matthmaticaly determine the resultant force,AandB,act an object.force A is 85N and is at an angle of 20° to the horzontal,force B is125N and is angle of 60° to the horzontal.
2 answers
answer
We could use vectors
resultant = 85(cos20°, sin20°) + 125(cos 60°, sin60°)
= (78.8739, 29.0717) + (62.5, 108.2532)
= (142.3739, 137.3249)
magnitude = √(142.3739^2 + 137.3249^2) = appr 197.8 N
angle of resultant = tan^-1 (137.3249/142.3739) = 43.97..° = appr 44°
or:
make a sketch to get a triangle with sides 85 and 125 and the contained
angle of 140° (use basic geometry to get that angle)
by cosine law:
|R|^2 = 85^2 + 125^2 - 2(85)(125)cos140
|R| = 197.8 , just like before
resultant = 85(cos20°, sin20°) + 125(cos 60°, sin60°)
= (78.8739, 29.0717) + (62.5, 108.2532)
= (142.3739, 137.3249)
magnitude = √(142.3739^2 + 137.3249^2) = appr 197.8 N
angle of resultant = tan^-1 (137.3249/142.3739) = 43.97..° = appr 44°
or:
make a sketch to get a triangle with sides 85 and 125 and the contained
angle of 140° (use basic geometry to get that angle)
by cosine law:
|R|^2 = 85^2 + 125^2 - 2(85)(125)cos140
|R| = 197.8 , just like before
5 answers