Need help with my writing homework on The Equilibrium States in Vector Mechanics. Write a 1750 word paper answering; Practically, determining a static object’s net force involves either drawing an accurate vector summation diagram and adding all the individual forces, or using trigonometric functions to convert individual forces into their vertical and horizontal components. hence comparing whether vertical and horizontal force components are balanced.

Objectives

The main objective of this experiment is to employ trigonometric functions in resolving the net force of an object at static equilibrium. In theory, vertical forces are determined using the sine rule whereas horizontal forces involve the use of the cosine rule. Primarily, a suspended object exerts tension on the suspender string. In addition, the suspended object exerts weight due to gravitational acceleration. By suspending an object at an angle, the string’s tension can be used to determine the magnitude and direction of forces. Besides the use of trigonometric functions, this experiment also sought to practically determine the magnitude and effects of experimental errors in laboratory exercises. In vectors, errors propagate in two fronts. forces’ magnitude and direction (Beer 70). Therefore, another objective of this experiment is to examine the manner in which errors propagate through both angles and the magnitude of component forces. Finally, this experiment provides a means through which sources of experimental errors can be predicted and explained in a contextual manner.

Experimental Data

Data obtained from each procedure of the pulley experiment were tabulated below. The tabulated data include masses of weights, angle of tensile strings, and forces exerted by each weight.

Mass (g) Angles (in radians) Forces (N)

M1, 100.3 30o = 0.524 radians T1 = 9.830

M2, 150.15 50o = 0.8727 radians T2 = 14.715

M3, 162.64 86o = 1.5001 radians T3 = 15.939

Data Analysis

In this section, forces and angles tabulated above were used to deduce the magnitude of each force, directional components of each force, the net force experienced by the static object, and errors propagated through magnitude and direction parameters.

Vectors of Each Force

The formula for finding the magnitude of each force is given by. Fx = F cos θ and Fy = F sin θ where x and y are the directional components of each force in Cartesian coordinates (Beer 70).