# The analytical ultracentrifuge olympics

**Classical Mechanics**Level 5

Suppose a particle if found to travel at the rate \(v\) through sucrose. Now, we measure the sedimentation rate of a dimer (two of the particles stuck together). This new particle travels down the gradient at the rate \(v^\prime\), what is \(v^\prime /v\)?

**Notes and assumptions**

- Assume the particles are spherical.
- Assume that the dimer is formed by melting down two particles and forming a sphere with twice the volume of the monomer.
- For simplicity, assume that the force pulling particles down the gradient is provided by a strong, constant gravitational field.
- The friction the particle feels is Stokes drag \(F \sim rv\) where \(r\) is the radius of the particle.