Two forces F1 and F2 act on a 9.20-kg object. F1 = 30.0 N and F2 = 12.0 N.
Determine the magnitude and the direction of the acceleration if the angle between F1 (horizontal line) and F2 (slanted line) is 60 degrees.
Determine the magnitude and the direction of the acceleration if the angle between F1 (horizontal line) and F2 (slanted line) is 60 degrees.
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F1 = 30i + 0j
F2 = 12*cos 60 i + 12*sin 60 j
= 6i + 6*sqrt(3) j
Adding, the final force is 36i + 6*sqrt(3)j
Magnitude of the force = sqrt(36^2 + (6^2)*3) = sqrt(1296 + 108) = sqrt(1404) = 37.4699
Direction = tan inverse of (6*sqrt(3)/36) = tan inverse of (sqrt(3)/6) = 16.102 degrees.
Force = mass * acceleration,
.'. a = F/m = 37.4699/9.2 = 4.072m/s in a direction of 16.102 degrees from the horizontal.
F2 = 12*cos 60 i + 12*sin 60 j
= 6i + 6*sqrt(3) j
Adding, the final force is 36i + 6*sqrt(3)j
Magnitude of the force = sqrt(36^2 + (6^2)*3) = sqrt(1296 + 108) = sqrt(1404) = 37.4699
Direction = tan inverse of (6*sqrt(3)/36) = tan inverse of (sqrt(3)/6) = 16.102 degrees.
Force = mass * acceleration,
.'. a = F/m = 37.4699/9.2 = 4.072m/s in a direction of 16.102 degrees from the horizontal.