# Acceleration of Proton (Kinetic Energy & relativity)

• Lauren12
In summary, the homework states that to accelerate a proton from rest to 0.9999c, you would need 1.5*10^-10 Joules of energy. However, this is not nearly enough energy to do so, as protons are only around 1.67*10^-27 Kg in mass.
Lauren12

## Homework Statement

a)
Calculate the kinetic energy required to accelerate a single proton from a rest position to 0.9999c. The mass of a proton is 1.67*10^-27 Kg.

b)
Find the ratio of kinetic energy to the energy of a proton at rest

## Homework Equations

Ekrest = mc2

Ek= (mc2)/√(1-(v2/c2))-mc2

## The Attempt at a Solution

a)
Ekrest = mc2
Ekrest = (1.67*10^-27)(c)2
Ekrest = 1.5*10^-10

Ek= (1.5*10^-10)/√(1.9999*10^-4)-(1.5*10^-10)
EK=1.047*10^-8J

I am not confident in this answer as that does not seem nearly enough energy to accelerate the proton...

B)
1.047*10^-8/ 1.5*10^-10
=69.66%

I am very confused! Any help is much appreciated.

Lauren12 said:

## Homework Statement

a)
Calculate the kinetic energy required to accelerate a single proton from a rest position to 0.9999c. The mass of a proton is 1.67*10^-27 Kg.

b)
Find the ratio of kinetic energy to the energy of a proton at rest

## Homework Equations

Ekrest = mc2

Ek= (mc2)/√(1-(v2/c2))-mc2
I think you might find it easier for this problem to first define gamma, $\gamma$ as

$$\gamma = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$$

and then just define the kinetic energy as

$$E_k = \left( \gamma - 1 \right) mc^2.$$

But of course, it's up to you.

## The Attempt at a Solution

a)
Ekrest = mc2
Ekrest = (1.67*10^-27)(c)2
Ekrest = 1.5*10^-10

Ek= (1.5*10^-10)/√(1.9999*10^-4)-(1.5*10^-10)
EK=1.047*10^-8J
That looks about right to me! Very nice.
I am not confident in this answer as that does not seem nearly enough energy to accelerate the proton...
Protons are pretty small, don't forget.
B)
1.047*10^-8/ 1.5*10^-10
=69.66%
Ignoring a rather minor difference in rounding errors (between your result and mine), why in the world did you throw on a "%" at the end?

(That "%" is throwing you off by two orders of magnitude. )

Thank you very much! and I honestly have no idea why I put the % haha thank you :)

## 1. What is the definition of acceleration of a proton?

The acceleration of a proton is the rate of change of its velocity over time. It is a vector quantity, meaning it has both magnitude and direction.

## 2. How is the kinetic energy of a proton related to its acceleration?

The kinetic energy of a proton is directly proportional to its acceleration. This means that as the acceleration of a proton increases, so does its kinetic energy.

## 3. How does relativity affect the acceleration of a proton?

According to Einstein's theory of relativity, the mass of a proton increases as its velocity approaches the speed of light. This means that as a proton's acceleration increases, its mass also increases, making it more difficult to accelerate further.

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

No, according to the theory of relativity, the speed of light is the maximum speed that any object can attain. Therefore, the acceleration of a proton cannot exceed the speed of light.

## 5. How is the acceleration of a proton measured in experiments?

The acceleration of a proton can be measured using particle accelerators, which use electromagnetic fields to accelerate particles to high speeds. The acceleration can also be calculated using the proton's mass, velocity, and the forces acting on it.

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