find the resultant for the following both analytically and graphically. calculate the percent deviation between the two methods.

Question

find the resultant for the following both analytically and graphically. calculate the percent deviation between the two methods.(where 1cm=50g) 50g at 110 degrees, 200g at 218 degrees, 150g at 298 degrees

Answer 1

In general, each vector is represented in component form by ⟨vcosθ,vsinθ⟩ where v is the magnitude.

So write each of v1, v2 & v3 in this form.

The resultant is  ⟨sum of all terms of the form vcosθ, sum of all terms of the form vsinθ⟩ 

Call the resultant r = ⟨a,b⟩ 

 

magnitude ||r|| = √(a²+b²)   θ_r = arctan(b/a)

 

This gives you the 'analytical' result to as much accuracy as you employ during all of the calculations.

 

Doing the problem graphically has the inherent problem of accuracy attained by a drawing, which cannot be as good as the former method. Read the graphical results as reasonably as you can, and then calculate thesdeviation of magnitude & direction.