Problema Solution
A point is pulled by two ropes: one to the left and up 34 degrees with a magnitude of 5, and the other to the right and up 16 degrees with a magnitude of 7. What is the resulting force on the point?
Answer provided by our tutors
The solution to this problem can depend on what picture is drawn for the angles, so here is a solution with the degrees given relative to the horizontal plane (dots required to keep the angle-lines aligned):
F=5...................F=7
....\ ................../
......\.............../
........\.........../
....34..\ ....../ 16
Force in the lateral direction (negative to the left, positive to the right):
5 * cos(34) - 7 * cos(16) = 4.15 - 6.72 = -2.58
Force in the upward direction (negative download, positive upward):
5 * sin(34) + 7 * sin(16) = 2.8 + 1.93 = 4.72
so the resulting force is to the left and upward:
sqrt((4.72543)^2 + (-2.58364)^2) = 5.38
at an angle of:
atan(4.72/(-2.58)) = -61, or 28.7 degrees above the horizontal