A satellite has a mass of 106 kg and is located at 1.96 106 m above the surface of Earth.

(a) What is the potential energy associated with the satellite at this location?
J

(b) What is the magnitude of the gravitational force on the satellite?
N

^ what the heck Alexa seriously did you even read the problem

better off asking Alexa the A.I

To find the potential energy of the satellite and the magnitude of the gravitational force acting on it, we can use the formulas for gravitational potential energy and gravitational force.

(a) The formula for gravitational potential energy is:

Potential Energy = mass × acceleration due to gravity × height

Given:
mass of the satellite (m) = 106 kg
height (h) = 1.96 × 10^6 m
acceleration due to gravity (g) = 9.8 m/s^2 (approximately)

Therefore, the potential energy associated with the satellite at this location is:

Potential Energy = 106 kg × 9.8 m/s^2 × 1.96 × 10^6 m

Calculating this value gives us the potential energy in terms of Joules (J).

(b) The formula for gravitational force is:

Force (F) = gravitational constant (G) × (mass of the satellite × mass of the Earth) / distance^2

In this case, we can simplify the equation by assuming that the mass of the Earth is concentrated at its center and that the distance between the satellite and the Earth's surface is the same as the distance between the satellite and the Earth's center.

Given:
mass of the satellite (m) = 106 kg
mass of the Earth (M) = 5.972 × 10^24 kg (approximately)
distance (r) = 1.96 × 10^6 m

The gravitational constant (G) is approximately 6.674 × 10^-11 N·(m/kg)^2.

Therefore, the magnitude of the gravitational force on the satellite is:

Force = (6.674 × 10^-11 N·(m/kg)^2) × (106 kg × 5.972 × 10^24 kg) / (1.96 × 10^6 m)^2

Calculating this value gives us the magnitude of the gravitational force in Newtons (N).

To determine the potential energy associated with the satellite and the magnitude of the gravitational force on the satellite, we can use the following formulas:

(a) Potential Energy (PE) = mass × acceleration due to gravity (g) × height

First, we need to find the acceleration due to gravity (g), which is a constant on Earth equal to approximately 9.8 m/s^2.

Now we can calculate the potential energy:

(a) PE = mass × g × height

Given:
mass (m) = 106 kg
height (h) = 1.96 × 10^6 m
g = 9.8 m/s^2

Substituting these values into the formula:

PE = 106 kg × 9.8 m/s^2 × 1.96 × 10^6 m

(b) To find the magnitude of the gravitational force (F) on the satellite, we can use the formula for gravitational force:

Gravitational Force (F) = mass × acceleration due to gravity (g)

Given the same values as above:

F = 106 kg × 9.8 m/s^2

Now, let's calculate the values:

(a) PE = 106 kg × 9.8 m/s^2 × 1.96 × 10^6 m

To solve this equation, simply multiply the numbers together:

PE = 2.09888 × 10^12 J

Therefore, the potential energy associated with the satellite at this location is approximately 2.09888 × 10^12 Joules.

(b) F = 106 kg × 9.8 m/s^2

To solve this equation, multiply the numbers together:

F = 1.0408 × 10^3 N

Therefore, the magnitude of the gravitational force on the satellite is approximately 1.0408 × 10^3 Newtons.

a) Gravitational potential energy = mgh

= (106kg)(10m/2^2)(1.96106m)
= 2078.7236 J

b) F = ma
= (10kg)(10 m/s^2)
= 100 N