a man has a mass of 80,0 kg is standing on the surface of the earth.
a )calculate the magnitude of the attractive force (gravity) that the earth exerts on the man.(784n)
b)how does your answer in a) compare to the magnitude of the force that the man exerts on earth?
c)use your answer I a) to caculate the radius of the earth
b) same
c) you need the mass of the earth (5.98e24)
g = GM/r^2
Solve for r
a) Well, the earth sure loves attracting things! The magnitude of the attractive force (gravity) that the earth exerts on the man can be calculated using Newton's law of gravitation. Given that the mass of the man is 80.0 kg, we can calculate the force using the equation: F = mg, where F is the force, m is the mass, and g is the acceleration due to gravity, which is approximately 9.8 m/s^2. So, F = (80.0 kg)(9.8 m/s^2) = 784 N.
b) Now, comparing this force to the force that the man exerts on the earth is quite amusing! According to Newton's third law of motion, every action has an equal and opposite reaction. So, the magnitude of the force that the man exerts on the earth would be the same, 784 N. Imagine that! The earth and the man engaging in a friendly tug of war.
c) Ah, now we can use our answer from part a) to crack this riddle! We can utilize the formula for the acceleration due to gravity, g = GM/r^2, where G is the gravitational constant (6.67430 x 10^-11 m^3/kg/s^2), M is the mass of the earth (approximately 5.972 × 10^24 kg), and r is the radius of the earth. Rearranging the equation, we get r^2 = GM/g. Plugging in the values, r^2 = [(6.67430 x 10^-11 m^3/kg/s^2)(5.972 × 10^24 kg)] / (9.8 m/s^2). After the math magic, we find that the radius of the earth is approximately 6,371 km. Voila! The earth has been unveiled!
a) To calculate the magnitude of the attractive force (gravity) that the Earth exerts on the man, we need to use the formula:
Force = mass x acceleration due to gravity
The acceleration due to gravity on Earth is approximately 9.8 m/s^2. Plugging in the given mass of 80.0 kg into the formula, we get:
Force = 80.0 kg x 9.8 m/s^2
Force = 784 N
Therefore, the magnitude of the attractive force (gravity) that the Earth exerts on the man is 784 N.
b) According to Newton's third law of motion, which states that for every action, there is an equal and opposite reaction, the magnitude of the force that the man exerts on the Earth is also 784 N. Therefore, the force exerted by the man on the Earth is equal in magnitude to the force exerted by the Earth on the man.
c) To calculate the radius of the Earth, we can use the following formula:
Force = (gravitational constant x mass of the man x mass of the Earth) / (radius of the Earth)^2
The gravitational constant (G) is approximately 6.674 × 10^-11 N m^2/kg^2, and the mass of the Earth is approximately 5.972 × 10^24 kg.
Plugging in the given force of 784 N, the mass of the man of 80.0 kg, the mass of the Earth of 5.972 × 10^24 kg, and the known value of the gravitational constant, the formula becomes:
784 N = (6.674 × 10^-11 N m^2/kg^2 x 80.0 kg x 5.972 × 10^24 kg) / (radius of the Earth)^2
Rearranging the formula to solve for the radius of the Earth:
(radius of the Earth)^2 = (6.674 × 10^-11 N m^2/kg^2 x 80.0 kg x 5.972 × 10^24 kg) / 784 N
Simplifying the equation, we have:
(radius of the Earth)^2 = (3.212 × 10^14 N m^2/kg^2) / 784 N
(radius of the Earth)^2 = 4.1 × 10^11 m^2
Taking the square root of both sides, we get:
radius of the Earth = square root of (4.1 × 10^11 m^2)
Therefore, the radius of the Earth is approximately 6,370 km.
To calculate the magnitude of the attractive force (gravity) that the Earth exerts on the man, we can use Newton's law of universal gravitation. The formula is:
F = (G * m1 * m2) / r^2
Where:
F = Force of gravity
G = Gravitational constant (approximately 6.67430 × 10^-11 m^3⋅kg^-1⋅s^-2)
m1 = Mass of the man
m2 = Mass of the Earth
r = Distance between the center of the man and the center of the Earth
a) In this case, the mass of the man is 80.0 kg, and the mass of the Earth is approximately 5.972 × 10^24 kg. The radius of the Earth is approximately 6,371 km (or 6,371,000 m). Plugging these values into the equation, we get:
F = (6.67430 × 10^-11 * 80.0 * 5.972 × 10^24) / (6,371,000)^2
Calculating this gives us a magnitude of approximately 784 Newtons.
b) According to Newton's third law of motion, for every action, there is an equal and opposite reaction. So, the magnitude of the force that the man exerts on the Earth is also 784 Newtons. Therefore, the forces are the same in magnitude but opposite in direction.
c) To calculate the radius of the Earth using the force of gravity you calculated in part (a), we can rearrange the formula:
F = (G * m1 * m2) / r^2
Rearranging the equation, we get:
r = sqrt((G * m1 * m2) / F)
Plugging in the values, we get:
r = sqrt((6.67430 × 10^-11 * 80.0 * 5.972 × 10^24) / 784)
Calculating this gives us a radius of approximately 6,371,000 meters, which is the actual radius of the Earth.