Accelerating Proton: Calculating Speed and Kinetic Energy

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In summary, the question involves a proton being accelerated along a straight line at 2.0x10^15 m/s^2 in a machine. The initial speed is 2.4x10^7 m/s and it travels 2.5 cm. The problem asks for the final speed of the proton and the increase in its kinetic energy. To solve, the equations v^2 = v_0^2 + 2a(Delta x) and KE= 1/2mv^2 are used. The final answer for part b) should include the 1/2 factor.
  • #1
wadesweatt
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Homework Statement



A proton (mass m = 1.67x10^-27 kg) is being accelerated along a straight line at 2.0x10^15 m/s^2 in a machine. The proton has an initial speed of 2.4x10^7 m/s and travels 2.5 cm.

(a) What is its speed?

(b) What is the increase in its kinetic energy?

The Attempt at a Solution



Is it ok to have no idea where to begin?

I know F=ma, and that V=Vo+1/2at... but I can't see how that helps.

Help me begin?
 
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  • #2
wadesweatt said:
1. Homework Statement

A proton (mass m = 1.67x10^-27 kg) is being accelerated along a straight line at 2.0x10^15 m/s^2 in a machine. The proton has an initial speed of 2.4x10^7 m/s and travels 2.5 cm.

(a) What is its speed?

(b) What is the increase in its kinetic energy?

3. The Attempt at a Solution

Is it ok to have no idea where to begin?

I know F=ma, and that V=Vo+1/2at^2... but I can't see how that helps.

Help me begin?

You just need two equations.

Kinetic energy.

And an equation that relates Velocity, distance and acceleration.
https://www.physicsforums.com/showpost.php?p=905663&postcount=2
 
  • #3
no lowly pion you are wrong what he needs is the other SUVAT equations namely.

S=0.5(u+v)t then rearrange to get V
(u is intitial velocity)

then you put that into the the kenetic energy equation

KE=0.5mv^2

then you have got your anser
 
  • #4
ffrog said:
no lowly pion you are wrong what he needs is the other SUVAT equations namely.

S=0.5(u+v)t then rearrange to get V
(u is intitial velocity)

then you put that into the the kenetic energy equation

KE=0.5mv^2

then you have got your anser

And what is the time the proton is in the machine?
 
  • #5
LowlyPion said:
You just need two equations.

Kinetic energy.

And an equation that relates Velocity, distance and acceleration.
https://www.physicsforums.com/showpost.php?p=905663&postcount=2


So, using v^2 = v_0^2 + 2a(Delta x), I can find the final velocity I think. For the delta x part, would it be (2.5 - 0)?

And can I use KE= 1/2mv^2 to find the kinetic energy? If so, wouldn't I use the final velocity found in part a for "v"?

Thanks.
 
  • #6
wadesweatt said:
So, using v^2 = v_0^2 + 2a(Delta x), I can find the final velocity I think. For the delta x part, would it be (2.5 - 0)?

And can I use KE= 1/2mv^2 to find the kinetic energy? If so, wouldn't I use the final velocity found in part a for "v"?

Thanks.

Yes the V2 = Vi2 + 2ax should do you well.

Part b) is looking for ΔKE. So you are needing to calculate the final KE and subtract the initial.
 
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  • #7
LowlyPion said:
Yes the V2 = Vi2 + 2ax should do you well.

Part b) is looking for ΔKE. So you are needing to calculate the final KE and subtract the initial.

Ahhhh so I do change in KE=m(v_f)^2 - m(v_i)^2 , right?
 
  • #8
wadesweatt said:
Ahhhh so I do change in KE=m(v_f)^2 - m(v_i)^2 , right?

Half right anyway.

... i.e don't forget the 1/2.
 
  • #9
LowlyPion said:
Half right anyway.

... i.e don't forget the 1/2.

haha yes! I knew that I was just typing in a hurry.

Thanks.
 

1. What is a proton and why is it being accelerated?

A proton is a subatomic particle with a positive charge found in the nucleus of an atom. It is being accelerated in order to increase its energy and speed, allowing it to collide with other particles and produce high-energy reactions.

2. How is a proton accelerated?

Protons can be accelerated using various methods such as electromagnetic fields, radio frequency cavities, and particle accelerators. These techniques use a combination of electric and magnetic fields to increase the proton's energy and speed.

3. What is the purpose of accelerating protons?

Accelerating protons allows scientists to study their properties and interactions with other particles. It also enables the production of high-energy collisions, which can help researchers understand the fundamental laws of physics and potentially discover new particles.

4. How fast can protons be accelerated?

The speed at which protons can be accelerated depends on the method and equipment used. Some accelerators can reach speeds close to the speed of light, while others may only reach a fraction of that speed.

5. What are the potential applications of accelerated protons?

Accelerated protons have a wide range of applications in fields such as medicine, energy, and materials science. They can be used in cancer treatment, nuclear power generation, and material analysis, among other things.

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