Asked by Clarissa
three people are trying to hold a lion still for the vet. The lion, in the center, is wearing a collar with three ropes attached to it and each person has a hold of the rope. charlie is pulling in the direction of 62 degrees west of north with a force of 175 newtons. Sam is pulling in the direction of 43 degrees east of north with a force of 200 newtons. What is the direction and magnitude of the force which must be exerted by Alice on the third rope to counterbalance Sam and Charlie?
Answers
Answered by
Henry
Charlie: 175 N. @ 152 Deg.,CCW.
Sam: 200 N. @ 47 Deg.,CCW.
X = 175*cos152 + 200*cos47 = -18.1 N.
Y = 175*sin152 + 200*sin47 = 228.4 N.
Alice: Force must be equal and opposite
The vector sum of Charlie and Sam's force.
X = 18.1 N.
Y = -228.4 N.
tanA = Y/X = -228.4 / 18.1 = -12.61878.
A = -85.5 Deg. = 85.5 Deg S of E
A = -85.5 + 360 = 274.5 Deg.,CCW..
M = X / cosA = 18.1 / cos274,5 = 230.7 N.@ 274.5 Deg.
Sam: 200 N. @ 47 Deg.,CCW.
X = 175*cos152 + 200*cos47 = -18.1 N.
Y = 175*sin152 + 200*sin47 = 228.4 N.
Alice: Force must be equal and opposite
The vector sum of Charlie and Sam's force.
X = 18.1 N.
Y = -228.4 N.
tanA = Y/X = -228.4 / 18.1 = -12.61878.
A = -85.5 Deg. = 85.5 Deg S of E
A = -85.5 + 360 = 274.5 Deg.,CCW..
M = X / cosA = 18.1 / cos274,5 = 230.7 N.@ 274.5 Deg.