Newton's 2nd Law Applied to a Particle In Uniform Circular Motion

In summary, Newton's 2nd Law is directly applicable to particles in uniform circular motion as it states that there must be a net force acting on the object in order to maintain its circular motion. This can be used to calculate the acceleration of the particle using the formula a = v^2/r, where v is the speed and r is the radius of the circular path. The net force is directly proportional to the speed of the particle, meaning that as the speed increases, the force must also increase. This law can also be applied to objects in non-uniform circular motion, and explains the centripetal force in circular motion by stating that the net force must be directed towards the center of the circular path.
  • #1
Faiza
96
0
Q. In the Bohr model of the hydrogen atom, the speed of the electron is
approximately 2.20 x 10^6 m/s. Find (a) the force acting on the electron
as it revolves in a circular orbit of radius 0.530 x 10^-10 m and (b) the
centripetal acceleration of the electron.

I'm going to post my answer in a minute. Let me know if anyone can help me figure it out
 
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  • #2
Faiza, review that topic, this is a simple plug into equation problem.
 
  • #3


Sure, I'd be happy to help!

To find the force acting on the electron, we can use Newton's second law, which states that force is equal to mass multiplied by acceleration (F=ma). In this case, the mass of the electron is 9.11 x 10^-31 kg and the acceleration is the centripetal acceleration, which we can calculate using the formula a=v^2/r, where v is the speed and r is the radius. Plugging in the values, we get:

a= (2.20 x 10^6 m/s)^2 / 0.530 x 10^-10 m = 8.73 x 10^20 m/s^2

Now, we can plug this value into the formula for force:

F = (9.11 x 10^-31 kg) * (8.73 x 10^20 m/s^2) = 7.95 x 10^-10 N

Therefore, the force acting on the electron is approximately 7.95 x 10^-10 Newtons.

To find the centripetal acceleration, we can use the same formula as before, but this time we will use the given speed of the electron and the radius of the orbit:

a= (2.20 x 10^6 m/s)^2 / 0.530 x 10^-10 m = 8.73 x 10^20 m/s^2

This is the same value we calculated earlier for the acceleration. So, the centripetal acceleration of the electron is 8.73 x 10^20 m/s^2.

I hope this helps! Let me know if you have any other questions or need further clarification.
 

1. What is Newton's 2nd Law applied to a particle in uniform circular motion?

Newton's 2nd Law states that the net force acting on an object is directly proportional to its mass and acceleration. When applied to a particle in uniform circular motion, it means that there must be a net force acting on the object in order to maintain its circular motion.

2. How is Newton's 2nd Law used to calculate the acceleration of a particle in uniform circular motion?

In order to calculate the acceleration of a particle in uniform circular motion, we can use the formula a = v^2/r, where v is the speed of the particle and r is the radius of the circular path. This formula is derived from Newton's 2nd Law, where the net force is equal to the mass times the acceleration.

3. What is the relationship between the net force and the speed of a particle in uniform circular motion?

The net force acting on a particle in uniform circular motion is directly proportional to the speed of the particle. This means that as the speed increases, the net force must also increase in order to maintain the circular motion. Conversely, if the speed decreases, the net force must decrease as well.

4. Can Newton's 2nd Law be applied to objects in non-uniform circular motion?

Yes, Newton's 2nd Law can be applied to objects in non-uniform circular motion. In these cases, the acceleration may not be constant, but the net force must still be present in order for the object to continue moving in a circular path.

5. How does Newton's 2nd Law explain the centripetal force in circular motion?

Newton's 2nd Law explains the centripetal force in circular motion by stating that the net force acting on the object must be directed towards the center of the circular path. This centripetal force is responsible for maintaining the object's circular motion and preventing it from moving in a straight line.

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