Gravitation Help: Calculating Attractive Force & Velocity

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In summary, the problem involves finding the speed of a rocket that is being pulled towards a star with a known mass and radius, using the gravitational equation and the equations for work and kinetic energy. The distance between the centers of the two bodies and the radius of the star need to be taken into account when calculating the force and work.
  • #1
Meowzers
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I'm having trouble distinguishing the values of the components in the gravitation equation for the following problem:

The magnitude of the attractive force of gravity between two bodies is F = GMm/r^2. G is a constant equal to 6.67×10^−11 N·m2/kg2, M and m are the masses, and r is the distance between the centers of the two bodies. The gravitational force of a star of mass 1.14×10^32 kg and radius 3.48×10^9 m is the sole force acting on a rocket of mass 1.25×10^6 kg. The rocket is stationary relative to the star at distance of 1.85×10^11 m. Sadly, the rocket has exhausted its fuel, and it will be pulled to its doom inside the star. How fast will it be moving when it reaches the surface of the star?

Here is how I approached it -

The equations I will be using are:
F = G*M*m/r^2
W=KE
[tex]KE=\frac{1}{2}m v^2[/tex]

So first off, I solved for the force using the gravitation equation -
G constant = 6.67e-11 Nm^2/kg^2
M (of star) = 1.14*10^32 kg
m (of rocket) = 1.25*10^6 kg
r = now this is where my question is. :yuck: The problem says that r is the distance between the centers of the two bodies. So, I assumed that it's the radius given 3.48*10^9 m added to the distance between the rocket and the star (1.85*10^11 m) and then squared. Is this correct? Or is it just supposed to be the radius of the star squared?

After that first assumption, I plugged the force value I found into
[tex]W=F*cos(\theta)(delta x)[/tex]
which brings me to the second question. Is the delta x value = 1.85*10^11 m?

Then, I plugged that value I found for W into [tex]KE=\frac{1}{2}m v^2[/tex], where m=1.25*10^6.

Is this a correct approach and did I assume anything wrong?

Thanks in advance!
 
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  • #2
The gravitational force is a function of r. Which means that you need to integrate in order to find the work done by this force on the rocket in pulling it towards the star.
 
  • #3


Hello,

Thank you for your question. Let me help clarify the values in the gravitation equation for this problem. The value of r in the equation represents the distance between the centers of the two bodies, in this case, the center of the star and the center of the rocket. Therefore, r should not be added to the radius of the star, but rather it should be the distance between the two centers, which is given as 1.85*10^11 m.

In terms of the delta x value, it should also be the distance between the centers of the two bodies, which is 1.85*10^11 m. This is because the force is acting along this distance, and we are calculating the work done by this force.

Your approach in solving for the velocity using the kinetic energy equation is correct. However, I would recommend using the equation F=ma to solve for the acceleration first, and then using the equation v^2=u^2+2as to solve for the final velocity. This will give you a more accurate result.

I hope this helps clarify the values in the gravitation equation and your approach to solving the problem. Let me know if you have any further questions.
 

1. What is gravitation and how does it work?

Gravitation is the force of attraction between two objects with mass. It is described by Newton's Law of Universal Gravitation, which states that every object in the universe attracts every other object with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

2. How do you calculate the attractive force between two objects?

The attractive force between two objects can be calculated using the formula F = G * (m1 * m2)/d^2, where F is the force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and d is the distance between them.

3. Can you explain the relationship between mass and gravitational force?

The greater the mass of an object, the greater its gravitational force will be. This means that objects with larger masses will have a stronger pull towards each other compared to objects with smaller masses.

4. How does velocity affect the force of gravity?

Velocity does not directly affect the force of gravity between two objects. However, an increase in velocity can cause an increase in the distance between two objects, which will decrease the force of gravity between them.

5. What is the significance of gravitational force in our everyday lives?

The force of gravity is responsible for keeping objects on the surface of the Earth, as well as the orbits of planets and other celestial bodies. It also plays a crucial role in many natural phenomena, such as tides and the formation of galaxies.

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