1. NASA launched a 550kg satellite into space. Its engines have a thrust of 8000N.

a) What is the downward froce of gravity acting on the rocket at blast off? (is it 5390N?)
b) What is the acceleration of the rocket at blast-off? (Hint: Fine Fnet first)

2. A planet has a mass of 6.0x10^23kg. The force of gravity acting on a 2kg surface of the planet is 960N. What is the radius of the planet?

1a correct

b. fnet=ma
8000-5390=ma solve for a

2. 960=G*Mp*2/r^2 solve for r.

To solve the given problems, we need to apply Newton's laws of motion and the law of universal gravitation.

1.
a) The downward force of gravity acting on the rocket at blast-off can be calculated using the formula for gravitational force:
F = mg, where F is the force of gravity, m is the mass, and g is the acceleration due to gravity.
In this case, m = 550 kg and g (approximately 9.8 m/s^2).
Therefore, the downward force of gravity is:
F = (550 kg) * (9.8 m/s^2) = 5390 N.

b) To find the acceleration of the rocket at blast-off, we can use Newton's second law:
Fnet = ma, where Fnet is the net force and a is the acceleration.
In this case, the net force is the difference between thrust and gravitational force:
Fnet = Thrust - Fgravity.
Given that the thrust of the rocket engines is 8000 N and the downward force of gravity is 5390 N, we have:
Fnet = 8000 N - 5390 N = 2610 N.
With Fnet known, we can substitute it into Newton's second law, along with the mass of the rocket:
Fnet = ma => 2610 N = (550 kg) * a.
Solving for a, we get:
a = (2610 N) / (550 kg) ≈ 4.75 m/s^2.

2.
To find the radius of the planet, we can use the formula for gravitational force between two objects:
F = (G * m1 * m2) / r^2,
where F is the force of gravity, G is the gravitational constant (approximately 6.67 × 10^(-11) N * m^2 / kg^2), m1 and m2 are the masses of the two objects, and r is the distance between the centers of the objects.
In this case, m1 is the mass of the surface (2 kg), m2 is the mass of the planet (6.0 × 10^23 kg), and F is given as 960 N.
Rearranging the formula, we can solve for r:
r^2 = (G * m1 * m2) / F,
r = sqrt((G * m1 * m2) / F).
Plugging in the values, we have:
r = sqrt((6.67 × 10^(-11) N * m^2 / kg^2) * (2 kg) * (6.0 × 10^23 kg) / (960 N)).
Evaluating this expression will give us the radius of the planet in meters.

a) To find the downward force of gravity acting on the rocket at blast off, you can use Newton's second law, which states that force (F) equals mass (m) multiplied by acceleration (a). In this case, the force of gravity (F) is acting on the rocket, so we have:

F = m * a

Rearranging the equation to solve for the force of gravity (F), we get:

F = m * a

Given the mass of the satellite (m = 550kg), we need to calculate the acceleration (a). Since the satellite is at blast-off, we can assume the acceleration is zero (as it hasn't started moving yet). Therefore, the downward force of gravity would be:

F = m * a
F = 550kg * 0
F = 0N

So, the downward force of gravity acting on the rocket at blast-off is 0N, not 5390N.

b) The acceleration of the rocket at blast-off can be calculated using Newton's second law, which states that force (F) equals mass (m) multiplied by acceleration (a). In this case, the thrust force of the rocket's engines (F) is acting on the rocket, so we have:

F = m * a

Rearranging the equation to solve for acceleration (a), we get:

a = F / m

Given the thrust force of the engines (F = 8000N) and the mass of the satellite (m = 550kg), we can substitute these values into the equation to find the acceleration:

a = 8000N / 550kg
a ≈ 14.5 m/s^2

Therefore, the acceleration of the rocket at blast-off is approximately 14.5 m/s^2.

2. To find the radius of the planet, we can use Newton's law of universal gravitation, which states that the force of gravity (F) between two objects is equal to the gravitational constant (G) multiplied by the mass of the first object (m1) multiplied by the mass of the second object (m2), divided by the square of the distance (r) between them. Mathematically, it is expressed as:

F = G * (m1 * m2) / r^2

In this case, we are given the force of gravity acting on a 2kg surface of the planet (F = 960N), and the mass of the planet (m2 = 6.0x10^23kg). We need to find the radius of the planet (r).

Rearranging the equation, we can isolate the radius (r):

r^2 = G * (m1 * m2) / F
r = sqrt(G * (m1 * m2) / F)

The gravitational constant (G) is approximately 6.67x10^-11 N⋅m^2/kg^2.

Substituting the given values into the equation, we get:

r = sqrt((6.67x10^-11 N⋅m^2/kg^2) * (2kg) * (6.0x10^23kg) / 960N)

Simplifying the expression, we find:

r ≈ 5.9x10^6 meters

Therefore, the radius of the planet is approximately 5.9x10^6 meters.