Experiment: Finding the Terminal Velocity of a Metal Sphere Through Castor Oil

Objective:  

To determine the terminal velocity of a metal sphere called as the  ‘viscous velocity drop’ as it falls through a viscous liquid like castor oil, and to understand the relationship between drag force, viscosity, and terminal velocity.

Terminal Velocity of a Metal Sphere-Materials Required

A tall, transparent  measuring cylindrical container filled with castor oil of density 960 kg/m³

Metallic spheres  of density 7800 kg/m³ (e.g., steel ball bearings).  

A stopwatch   

A scale or measuring tape.  

A marker or tape to mark positions on the container.  

A vernier caliper  to measure the diameter of the sphere.   

Terminal velocity of a metal sphere- Image

Terminal velocity of a metal sphere- Definition and Theory:  

Definition:

The terminal velocity is the constant speed accomplished by the falling item through a viscous liquid or the environment with no speed increase as portrayed by Newton’s first law.The viscous force/drag experienced by the falling article adjusts the power because of speed increase.

Terminal velocity of a metal sphere-Theory

A metal sphere first accelerates because of gravity when it is dropped into a viscous liquid, such as castor oil. Nevertheless, the fluid’s drag force, or resistance, also rises with speed. The sphere eventually reaches a constant speed known as the terminal velocity when the drag force equals the gravitational force.

The outer(external) forces that are impacting the item that is falling through the thick fluid are, one is the gravitational force, also called the heaviness of the falling article, and the other two forces are upthrust and the viscous force. 

At the point when the descending power of gravity approaches the viscous force plus buoyant force then the net acceleration on the article becomes zero.

The speed of the item stays consistent. mg = F + B

Terminal velocity of a metal sphere- Procedure:  

The process for determining a metal sphere’s terminal velocity  

Get the setup ready: 

Make sure there are no air bubbles as you pour castor oil into the tall, cylindrical graduated glass container.On the container, mark two places that are known to be 50 cm apart. The time it takes for the sphere to move between them can be measured with the aid of these markings. 

Measure the Sphere: 

Determine the metal sphere’s radius by measuring its diameter with a vernier caliper and calculate its radius.

Drop the metallic sphere:

Gently release the sphere into the castor oil, ensuring it does not touch the sides of the container.  

Record Observations:

Start the stopwatch as the sphere passes the first mark and stop it as it passes the second mark.  

Repeat the experiment multiple times to ensure accuracy.  

Record the time taken for the sphere to travel between the two marks.  

Terminal velocity of a metallic sphere-Observations and Calculations: 

A tabular column is an excellent way to organize and record observations for this experiment. Below is an example of how you can structure the table to record your observations and calculationsTabulate the time taken for each trial and calculate the average time.  

Use the known distance between the marks to calculate the terminal velocity.Compare the experimental terminal velocity with the theoretical value. 

Terminal velocity of a metal sphere in Castor Oil- Observational Table

Trials	Radius     (r)     m	Distance between the marks  (s)                             m	Time taken (t)          seconds	Terminal velocity         v=s/t         m/s	Average terminal velocity                   m/s
1.	0.002	0.5	10	0.050
2.	0.002	0.5	9.8	0.051
3.	0.002	0.5	9.7	0.051	0.0505
4.	0.002	0.5	9.9	0.050
5.	0.002	0.5	10.1	0.049

Terminal velocity of a metallic sphere- Observations

Radius of Sphere (r)                                 : 0.002 m

Distance Travelled (s)                              : 0.50 m

Density of Sphere Material                     : 7800 kg/m³

Density of Liquid                                      : 960 kg/m³

Acceleration due to Gravity (g)             : 9.8 m/s²

Average Terminal Velocity (v)               : 0.0505 m/s

Terminal velocity of a metallic sphere-Result 

The terminal velocity of the metallic sphere is 0.0505  m/s

Examine the differences between the theoretical and experimental numbers for the metallic sphere’s terminal velocity. A small fluctuation could be the result of contaminants in the liquid, temperature effects, or experimental errors.

Conclusion:

The experiment shows that when the drag force equals the gravitational force, terminal velocity is reached. It also emphasizes how viscosity affects how quickly an object moves through a fluid. This experiment is a fantastic method to investigate fluid dynamics and practical physics applications!

Important precautions to minimize experimental errors

Crucial measures to reduce experimental errors

Make the surface clean:

Before dropping the metallic sphere in the liquid, make sure it is dry and clean. Its motion may be impacted by any moisture or dust.

Make sure to accurately mark the distance:

To enable the sphere to attain its terminal velocity, points A and B on the measuring cylinder should be accurately marked and separated by a suitable amount of space.

Measure Precisely:

Carefully measure the sphere’s diameter with a vernier caliper because even a tiny inaccuracy might have an impact on the radius estimate. (The explanation of vernier’s least count is given above.)

Steer clear of temperature fluctuations:

Castor oil’s viscosity varies with temperature. Avoid drafts and direct sunlight while conducting the experiment at room temperature.

Make sure to accurately mark the distance:

To enable the sphere to attain its terminal velocity, points A and B on the measuring cylinder should be accurately marked and separated by a suitable amount of space.

Gently drop the sphere:

Vertically drop the spherical without exerting any force. Pushing and tilting might add horizontal motion and change the outcome.

Prevent the Parallax error:

To prevent parallax error as the sphere crosses points A and B, keep your eyes level with the marking while you measure the time.

Do the experiment again:

To reduce random errors and increase accuracy, run several trials and average them.

Await steady motion.

It takes a while for the sphere to reach terminal velocity. Only once the sphere has covered a brief initial distance should you start the stopwatch.

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