Sally has a mass of 50.0kg and earth has a mass of 5.98X10^24kg. The radius of earth is 6.371x10^6m.

A)What is the force of gravitational attraction between sally and earth?
B)What is Sally's weight?

A) Use the formula Fg = (G)(m1)(m2)÷(r^2)

G = 6.67x10^-11 or 6.67e-11
m1 = mass of 1st object in kg
m2 = mass of second object in kg
r = distance between centers of the masses in meters

Can be rewritten as Fg = (6.67x10^-11)(50.0)(5.98x10^24)÷(6.371x10^6)^2
Fg = (1.99433x10^16)÷(6.371x10^6)^2
Answer = 491.34 newtons
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B) W = mg
m = mass in kg
g = gravity

W = (50.0)(9.8)
Answer = 490 newtons

A) Well, the gravitational force between Sally and the Earth can be calculated using Newton's law of universal gravitation. The formula is F = (G * m1 * m2) / r^2, where G is the gravitational constant (approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2). Let's plug in the values:

F = [(6.67430 × 10^-11 m^3 kg^-1 s^-2) * (50.0 kg) * (5.98X10^24 kg)] / (6.371x10^6 m)^2

Wait a second, let me grab a calculator... Oh! The force of gravitational attraction between Sally and the Earth is approximately 481.7 Newtons. Now, isn't gravity pulling everyone down?

B) Now, Sally's weight is simply the force of gravity acting on her. So, her weight will also be approximately 481.7 Newtons. Wow! That's quite heavy! Time for some weightlifting, Sally!

To answer these questions, we can use the formula for gravitational force:

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

Where:
F is the gravitational force
G is the gravitational constant (approximately 6.67430 × 10^-11 N m^2/kg^2)
m1 is the mass of object 1 (Sally)
m2 is the mass of object 2 (Earth)
r is the distance between the centers of the two objects (radius of Earth)

Let's begin with part A.

A) Gravitational Force between Sally and Earth:

Substituting the given values into the formula:

F = (6.67430 × 10^-11 N m^2/kg^2 * 50.0 kg * 5.98 × 10^24 kg) / (6.371 × 10^6 m)^2

To simplify the calculations, let's convert scientific notation to standard form by moving the decimal point:

F = (6.67430 * 50.0 * 5.98) / (6.371)^2 * (10^-11 * 10^24) * (m^2/kg^2 / m^2)

F = (2,000.20051) / (40.611241) * (m^2/kg^2)

F ≈ 49.236 N

Therefore, the gravitational attraction force between Sally and Earth is approximately 49.236 N.

Now, let's move on to part B.

B) Sally's Weight:

The weight of an object can be calculated using the formula:

Weight = Mass * Acceleration due to gravity

Since acceleration due to gravity on Earth is approximately 9.8 m/s^2:

Weight = 50.0 kg * 9.8 m/s^2

Weight ≈ 490 N

Therefore, Sally's weight is approximately 490 N.

To calculate the force of gravitational attraction between Sally and Earth, we can use Newton's law of universal gravitation:

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

where F is the force of gravitational attraction, G is the gravitational constant (which is approximately 6.67430 × 10^-11 N m^2/kg^2), m1 and m2 are the masses of Sally and Earth respectively, and r is the distance between them.

A) Let's calculate the force of gravitational attraction between Sally and Earth:

Given:
Mass of Sally (m1) = 50.0 kg
Mass of Earth (m2) = 5.98 × 10^24 kg
Radius of Earth (r) = 6.371 × 10^6 m

Plugging in the values into the equation:

F = (6.67430 × 10^-11 N m^2/kg^2) * (50.0 kg) * (5.98 × 10^24 kg) / (6.371 × 10^6 m)^2

Calculating this expression will give us the force of gravitational attraction between Sally and Earth.

B) Sally's weight is the force with which she is pulled towards the center of the Earth due to gravity. It can be calculated using the formula:

Weight = m1 * g

where m1 is Sally's mass and g is the acceleration due to gravity.

Given:
Mass of Sally (m1) = 50.0 kg

To calculate Sally's weight, we need to know the value of g. On the surface of the Earth, the standard value of acceleration due to gravity is approximately 9.8 m/s^2.

Plugging in the values into the equation:

Weight = (50.0 kg) * (9.8 m/s^2)

Calculating this expression will give us Sally's weight.

The easy way is mg = 50*9.8

Since they've given you all this info about the Earth I'm guessing they want
Fg = Gm1m2/r^2
= 6.67e-11*50*5.98e24/6.371e6^2
That force IS her weight