.
Given that 10^-9 of the volume of saliva consists of viral particles and the total volume of coughed saliva is 0.010 cm^3, we can calculate the volume of viral particles as:
Volume of viral particles = (10^-9) * (0.010 cm^3)
Step 2: Calculate the volume of a single virus.
The influenza A virus is spherical, and its diameter is given as 85 nm. We can calculate the volume of a single virus using the formula for the volume of a sphere:
Volume of a single virus = (4/3) * π * (85 nm / 2)^3
Note: The diameter of the virus needs to be converted to the same unit as the volume of viral particles (cm^3) in order to obtain the correct result.
Step 3: Divide the volume of viral particles by the volume of a single virus to find the number of influenza viruses that have landed on you.
Number of influenza viruses = Volume of viral particles / Volume of a single virus
Plug in the values into the respective formulas and perform the calculations to obtain the final answer.
2. According to Kepler's Law of planetary motion, the square of the period of a planet (T^2) is proportional to the cube of the distance of the planet from the sun (r^3).
Given that Mars is about twice as far from the sun as Venus, we can calculate how the period of Mars compares with the period of Venus by comparing the ratios of their distances to the sun.
Let's denote the period of Venus as T_v and the period of Mars as T_m.
Given r_v (distance of Venus from the sun) and r_m (distance of Mars from the sun), we have:
(r_m / r_v) = 2
Taking the cube of both sides, we get:
(r_m / r_v)^3 = 2^3
r_m^3 / r_v^3 = 8
According to Kepler's Law, the square of the period is proportional to the cube of the distance. So, we can rewrite the equation using the ratios of the periods:
(T_m / T_v)^2 = (r_m / r_v)^3
(T_m / T_v)^2 = 8
To find the relationship between the periods of Mars and Venus, we need to calculate the square root of 8:
(T_m / T_v) = sqrt(8)
By simplifying the square root of 8, you can determine the relationship between the periods of Mars and Venus.