How Much Work Is Needed to Accelerate a Particle to 0.897c?

[zmike]

Homework Statement

How much work must be done on a particle with a mass (m) to accelerate from rest to 0.897c (speed)?

Homework Equations

http://hyperphysics.phy-astr.gsu.edu/hbase/HFrame.html

The Attempt at a Solution

Use work energy theorem.

W=K2-K1
since K1 =0

W=K2

K2=E2-E1 (E1=0 since it was at rest)

E2= [1/sqrt(1-0.897^2)]*m(0.897c)^2

but apparently this is wrong so I donno what I did wrong??

thanks

 

[tiny-tim]

Hi zmike!

How much work must be done on a particle with a mass (m) to accelerate from rest to 0.897c (speed)?
…
Use work energy theorem.

W=K2-K1
since K1 =0
…
but apparently this is wrong so I donno what I did wrong??

erm … K1 isn't zero.

 

[nlightner]

Your approach using the work-energy theorem is correct. However, there is a mistake in your calculation of the final kinetic energy, E2. The correct expression for the final kinetic energy of a particle moving at a speed of 0.897c is:

E2 = [(1/√(1-0.897^2)) - 1] * mc^2

This expression takes into account the relativistic factor, which accounts for the increase in mass as the particle approaches the speed of light. Once you have the correct expression for E2, you can substitute it into your equation for W and solve for the work done on the particle.

Additionally, make sure that you are using consistent units throughout your calculation. The mass (m) should be in kilograms (kg) and the speed (c) should be in meters per second (m/s).

I hope this helps! Keep up the good work as a scientist.