APPLIED MECHANICS- Verification of the Polygon Law of Forces

EXPERIMENT

 

OBJECTIVE:

To verify the law of polygon of forces with the help of universal force table apparatus.

 

APPARATUS:

Universal Forces table with five pulleys, rings with five string weight, slotted weight, plain paper and geometry box.

 

THEORY:

Polygon law of forces states that if a number of concurrent forces are acting simultaneously on a body, are represented in magnitude and direction by the sides of a polygon, taken in order, then the resultant is represented in magnitude and direction by the closing side of the polygon, taken in opposite order.

 

 

PROCEDURE:

  • Before starting the experiment make the graduated table horizontal with the help of leveling screw.
  • Clamp the pulley to the graduated disc of the force table.
  • Tie one and of thread to the circumference of small rings and place it around the central axis of the apparatus.
  • Attach other end of the string to the weight hangs which will carry small slotted weight.
  • Pass one string over each pulley.
  • Place slotted weight on the weight hanger in such a manner that ring is placed around the center.
  • Note down the angle between different threads and corresponding weights.
  • Draw a space diagram of the force acting a part such that the time of action of each force corresponding to the angles of forces between them.
  • Chose a suitable scale and make mark a point on a paper and draw the vector diagram of force system acting at a point by drawing parallel line of each force proportional to the chosen scale.

 

Procedure to draw vector diagram:

  • Draw a line OA parallel and equal to W1 assuming a suitable scale.
  • Draw a line AB parallel and equal to W2 from point A assuming the same scale.
  • Similarly draw BC and CD parallel and equal to the force W3 and W4.
  • Join OD i.e. the closing side by dotted line, which represents the resultant of polygon (graphically).
  • Measure the line OD and compare it with W5 by using the same scale.
  • Find the error by using the formula given in the observation table. Error should be positive.

 

OBSERVATION TABLE:

FORCE (in grams)

ANGLE ( in degree)

S. No. W1 W2 W3 W4 W5  θ1  θ2  θ3  θ4

 θ5

RESULTANT OF FORCES (R) (OD)

ERROR IN %

(W5 –R)/W5 x 100

or

(R- W5)/R x 100

 

PRECAUTIONS:

  • Ring should not touch the control axle of the disc and should be at the center of the table.
  • Graduated disc should be made kept perfectly horizontal.
  • Positions of the strings should be at the center of the table.
  • Pulley should be frictionless.

 

 

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