As shown in Figure 4.40, force vector F → 1 always points in the + x direction, but 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, F → = F 1 → + F 2 → , for several different values of θ . The magnitudes of F 1 → and F 2 → remain unchanged; only the angle θ is varied. The table shows the student’s results: Figure 4.40 Problem 43. θ F x (N) F y (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 F 1 and F 2 . (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 F 1 and F 2 . (d) Repeat this process for the F 1 data and compare your result with what you obtained in part(c).
As shown in Figure 4.40, force vector F → 1 always points in the + x direction, but 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, F → = F 1 → + F 2 → , for several different values of θ . The magnitudes of F 1 → and F 2 → remain unchanged; only the angle θ is varied. The table shows the student’s results: Figure 4.40 Problem 43. θ F x (N) F y (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 F 1 and F 2 . (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 F 1 and F 2 . (d) Repeat this process for the F 1 data and compare your result with what you obtained in part(c).
As shown in Figure 4.40, force vector
F
→
1
always points in the +x direction, but
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,
F
→
=
F
1
→
+
F
2
→
, for several different values of θ. The magnitudes of
F
1
→
and
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).
Vector v = <-4,4> and vector w = <-2,-1>. Draw the vector v+w and give its component form.
Given the vectors A = -5i - 3j - 8k ; B = 4i - 2j + 3k ; C = 10i -12j - 8k
a. Find A x B
b. Evaluate the mixed triple products A . (B x C)
c. Find : A x (A x B)
Use the law of sines and the law of cosines, in conjunction
with sketches of the force triangles, to solve the following
problems. Determine the magnitude of the resultant R and
the angle e between the x-axis and the line of action of the
resultant for the following:
180 N
240 N
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