Polígono de forças

Polygon of forces

Introduction and Object:

Physical quantities that require both a magnitude and direction for their description are vector quantities. Vectors must be added by special rules that take both parts of the description into account. One method for adding vectors is graphical, constructing a diagram in which the vectors are represented by arrows drawn to scale and oriented with respect to a fixed direction. Using the graphic method we can rapidly solve problems involving the equilibrium of a particle, in which the vector sum of the forces acting on the particle must be equal to zero. In mechanics, forces are usually associated whit any action that tends to maintain the position of a body. It is very useful to continue thinking about forces in terms of push and pull, or effort. The purpose of this experiment is to show that the magnitude and direction of the resultant of several forces.

Theory:

Three or more forces are in equilibrium if they can be arranged to form a polygon components resolve all forces into components in some convenient coordinate system, combine the components along each axis. Add the components parallel to the axis and subtract the components anti-parallel to the axis. If the resultant along each axis is zero the object is in equilibrium.

Apparatus:

A force table equipped with a ring, pin, ruler, four pulleys, cords, masking tape ,pans a set of known masses (slotted type)

Procedures:

1 – Once the pulleys sated, place a A4 sheet on the back of the cords

2. Using the strings and the masses supplied, set up a system of four forces (three over the pulleys and one hanging downward) so that the knot is suspended in equilibrium near the center of the clear space on the force board.

Displace the knot from its equilibrium position and release it. The force system should oscillate freely, coming to rest at its original position. Tap (vibrate) the force board in order to minimize the effects of static friction in the pulleys.

3. Slide a sheet of paper between the strings and the force board, and locate it so that a reasonable length of each string lies over the paper. Adjust the forces if necessary. Tape the paper in place. The paper does not need to be square with the force board.

4. Remove the sheet of paper from the force board,

5. Repeat the above for two more sets of masses, with differing pulley positions

Analytical Method – The following points identifies how the resultant force may be calculated using the analytical method Resolve the given forces vertically and calculate the algebraic total of all the vertical parts or Σ V. Resolve the given forces horizontally and calculate the algebraic total of all the horizontal parts or Σ H. The resultant force R of all the given forces can be expressed as: R = (Σ V)^2 + (√ H)^2 The inclination of the above resultant force will be at an angle Ɵ with the horizontal component and may