a) Determine the order of magnitude of the gravitational force that you exert on

Question

a) Determine the order of magnitude of the gravitational force that you exert on another person 2.0 m away. In your solution, state the quantities you measure / estimate and their values.

b) Two ocean liners, each with a mass of 40 000 metric tons, are moving on parallel courses 100 m apart. What is the magnitude of the acceleration of one of the liners toward the other due to their mutual gravitational attraction? Model the ships as particles.

c) When a falling meteoroid is at a distance above the Earth’s surface of 3.00 times the Earth’s radius, what is its acceleration due to the Earth’s gravitation?

Explanation / Answer

a) using Newton’s law for gravitation:

Fg = GmM/r^2

with G = 6.673 · 1011 Nm2/kg2.

We need to estimate m and M. Both bodies are people, so I’ll use my weight for both:m M =165 lbs = 82.5 kg

So, Fg Gm^2/r^2

= G(m/r)^2

= 6.673 · 1011 Nm2/kg2 (82.5 kg/2 m)^2

1.14 * 107 N

b)

Use the inverse square force law for gravity to find the attractive force between the ocean liners.

F = G(m^2)/r^2 gives the force between two objects of equal mass (m=40,000,000kg) a distance of r (=100m) apart. G is Newtons universal gravitational constant. Newtons laws of motion give a = acceleration = F/m, so:

a = Gm/r^2. G = 6.674*10^-11 Nm^2/kg^2 or:

a = 2.67*10^-7 m/s^2

c) Force and acceleration is inversely proportional to the square of the distance.

If it is 3R from the surface, it is 4R from the center.

so a = 9.8/3.7² = 0.716 m/s² (a is acceleration due to gravity)

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