Proton accelerated thru potential difference - find final speed

In summary, the concept behind proton acceleration through potential difference is based on electrostatics and the force that a proton experiences in an electric field, resulting in an increase in kinetic energy. The final speed of a proton can be calculated using the equation v = √(2qV/m), which is derived from the conservation of energy. Several factors, including the magnitude of potential difference and the presence of other particles, can affect the final speed of a proton. However, it cannot exceed the speed of light, as stated in Einstein's theory of relativity. This concept has practical applications in various fields, including scientific research, medical imaging, and energy production, among others.
  • #1
AladdinSane
8
0

Homework Statement


A proton is accelerated from rest through a potential difference of 107 V. Calculate the final speed of this proton.


Homework Equations


I'm not really sure which equations to use, but I figured I give all I tried...
V=-Ed
V=PE/q
PE=-qEd
and I think this applies...v(f)^2= v(i)^2 + 2ad

The Attempt at a Solution



I really can't figure out what equation i should use. What I did was..
1)used the equation V = Ed
2) becomes V= Kc(q/d^2)d
3) becomes V=Kc(q/d)
4)107= 8.99x10^9 (1.602x10^-19)/d
5)Solved for d and found it was 1.34598 x 10^-11
6) used the equation v(f)^2= v(i)^2 + 2ad
7) became v = sqrt (2a (1.34598x10^-11)
...but I don't know what "a" is so I can't solve. Any help would be greatly appreciated. I gave this a shot and really couldn't figure it out. Thanks, everyone.
 
Physics news on Phys.org
  • #2
AladdinSane said:

Homework Statement


A proton is accelerated from rest through a potential difference of 107 V. Calculate the final speed of this proton.


Homework Equations


I'm not really sure which equations to use, but I figured I give all I tried...
V=-Ed
V=PE/q
PE=-qEd
and I think this applies...v(f)^2= v(i)^2 + 2ad

The Attempt at a Solution



I really can't figure out what equation i should use. What I did was..
1)used the equation V = Ed
2) becomes V= Kc(q/d^2)d
3) becomes V=Kc(q/d)
4)107= 8.99x10^9 (1.602x10^-19)/d
5)Solved for d and found it was 1.34598 x 10^-11
6) used the equation v(f)^2= v(i)^2 + 2ad
7) became v = sqrt (2a (1.34598x10^-11)
...but I don't know what "a" is so I can't solve. Any help would be greatly appreciated. I gave this a shot and really couldn't figure it out. Thanks, everyone.

Try energy method.
Find relationship between initial energy, and final energy.
What is the initial energy?, and what's the final energy?
 
  • #3
Yes, by far the easiest method is to just use energy conservation.

Proton KE = potential difference
 
  • #4
Don't forget that 1eV = 1.60E-19 J

Since the potential difference is given (107 V), you have to find the kinetic energy that it would take for that to happen. Set up a ratio like this: (1 eV)/(1.60E-19 J)=(107 V)/(x). Solve for x. This value, x, is the kinetic energy (in J) that this would take.

Now, use 1/2mv^2=KE. Since you have the KE to be x, solve for v.

v=sqrt(2KE/m)
 
  • #5
Now, use 1/2mv^2=KE. Since you have the KE to be x, solve for v.

v=sqrt(2KE/m)

what is "m"?
what is "sqrt"?
 
  • #6
osulongboard said:
what is "m"?
what is "sqrt"?

m: meters
sqrt: square root of
 

1. What is the concept behind proton acceleration through potential difference?

The concept behind proton acceleration through potential difference is based on the principles of electrostatics. When a proton is placed in an electric field, it experiences a force due to its positive charge. This force causes the proton to accelerate, gaining kinetic energy as it moves through the electric field.

2. How is the final speed of a proton calculated when accelerated through potential difference?

The final speed of a proton can be calculated using the equation v = √(2qV/m), where v is the final speed, q is the charge of the proton, V is the potential difference, and m is the mass of the proton. This equation is derived from the conservation of energy, where the initial potential energy is converted into kinetic energy as the proton accelerates.

3. What factors affect the final speed of a proton when accelerated through potential difference?

The final speed of a proton is affected by several factors, including the magnitude of the potential difference, the charge of the proton, and the mass of the proton. Additionally, the presence of other particles or objects in the electric field can also affect the final speed of the proton.

4. Can the final speed of a proton be greater than the speed of light?

No, the final speed of a proton cannot exceed the speed of light. According to Einstein's theory of relativity, the speed of light is the maximum speed at which any object with mass can travel. Therefore, the final speed of a proton, or any other particle with mass, cannot exceed the speed of light.

5. How is the concept of proton acceleration through potential difference used in practical applications?

Proton acceleration through potential difference is used in various practical applications, including particle accelerators for scientific research, medical imaging techniques such as proton therapy for cancer treatment, and in the production of electricity through nuclear fusion reactions. It is also used in the development of new materials and technologies, such as semiconductors and nanotechnology.

Similar threads

  • Introductory Physics Homework Help
Replies
6
Views
3K
  • Introductory Physics Homework Help
Replies
4
Views
3K
  • Introductory Physics Homework Help
Replies
1
Views
955
Replies
22
Views
1K
  • Introductory Physics Homework Help
Replies
30
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
808
  • Introductory Physics Homework Help
Replies
1
Views
770
  • Introductory Physics Homework Help
Replies
4
Views
942
  • Introductory Physics Homework Help
Replies
23
Views
286
  • Introductory Physics Homework Help
Replies
3
Views
2K
Back
Top