Uniform circular motion question

In summary, the problem appears to be an arithmetic mistake on my part. My professor may have done everything correctly.
  • #1
discostu
2
0
I'm trying to solve this problem correctly, but my calculations yield a different result than the correct answer according to my professor.

In a semi-classical model of the neutral hydrogen atom, an electron of charge -e and of mass 9.1*10^-31 undergoes uniform circular motion around the much more massive proton with charge +e. The radius of the electron's orbit is 5.3*10^-11 m. The speed of the electron in its orbit is ____ m/s.

Code:
(Force Elec) = (m * a)

=> e^2/(4*pi*E0*radius^2) = mass*velocity^2/radius

=>velocity = (e^2/(4*pi*E0*radius*mass))^(1/2)

where 1/(4*pi*E0) = 8.99*10^9 Nm^2/C^2 and e = 1.602*10^-19

When I solve the equation I get ((1.6*10^-19)^2/(8.99*10^9 * 5.3*10^-11 * 9.1*10^-31))^(1/2) = 2.43*10^-4 m/s, however they say the correct answer is 2.2*10^6 m/s

Maybe I'm doing something wrong? I would hope the prof did everything correctly. :smile:
 
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  • #2
I get 2.184 x 10[tex]^6[/tex] -same as your professor's, and using the same numbers as you posted. Check your arithmetic.
 
  • #3
...

What you should do is equate the electric potential energy to the kinetic energy of the electron...Thats all that you need to do and lo behold you have the answer.

i.e.


[tex](e^2)/(4\Pi \epsilon_{0}r) = 1/2*(mv^2 )[/tex]

From the above equation you can find the velocity...


Sridhar
 
  • #4


Originally posted by sridhar_n
What you should do is equate the electric potential energy to the kinetic energy of the electron...Thats all that you need to do and lo behold you have the answer.

i.e.


[tex](e^2)/(4\Pi \epsilon_{0}r) = 1/2*(mv^2 )[/tex]

From the above equation you can find the velocity...


Sridhar

This is the equation I was using. The mistake I made was putting the value for [tex]1/(4\Pi \epsilon_{0}) = 8.99*10^9[/tex] in the denominator of my calculation, instead of the numerator where it should go.
 
  • #5
...

As u said you must substitute [tex]1/4\Pi\epsilon_{0} = 8.99 * 10^9 [/tex] in the numerator.

i.e.

[tex]8.99*10^9 * (e^{2})/r = 1/2 * mv^2[/tex]


Sridhar
 

1. What is uniform circular motion?

Uniform circular motion is the movement of an object along a circular path at a constant speed. This means that the object is moving at the same speed and direction at all points along the path.

2. What is the difference between uniform circular motion and non-uniform circular motion?

The main difference between uniform and non-uniform circular motion is the speed of the object. In uniform circular motion, the object moves at a constant speed, while in non-uniform circular motion, the speed may vary at different points along the path.

3. What is the role of centripetal force in uniform circular motion?

In uniform circular motion, centripetal force is the force that keeps the object moving along the circular path. It acts towards the center of the circle and is responsible for changing the direction of the object's velocity.

4. How is the velocity of an object in uniform circular motion related to its acceleration?

The velocity of an object in uniform circular motion is always tangent to the circular path. Its acceleration, on the other hand, is directed towards the center of the circle and is perpendicular to the velocity. The magnitude of the acceleration is equal to v^2/r, where v is the velocity and r is the radius of the circle.

5. What are some real-life examples of uniform circular motion?

Some examples of uniform circular motion include the motion of a satellite orbiting the Earth, the motion of a Ferris wheel, and the motion of a car driving around a roundabout.

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