24/02/2014
Force Table Lab: Forces on Bodies can be represented by vectors
Force Table is used to study and verify the addition and subtraction of vectors, which unlike scalars, have both magnitude and direction and therefore have more sophisticated algebra. To be more specific we will be studying the algebra of concurrent vectors, vectors which pass through one point. The vectors at play here are Forces, all acting upon the same object, a small metal ring to which are attached three strings. Three different forces will be applied to this ring by attaching weights to the free ends of the strings and allowing the weights to hang over the edge of the force table (using pulleys to reduce friction).
The idea is to try different combinations of weights (the masses hanging on the free end of the three strings) and angles (the place where pulley is attached on the circumference of the fore table) so as to maintain the ring at the center of the table. Such a situation is called an equilibrium condition in which the sum of all the forces acting on the center ring must be zero.
We have physically confirmed that the sum of the three forces acting on the center ring must be zero otherwise the string would not be at the center of the table in this is setting. Now we can theoretically prove by graphical and analytic methods that the resultant sum of vectors is indeed zero. This would prove that our methods of vector addition apply to these forces and therefore the forces on bodies can indeed be represented by vectors.
Notes:
1. Include the mass of the hanger in calculating the weight acting on each string.
2. The weight of the strings and the friction in the pulley is assumed to be zero.
3. Keep the direction of the strings at ninety degrees to the tangent to the table.
4. Friction in the pulley creates tension in the string so that the actual force acting on the centre ring is less than it would have been in case of frictionless pulleys.
