Chapter 4, Problem 43GP

As shown in Figure 4.40, force vector ${\stackrel{\to }{F}}_1$ always points in the +x direction, but ${\stackrel{\to }{F}}_2$ makes an angle θ with the +x axis. A physics student is given the task of graphically determining the x and y components of the sum of these vectors, $\stackrel{\to }{F}=\stackrel{\to }{F_1}+\stackrel{\to }{F_2}$, for several different values of θ. The magnitudes of $\stackrel{\to }{F_1}$ and $\stackrel{\to }{F_2}$ remain unchanged; only the angle θ is varied. The table shows the student’s results:

Figure 4.40

Problem 43.

θ	Fx(N)	Fy(N)
20*	11.4	3.1
35*	10.4	5.2
60*	7.5	7.8
75*	5.3	8.7

(a) Write an expression for F in terms of θ F₁ and F₂. (b) Make a linearized graph of the x component data with the value F, values on the y axis and the appropriate trig function of 0 on the x axis. (c) Draw a best-fit line through your plotted points and use this line to determine the magnitude F₁ and F₂. (d) Repeat this process for the F₁ data and compare your result with what you obtained in part(c).