Physics, 26.10.2020 17:00 b2cutie456

At what height in kilometers above the surface of the Earth is there a 7% difference between the approximate gravitational force mg and the actual gravitational force on an object

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Answer from: ari9425

There is a 7 % difference between the approximate gravitational force and the actual gravitational force at a height of 240 kilometers.

Explanation:

We can calculate gravity as a function of mass of the Earth (), measured in kilograms, radial distance from center of the planet (), measured in meters, and gravitation constant (), measured in newton-square meters per square kilogram:

$g' = G\cdot \frac{M}{r^{2}}$ (Eq. 1)

And we solve the equation for :

$r =\sqrt{\frac{G\cdot M}{g'} }$ (Eq. 1b)

If we know that $G = 6.674\times 10^{-11}\,\frac{N\cdot m^{2}}{kg^{2}}$ , $M = 5.972\times 10^{24}\,kg$ and $g' = 9.121\,\frac{m}{s^{2}}$ , the radial distance from the center of the Earth is:

$r = \sqrt{\frac{(6.674\times 10^{-11}\,\frac{N\cdot m^{2}}{kg^{2}} )\cdot (5.972\times 10^{24}\,kg)}{9.121\,\frac{m}{s^{2}} } }$

$r \approx 6.611\times 10^{6}\,m$

The height above the surface of the Earth is the difference between the value above and the radius of the planet. That is:

$h = 6.611\times 10^{6}\,m - 6.371\times 10^{6}\,m$

$h = 2.40\times 10^{5}\,m$ ( $240\,km$ )

There is a 7 % difference between the approximate gravitational force and the actual gravitational force at a height of 240 kilometers.

Answer from: Quest

Sublimation- which change of state is shown in model

Answer from: Quest

m₁v₁ + m₂v₂ = (m₁ + m₂)vmomentum is conserved.the left-hand side of the equation represents the momentum in the system before the collision.the right-hand side represents the momentum in the system after the collisionm₁ and v₁ represents the mass and the velocity of the physics blockm₂ and v₂ represents the mass and velocity of the ball of puttyv represents the final velocity of the combined mass.the question states the two masses stick together. they combined mass has its own velocity with the body mass the sum of the two objects' massestheir combined momentum is (m₁ + m₂)vto find the magitude of (m₁ + m₂)v, we need to add the vectors on the left-hand side of the equation: m₁v₁ + m₂v₂.note the diagram. i have positioned the vectors in accordance with their directions.the magnitude of the resultant can be calculated using the pythagorean theorem since this is a right triangle situation (north and west are perpendicular)|(m₁ + m₂)v| = √[ (m₁v₁)² + (m₂v₂)² ]|(m₁ + m₂)v| = √[ (1.5kg·8.0m/s)² + (0.40kg·20m/s)² ]|(m₁ + m₂)v| = 14.4 kg m/sfor two significant figures (assuming that 20m/s is two), this rounds to 14 kg m/s

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At what height in kilometers above the surface of the Earth is there a 7% difference between the app...