Circular Motion of a ball around the earth

In summary, to calculate the time it would take a ball to orbit the Earth once at a speed of 7920 ms^-1 just above the surface, you can use the formula Time = Distance / Speed, with the known radius of Earth and speed of the ball. No need for SUVAT equations.
  • #1
Psycotic.Goth
5
0

Homework Statement


Calculate thow long it would take a ball to orbit the Earth once , just above the surface , at a speed of 7920 ms^-1 . The radius of Earth is 6400km.


Homework Equations


Well I am not sure to be honest.


The Attempt at a Solution


I tried using S=ut+1/2(a)(t)^2

Then used (-b +/- √b^2-4ac)/2a

But got stuck in (-b +/- √b^2-4ac)/2a because got a negative sign answer in the √

Cant find a formula in the book for this - probably have to manipulate some other formulas, but as I said I am not sure
 
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  • #2
If you know the radius of the earth, you can calculate the circumference.

You know the speed of the ball.

With those two pieces of data you can calculate the time taken to complete the journey:

Time = Distance / Speed

No need for SUVAT equations here.

Jared
 
  • #3
Thanks a lot Jared - I feel dumb now for using SUVAT lol

-PsyG
 

Related to Circular Motion of a ball around the earth

1. How does the mass of the ball affect its circular motion around the earth?

The mass of the ball has no effect on its circular motion around the earth. According to Newton's Law of Universal Gravitation, the force of gravity between two objects is dependent on their masses and the distance between them. However, since the mass of the earth is much greater than that of the ball, the ball's mass has a negligible effect on its circular motion around the earth.

2. What is the relationship between the radius of the circular path and the speed of the ball?

The speed of the ball is directly proportional to the radius of the circular path. This means that as the radius increases, the speed of the ball also increases. This relationship can be expressed mathematically as v = rw, where v is the speed, r is the radius, and w is the angular velocity.

3. How does the angle of inclination affect the circular motion of the ball?

The angle of inclination has a direct effect on the circular motion of the ball. If the angle of inclination is 0 degrees, the ball will move in a perfect circular path around the earth's equator. However, if the angle of inclination is greater than 0 degrees, the ball will have a more elliptical orbit, with a higher speed at the perigee (closest distance to the earth) and a lower speed at the apogee (farthest distance from the earth).

4. What is the role of gravity in the circular motion of the ball around the earth?

Gravity is the force that keeps the ball in its circular motion around the earth. The earth's gravitational pull on the ball creates a centripetal force that pulls the ball towards the center of the earth, keeping it in its circular path. Without gravity, the ball would continue moving in a straight line tangent to its circular path.

5. How does air resistance affect the circular motion of the ball?

Air resistance, also known as drag, can affect the circular motion of the ball by slowing it down. This is because as the ball moves through the air, it experiences a force in the opposite direction of its motion. This force can decrease the speed of the ball, causing it to have a more elliptical orbit. However, the effects of air resistance are often negligible in the circular motion of a ball around the earth, as the ball is constantly accelerating due to the earth's gravitational pull.

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