Linear Drag Force Homework: Acceleration & Constant Speed Calculations

[antoman]

Homework Statement

We sink ball with density 1450 kg/m^3 in some liquid with density 1400 kg/m^3

a) What's acceleration in moment we drop the ball?
b) With what constant speed will the ball sink in balace? Assuming that the drag force is linear. Radius of ball is 3mm and viscosity of liquid is 200 Pa s.

Homework Equations

a=(g*(ρb-ρl))/ρb

The Attempt at a Solution

a... acceleration
ρb=1450 kg/m^3
ρl=1400 kg/m^3
g=9,81 m/s^2

a) That's easy, using the formula and you get a=0,338 m/s^2
b) Need help here, no idea how to solve

 

[Chestermiller]

Homework Statement

We sink ball with density 1450 kg/m^3 in some liquid with density 1400 kg/m^3

a) What's acceleration in moment we drop the ball?
b) With what constant speed will the ball sink in balace? Assuming that the drag force is linear. Radius of ball is 3mm and viscosity of liquid is 200 Pa s.

Homework Equations

a=(g*(ρb-ρl))/ρb

The Attempt at a Solution

a... acceleration
ρb=1450 kg/m^3
ρl=1400 kg/m^3
g=9,81 m/s^2

a) That's easy, using the formula and you get a=0,338 m/s^2
b) Need help here, no idea how to solve

Have you learned the equation for calculating the viscous drag force (in creeping flow) on a sphere of diameter, when the sphere is moving with a velocity v relative to the viscous fluid?

 

[antoman]

Have you learned the equation for calculating the viscous drag force (in creeping flow) on a sphere of diameter, when the sphere is moving with a velocity v relative to the viscous fluid?

If you mean in colledge probably yes, but me personaly don't know that equation.

 

[Chestermiller]

If you mean in colledge probably yes, but me personaly don't know that equation.

Google Stokes Law.

 

[Nickie]

this.


Great job on calculating the acceleration in part a)! To solve part b), we can use the equation for linear drag force, F = 6πηrv, where η is the viscosity of the liquid, r is the radius of the ball, and v is the velocity of the ball. Since we are looking for the constant speed at which the ball will sink, we can set the drag force equal to the weight of the ball (mg). So we have:
mg = 6πηrv
Solving for v, we get:
v = mg / (6πηr)
Substituting in the values given, we get:
v = (0.003kg)(9.81m/s^2) / (6π(200Pa s)(0.003m)) = 0.082 m/s
Therefore, the ball will sink at a constant speed of 0.082 m/s in the given liquid. Keep up the good work!