Topic 4b - model answers

Question 1

define upthrust

Answer 1

the weight of fluid displaced

Question 2

derive the expression for upthrust

Answer 2

U=W_fluid=m_fluid g
U=ρ_fluid Vg

Question 3

define terminal velocity

Answer 3

a. the constant velocity reached when an object is falling through a fluid and there is no resultant force acting upon it

Question 4

4. State the equation for Stoke’s drag force

Answer 4

a. F = 6πrηv where r is the radius of a sphere, v is its terminal velocity, η is the viscosity of the fluid – this force acts on an object in the opposite direction to its velocity

Question 5

5. State the conditions for which Stoke’s law applies

Answer 5

a. Only applies for small spheres (small relative to the container containing the fluid)
b. travelling slowly through a fluid
c. with laminar flow

Question 6

6. Describe how to determine the viscosity of a fluid

Answer 6

a. Measure the diameter of a small sphere using a micrometer in three places and take an average.
b. Drop the ball through a measuring cylinder filled with the fluid and marked with two rubber bands – the first of which should be placed about 10cm below the fluid level as the ball will be at terminal velocity there. The second should be the maximum possible distance away from the first.
c. Measure the time taken for the ball to fall between the two rubber bands, t using a stopwatch
d. Calculate the terminal velocity of the ball, v = s/t where s is the distance between the bands.
e. Repeat for balls with different diameters.
f. Measure the mass of each ball using a mass balance. Calculate the density of the ball by using the equation ρobject = mass / volume = m /4/3 πr3 .
g. Calculate the density of the fluid by measuring the mass of a known volume of fluid and dividing mass/volume.
h. For an object at terminal velocity obeying Stokes’ law,
i. W = U + F,
j. so 4/3 πr3 ρobject g = 4/3 πr3 ρfluid g + 6πηrv.
k. Rearranging this, v = (2/9) gr2 (ρobject - ρfluid) / η.
l. Plot a graph of r2 on the x axis and v on the y axis and the gradient of the graph should be (2/9) g(ρobject - ρfluid) /η.
m. Determine the gradient of the line of best fit and η = 2/9 g(ρobject - ρfluid) /gradient

Question 7

explain how to confirm that the object is falling at terminal velocity

Answer 7

a. Include another rubber band in the middle of the other two
b. Measure the time taken from the top band to the middle band, and from the middle band to the bottom band
c. If the time taken for the ball to travel the equal distances is the same, the ball is falling at terminal velocity

Question 8

well done!!! keep learning!!!
:)

Answer 8

treat yourself afterwards:D