The largest and the smallest balls used in the experiment are with diameter 9.52 mm, and 2.38 mm respectively. For a glycerin with viscosity 1.0 Pa. s, what is the time necessary for each ball to reach a velocity 95% of the terminal velocity? Density of the ball material is 1.42 g/cm^3. Round the result to three decimal places.

The answer is = 0.0080

Explanation:

From the stokes law,

           v = g * D^2 *(d p - d m) / (18 V)

Here, v is the terminal Velocity, D is the diameter Of a Particle, V is the Viscosity of Medium, dp is the density Of Particle, dm is the density Of Medium.

The density of ball is 1.42 gm/cc

           v = 9.81 x 9.52 x 10^-3 ^2 (1420 - 1300) / 18 x 1.0

              =5.92x10^-4

          v(t) =0 .99 x V trm

                =0 .99 x  0.0059

                  = 0.00059 m/s

                v(t)/Vterm =1-e^(-t/r)

                         0.99 = 1 - e ^ (-t / 9.52 x 10^-3)

e ^ (-t / 9.52 x 10^-3) = 0.01

Take natural log

         -t / 9.52 x 10^-3 = -4.6

                                t = 0.0438 s

For the smaller ball

v = 9.81 x 2.38 x 10^-3 ^2 (1420 - 1300) / 18 x 1.0

             = 0.000037 m/s

                 v(t)/Vterm=1-e^(-t/r)

                         0.99 = 1 - e ^ (-t / 2.38 x 10^-3)

e ^ (-t / 2.38 x 10^-3) = 0.01

Take natural log

-t / 2.38 x 10^-3 = -4.6

                       t = 0.0109 s

Reynolds number is,

R= rho vd / mu

                = 1420 x  0.00059 x 9.52 x 10^-3 x / 1.0

               = 0.0080

a solenoid is created by wrapping a l = 90 m long wire around a hollow tube of diameter d = 4.5 cm.   the wire diameter is d = 0.9 mm.   the solenoid wire is then connected to a power supply so that a current of i = 9 a flows through the wire.

randomized variablesl = 90 m

d = 4.5 cm

d = 0.9 mm

i = 9 a                                          

write an expression for the number of turns, n, in the solenoid. you do not need to take into account the diameter of the wire in this calculation.

calculate the number of turns, n, in the solenoid.

write an expression for the length of the solenoid (l2) in terms of the diameter of the hollow tube d.

calculate the length of the solenoid (l2)   in meters.

calculate the magnitude of the magnetic field at the center of the solenoid in teslas.

explanation: