What is the magnitude of the net force exerted by three people pulling a stubborn donkey, and in what direction is this force acting?
The magnitude of the net force exerted by three people pulling a stubborn donkey is 289.8 N. The direction of this force is 26.2 degrees to the left of the page.
Calculating Net Force:
Magnitude of Force:
The net force, denoted as F, exerted by the three people pulling the donkey can be calculated using the formula:
F=sqrt(F1^2 + F2^2 + F3^2 + 2 F1 F2 cos(135) + 2 F1 F3 cos(-135) + 2 F2 F3 cos(90))
where F1, F2, and F3 represent the forces exerted by Jack, Jill, and Jane, respectively. Substitute the given values into the formula:
F = sqrt((88.5)^2 + (66.3)^2 + (125)^2 + 2 (88.5) (66.3) (-sqrt(2)/2) + 2 (88.5) (125) (-sqrt(2)/2) + 2 (66.3) (125) (0))
Calculating this gives:
F = sqrt(83858.16)
F = 289.8 N
Calculating Direction:
Angle of Force:
The direction of the net force, denoted as θ, can be calculated using the formula:
θ = tan^-1[(F1 sin(0) + F2 sin(-45) + F3 sin(45))/(F1 cos(0) + F2 cos(-45) + F3 cos(45))]
Substitute the given values into the formula:
θ = tan^-1[(66.3 - 88.5sqrt(2)/2 + 125sqrt(2)/2)/(88.5 + 66.3sqrt(2)/2 + 125sqrt(2)/2)]
Calculating this gives:
θ = 26.2 degrees
Therefore, the net force exerted by the three people pulling the stubborn donkey is 289.8 N, and it is directed at 26.2 degrees to the left of the page.