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Homework answers / question archive / To familiarize with the features an uses of force table; ' To apply the concepts of resultant and equilibrant vectors; and ' To appreciate real-life applications of mechanical equilibrium
To familiarize with the features an uses of force table; ' To apply the concepts of resultant and equilibrant vectors; and ' To appreciate real-life applications of mechanical equilibrium. II. Concepts A. Force table A force table or sometimes refers to as force board is a laboratory equipment that has a circular plate marked like a compass placed over a metallic stand. Minimum of three strings with weights freely hanging at the end are attached to the movable ring located at the center of the plate. Such weights represent forces under study being exerted along different directions. The strings are anchored on ideally frictionless pulleys as shown below. Source: h_ttps://www.unitedscLoom/product-catalog/force- tnbl e
table B. Mechanical equilibrium Consider the ring where the strings are attached to as a point particle being pulled by different forces in various direction. The system is said to be in mechanical equilibrium if the net force acting on the particle is zero. Say that the force table has three weights balancing the system, one weight among those three acts as equilibrant vector E. That is, the imaginary force exactly opposite to the direction of the equilibrant vector is called the resultant vector R. The magnitude of R is equal to the magnitude of E. Hence, eq. 1 Representing the two other forces as A and B, eq. 2 Note that vector addition can be done using graphical and analytic methods. Parallelogram and polygon methods are under the former while the latter is composed of law of sine cosine and component methods. This activity applies these methods using the concept of force table. III. Data Set A. Assume values obtained below using force weights in a force table experiment. Complete the table using analytic method. Percent errors pertain to calculated values for magnitude and direction of R versus the observed values of E from the experiment. Force m (g) w (N) = mg 0 () F, 20 15 F, 25 50 F 3 40 170 E, 30 280 R 1 Ez
Set B. Assume values obtained below using force weights in a force table experiment. Complete the table using graphical method. Percent errors pertain to find values for magnitude and direction of R versus the observed values of E from the experiment. Force m (g) w (N) = mg 0 () F, 20 15 F, 25 50 F 3 40 170 E, 30 280 IV. Analysis 1. Calculate the percentage error between the given force magnitude of E, and calculated force magnitude of E, obtained from calculated force magnitude of R,. 2. Calculate the percentage error between the given direction (i.e. theta value) of E and calculated direction of E, obtained from computed direction of R,. 3. Calculate the percentage error between the given force
IV. Analysis 1. Calculate the percentage error between the given force magnitude of E, and calculated force magnitude of E, obtained from calculated force magnitude of R,. 2. Calculate the percentage error between the given direction (i.e. theta value) of E and calculated direction of E, obtained from computed direction of R,. 3. Calculate the percentage error between the given force magnitude of E, and calculated force magnitude of E, obtained from calculated force magnitude of R,. 4. Calculate the percentage error between the given direction (i.e. theta value) of E and calculated direction of E, obtained from computed direction of R, V. Conclusion Force Table |3
