A steel ball is used to measure the viscosity of motor oil. The container used in this experiment has a bottom area of 20 cm^2. The steel ball is 3 mm in diameter. After the ball is dropped to the container it takes about 12 seconds to reach the bottom of the container whose height is 60 cm. Calculate the viscosity of the motor oil.
dragforce=6π*radius*vicosity*speed.
so if the ball is falling at a constant rate, the dragforce=forcegravity=m*9.8
so viscosity= 9.8/(6PI*0.0015*.6/12
To calculate the viscosity of the motor oil, we need to use the Stoke's law equation:
v = (2/9) * (g * (d^2) * η) / r
Where:
- v is the velocity of the steel ball (m/s)
- g is the acceleration due to gravity (9.8 m/s^2)
- d is the diameter of the steel ball (m)
- η is the viscosity of the fluid (Pa*s)
- r is the radius of the steel ball (m)
First, we need to convert the units of the given values:
- The diameter of the steel ball is 3 mm, which is equal to 0.003 m.
- The height of the container is given as 60 cm, which is equal to 0.6 m.
Next, let's calculate the radius of the steel ball:
- The radius, r = d/2 = 0.003/2 = 0.0015 m
Now, we can calculate the velocity, v:
- v = h/t, where h is the height of the container and t is the time taken to reach the bottom.
- v = 0.6/12 = 0.05 m/s
Now, we can rearrange the equation to solve for η, the viscosity of the fluid.
η = (v * r) * (9/2) / (g * (d^2))
η = (0.05 * 0.0015) * (9/2) / (9.8 * (0.003^2))
Calculating the value gives us:
η ≈ 0.00017 Pa*s
Therefore, the viscosity of the motor oil is approximately 0.00017 Pa*s.
To calculate the viscosity of the motor oil, we need to use Stokes' Law, which relates the viscosity of a fluid to the terminal velocity of a spherical object falling through that fluid.
The formula for Stokes' Law is:
v = (2/9) * (g * r^2 * Δρ) / η
Where:
v = velocity of the object (terminal velocity)
g = acceleration due to gravity (9.8 m/s^2)
r = radius of the object (diameter / 2)
Δρ = density difference between the object and the fluid (assumed to be negligible here)
η = dynamic viscosity of the fluid (what we want to calculate)
First, let's convert the given measurements to SI units:
The radius of the ball is 0.003 m (3 mm / 1000).
The height of the container is 0.6 m.
The terminal velocity of the ball (v) can be calculated using the following formula:
v = h / t
Where:
h = height of the container (0.6 m)
t = time taken for the ball to reach the bottom (12 s)
Substituting the values:
v = 0.6 m / 12 s = 0.05 m/s
Now we can solve for η.
The formula can be rearranged as follows:
η = (2/9) * (g * r^2 * Δρ) / v
Since Δρ is negligible (assumed to be 0), the equation becomes:
η = (2/9) * (g * r^2) / v
Substituting the known values:
η = (2/9) * (9.8 m/s^2 * (0.003 m)^2) / 0.05 m/s
η ≈ 0.0032704 kg/(m*s)
Therefore, the viscosity of the motor oil is approximately 0.0032704 kg/(m*s).