Experiment using a smart pulley in determining the gravitational constant-g

Background information
An object moving through a fluid experiences a resistive force, or drag, that is proportional to the viscosity of the fluid. If the object is moving slowly enough, the drag force is proportional to the speed v. if the object is a sphere of radius r, the force is

F = 6πnrv

Where n is the coefficient of viscosity. This equation is known as Stoke’s law.
By relating Newton’s second law and Stoke’s law, determine the value of g (gravitational constant) in ms-2.

*Hint* When the object reaches terminal velocity, the sum of forces will result in no net force, thus producing a terminal velocity.

Fgrav = Fbuoyant + Fdrag
Where Fbuoyant = Weight of fluid displaced (Archimedes’ principle)

Apparatus
· Smart pulley system (connected to the computer with science workshop)
· Data logging interface (with attached cables)
· 1 m long with a 7 cm diameter hollow cylindrical tube (rubber stopper at bottom)
· Retort stand (with two clamps)
· Pendulum (tied to string)
· Fluid medium (Air, water or glycerol)
· Dead weight

Experimental Procedure
1. Set up the apparatus as shown in the diagram

2. Open the science workshop program and drag the motion sensor interface icon to “input 1”
3. Select the graphing option on the interface and check the options for “Distance-time, velocity-time and acceleration-time”.
4. Before releasing the pendulum from dropping, get your lab partner to hold the ball at start point close to sensor.
5. Press the record button on the computer.
6. Release the pendulum and press the stop button as soon as the pendulum hits the bottom stopper.
7. The results would be available for analysis on the graph obtained.

Results and questions
1. Print out the various graphs obtained from the experimental proceedings.

2. Explain the trend of the values obtained on the acceleration time graph.

3. Calculate the value of g from the velocity-time graph obtained. What conclusions can you draw from the 2 graphs (Do you see any similarity/anomaly?)

4. Calculate the force due to gravity by relating Stoke’s law and Newton’s law.

5. Using Newton’s second law, find g.