(695, #31) Two forces F1 and F2 with magnitudes
10 lb and 12 lb act on an object at a point P as shown in the figure.
Find the resultant force F acting at P as well as
its magnitude and its direction. (Indicate the direction by finding
the angle theta shown in the figure.)
Solution:
F1 = F1( -cos45)i + F1( sin45)i =
10(-
)i +
10(
)j
= -5
i +
5
j
F2 = F2( cos30)i + F2( sin30)i
= 12(
)i + 12(1 / 2)j
= 6
i + 6 j
F = F1 + F2 = -5
i
+ 5
j+
6
i
+ 6 j = (-5
+
6
)i
+ ( 6 + 5
)j
F is the vector (-5
+
6
)i +
( 6 + 5
)j,
has a magnitude of 13.5, and is at an angle of 75.7 degrees.
by: nl