Momentum and Newton's Gravitation force question (2 stars)

In summary: You need to use vector equations to calculate your momentum. You've calculated the MAGNITUDE of the force that occurs between the two stars. Now you need to apply the other part of the vector property: the direction.The gravitational force acts along a line connecting the centers of the two stars. You need to find a unit vector that lies on that line in the direction which the force is acting on the star in question (star #1 in this scenario). The force vector will then be the magnitude of the force multiplied by that unit vector.
  • #1
physics1311
8
0
At t = 0 a star of mass 5.0×1030 kg has velocity < 6.0×10^4, 7.0×10^4, -7.0×10^4 > m/s and is located at < 1.00×10^12, -4.00×10^12, 4.00×10^12 > m relative to the center of a cluster of stars. There is only one nearby star that exerts a significant force on the first star. The mass of the second star is 3.5×10^30 kg, its velocity is < 1.0×10^4, -2.0×10^4, 9.0×10^4 > m/s, and this second star is located at < 1.04×10^12, -3.94×10^12, 3.96×10^12 > m relative to the center of the cluster of stars.
At t = 1.0×105 s, what is the approximate momentum of the first star? (in vector coordinates)
Was told to use Momentum principle, position update formula, and Newton's gravitational force law.
I keep on getting <3E35, 3.5E35, -3.5E35>kg m/s
The force of gravity I keep on calculating is not significant in that time to change the momentum of the particle.
 
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  • #2
physics1311 said:
At t = 0 a star of mass 5.0×1030 kg has velocity < 6.0×10^4, 7.0×10^4, -7.0×10^4 > m/s and is located at < 1.00×10^12, -4.00×10^12, 4.00×10^12 > m relative to the center of a cluster of stars. There is only one nearby star that exerts a significant force on the first star. The mass of the second star is 3.5×10^30 kg, its velocity is < 1.0×10^4, -2.0×10^4, 9.0×10^4 > m/s, and this second star is located at < 1.04×10^12, -3.94×10^12, 3.96×10^12 > m relative to the center of the cluster of stars.
At t = 1.0×105 s, what is the approximate momentum of the first star? (in vector coordinates)
Was told to use Momentum principle, position update formula, and Newton's gravitational force law.
I keep on getting <3E35, 3.5E35, -3.5E35>kg m/s
The force of gravity I keep on calculating is not significant in that time to change the momentum of the particle.

Hi physics1311, welcome to Physics Forums.

You'll have to show your attempt at a solution (how did you arrive at the momentum vector that you found) before we help.
 
  • #3
First I used Newtons gravitational force equation. Fg= GM1M2/r^2
M1=5E30 kg is given
M2 = 3.5E30 kg is given
G = 6.66E-11

Calculated R by using pythagorean theory for both coordinates and adding together
I got R =1.14E13

Then using the force calculated I used the momentum principle, delta p = Fnet delta t
 
  • #4
physics1311 said:
First I used Newtons gravitational force equation. Fg= GM1M2/r^2
M1=5E30 kg is given
M2 = 3.5E30 kg is given
G = 6.66E-11

Calculated R by using pythagorean theory for both coordinates and adding together
I got R =1.14E13

That distance doesn't look right. What's the formula for the distance between two points?

Then using the force calculated I used the momentum principle, delta p = Fnet delta t

That'll work for the Δp provided that Fnet remains fairly constant over the timestep Δt.

EDIT: Also, you'll need to express Fnet as a vector, since the resulting momentum will also be a vector quantity.
 
  • #5
Okay, thanks for that tip. I used the distance formula sqrt((x2-x1)^2+(y2-y1)^2+(z2-z1)^2) equals distance.
I got r = 8.25E10m

I then plugged it into the equation for gravitational force. F= GM1M2/r^2
I got Fg=1.72E29

Then using this force I did p(final)-p(initial) = Fg delta(t) for each coordinate

My answer was <3.17E35, 3.67E35, -3.33E35>

and I tried making Fg negative which gave me <2.83E35, 3.33E35, -3.67E35>
neiter answers were right, what am I doing wrong?
 
  • #6
How do you express Fnet as a vector?
 
  • #7
physics1311 said:
Okay, thanks for that tip. I used the distance formula sqrt((x2-x1)^2+(y2-y1)^2+(z2-z1)^2) equals distance.
I got r = 8.25E10m

I then plugged it into the equation for gravitational force. F= GM1M2/r^2
I got Fg=1.72E29

Then using this force I did p(final)-p(initial) = Fg delta(t) for each coordinate

My answer was <3.17E35, 3.67E35, -3.33E35>

and I tried making Fg negative which gave me <2.83E35, 3.33E35, -3.67E35>
neiter answers were right, what am I doing wrong?

physics1311 said:
How do you express Fnet as a vector?

You need to use vector equations to calculate your momentum. You've calculated the MAGNITUDE of the force that occurs between the two stars. Now you need to apply the other part of the vector property: the direction.

The gravitational force acts along a line connecting the centers of the two stars. You need to find a unit vector that lies on that line in the direction which the force is acting on the star in question (star #1 in this scenario). The force vector will then be the magnitude of the force multiplied by that unit vector.

attachment.php?attachmentid=43626&stc=1&d=1328661690.gif


How do you find a unit vector that lies along the line connecting two points?
 

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1. What is momentum and how is it related to Newton's Gravitation force?

Momentum is a measure of an object's motion and is defined as the product of its mass and velocity. It is related to Newton's Gravitation force through the law of universal gravitation, which states that every object in the universe exerts a gravitational force on every other object. This force is directly proportional to the product of the masses of the two objects and inversely proportional to the square of the distance between them. In other words, the larger the momentum of an object, the stronger its gravitational force.

2. How is momentum conserved in a system with multiple objects?

In a system with multiple objects, momentum is conserved as long as there are no external forces acting on the system. This means that the total momentum of all the objects remains constant, even if individual objects may have different momentums. This is known as the law of conservation of momentum and is a fundamental principle in physics.

3. How does the mass of an object affect its momentum?

The mass of an object directly affects its momentum. The larger the mass of an object, the more difficult it is to change its velocity, and therefore the greater its momentum. This is why it takes more force to move a heavier object compared to a lighter one.

4. Is momentum a vector or a scalar quantity?

Momentum is a vector quantity, meaning it has both magnitude and direction. This is because it is a product of two vector quantities, mass and velocity. The direction of an object's momentum is the same as its velocity, making it an important factor in understanding the motion of objects in a given system.

5. How does Newton's Gravitation force affect the motion of objects?

Newton's Gravitation force is a force that acts between all objects with mass in the universe. It is responsible for the motion of objects in our solar system, such as the planets orbiting around the sun. This force follows the law of universal gravitation, which causes objects to accelerate towards each other. The strength of the force depends on the mass and distance between the objects, and it is this force that keeps objects in orbit and governs the motion of celestial bodies.

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