Magnitude of Force exerted

In summary, the orbital speed of Earth around the sun, its distance from the sun, and the masses of both objects can be used to calculate the magnitude of the force exerted by the sun on Earth. This can be done using either Newton's 2nd Law or the centripetal force equation, but may result in a slight discrepancy due to approximations and the elliptic nature of Earth's orbit.
  • #1
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Homework Statement


The orbital speed of Earth about the Sun is 2.8x10^4 m/s and its distance from the Sun is 1.5x10^11 m. The mass of Earth is approximately 6.2x10^24 kg and that of the Sun is 2.0x10^30 kg. What is the magnitude of the force exerted by the Sun on Earth?


Homework Equations


F= Gm1m2/r^2 and F=mv^2/r


The Attempt at a Solution


I know I need to use Newtons 2nd Law but every time I plug the numbers in I get the wrong answer. I tried using F= Gm1m2/r^2 and F=mv^2/r
 
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  • #2
What's the text-book answer that's making you think you're doing it wrong?
You can solve this question in two different ways, and for both, there would be redundant data.

Well, since you were already on the right track already, I'll just show you what I got when I plugged the numbers in myself.

If you know that the force the sun exerts on the Earth is gravity, then you can simply use:

|F| = GMEMS/R² = (6.67*6.2*2)/1.5² * 10^(-11+24+30-22) = 36.75*10^21 N

If you don't know that the force is gravity, however, but do know that the Earth revolves around the sun is an approximately circular orbit, you can say that the magnitude of the force the sun exerts upon it is:
|F| = ME*V²/R = 6.2*2.8²/1.5 * 10^(24+8-11) = 32.40*10^21 N

We need to explain the discrepancy here somehow, though. I'd chalk it up to poor approximations of the sun's mass (Note how the centripetal force equation does not directly use the data about the mass of the sun) and the fact that the Earth orbits the sun in an elliptic orbit, and not a circular one.
 
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  • #3
but I'm not getting the right answer.

I would first check my calculations and make sure I am using the correct values for G, the gravitational constant, and the units are consistent. I would also double check the given values for Earth's orbital speed and distance from the Sun to make sure they are accurate.

Assuming the given values are correct, the magnitude of force exerted by the Sun on Earth can be calculated using Newton's Law of Gravitation, F=Gm1m2/r^2, where G is the universal gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them.

In this case, m1 is the mass of the Sun (2.0x10^30 kg) and m2 is the mass of Earth (6.2x10^24 kg). The distance between them, r, is 1.5x10^11 m.

Plugging in these values into the equation, we get:

F = (6.674x10^-11 Nm^2/kg^2) x (2.0x10^30 kg) x (6.2x10^24 kg) / (1.5x10^11 m)^2

Simplifying, we get:

F = 3.52x10^22 N

Therefore, the magnitude of the force exerted by the Sun on Earth is approximately 3.52x10^22 Newtons. This is a very large force, but it is necessary to keep Earth in its stable orbit around the Sun.
 

1. What is the magnitude of force exerted?

The magnitude of force exerted refers to the measurement of the strength or intensity of a force. It is typically measured in units of Newtons (N) in the metric system or pounds (lbs) in the imperial system.

2. How is the magnitude of force exerted calculated?

The magnitude of force exerted is calculated by multiplying the mass of an object by its acceleration. This is represented by the equation F=ma, where F is the force, m is the mass, and a is the acceleration.

3. What factors affect the magnitude of force exerted?

The magnitude of force exerted can be affected by several factors, including the mass of the object, the acceleration of the object, and the direction and angle of the force being applied.

4. How does the magnitude of force exerted impact an object?

The magnitude of force exerted can impact an object in a variety of ways, depending on the direction and angle of the force. It can cause an object to accelerate, decelerate, or change direction.

5. What is the difference between magnitude of force exerted and net force?

The magnitude of force exerted refers to the measurement of the strength of a single force acting on an object. Net force, on the other hand, takes into account all of the forces acting on an object and their combined effect. It is the overall force that determines an object's motion.

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