using focused laser light, optical tweezers can apply a force of about 10 pn to a 1.0-/un diameter polystyrene bead, which has a density about equal to that of water: a volume of 1.0 cm3 has a mas

Question

using focused laser light, optical tweezers can apply a force of about 10 pn to a 1.0-/un diameter polystyrene bead, which has a density about equal to that of water: a volume of 1.0 cm3 has a mass of about 1.0 g. estimate the bead’s acceleration in g’s.

Answer 1

One pn (piconewton) is 1.0 x 10^-12 N.

The volume of a 1.0 micrometer diameter spherical bead is V = 4/3 π (1.0 x 10^-6 m / 2)^3 = 5.23 x 10^-19 m^3.

As its density is about 1.0 kg / m^3, the mass of the bead is 1.0 kg/m^3 x 5.23 x 10^-19 m^3 = 5.23 10^-19 kg.

As F = ma, a = F / m = 1.0 x 10^-12 N / 5.23 10^-19 kg = 1.91 x 10^6 m/s^2. Since g = 9.8 m/s^2, the acceleration in terms of gs is 1.91 x 10^6 m/s^2 / 9.8 m/s^2 = 1.9 x 10^5 gs.

I assumed that you meant 1.0 um (micrometers) for the diameter of the bead.

Check all math.