Calculating Force & Weight of 50.0kg Mass on Earth

[xbeachbabeee]

Homework Statement

Assume that you have a mass of 50.0 kg and Earth has a mass of 5.97 x 10^24 kg. The radius of Earth is 6.38 x 10^6 m.
a) what is the force of gravitational attraction between you and Earth?
b) What is your weight?


please show your work..im so confused! thanks!

 

[G01]

Uhh how about YOU show YOUR work. The people helping here, have already passed the classes where these problems are assigned. We do not do homework here, we help with homework.

That said, give us something. There is a reason for the Formulas section of the homework template. What formulas and concepts apply to this problem?

 

[ogb p]

I can help you understand the concepts of force and weight and how they relate to the given scenario.

Firstly, it is important to understand that the force of gravitational attraction between two objects is directly proportional to their masses and inversely proportional to the square of the distance between them. This is described by Newton's Law of Universal Gravitation, which states that the force of gravity (F) is equal to the product of the masses (m1 and m2) divided by the square of the distance (r) between them, multiplied by the gravitational constant (G). Mathematically, this can be represented as F = G(m1m2)/r^2.

Now, let's apply this formula to the given scenario. We have a mass of 50.0 kg and Earth has a mass of 5.97 x 10^24 kg. The distance between you and Earth's center (since gravity acts towards the center of mass) is equal to the radius of Earth, which is 6.38 x 10^6 m. The gravitational constant (G) is a universal constant with a value of 6.67 x 10^-11 Nm^2/kg^2.

a) To calculate the force of gravitational attraction between you and Earth, we can substitute the given values into the formula. This gives us F = (6.67 x 10^-11 Nm^2/kg^2)(50.0 kg)(5.97 x 10^24 kg)/(6.38 x 10^6 m)^2 = 4.92 x 10^21 N. This is the force of gravity pulling you towards Earth.

b) Your weight, on the other hand, is a measure of the force of gravity acting on your mass. It is equal to your mass multiplied by the acceleration due to gravity (g), which is approximately 9.8 m/s^2 on Earth's surface. Therefore, your weight is equal to (50.0 kg)(9.8 m/s^2) = 490 N.

I hope this explanation and the calculations have helped clarify the concepts of force and weight for you. Remember, these values may vary on different planets or locations due to differences in mass and distance. Keep exploring and learning more about the fascinating world of physics!