Ch. Ex. 127 A winch at point B is used to slide a box up a chute CD in a warehou
ID: 1536848 • Letter: C
Question
Ch. Ex. 127 A winch at point B is used to slide a box up a chute CD in a warehouse. 1 out of 10 attempts Do not round intermediate calculations; however, for display purposes report intermediate Assistance steps rounded to four significant figures. Give your final answer (s to four significant Check My figures. View Hint View Ques A winch at point B is used to slide a box up a chute CD in a warehouse. If the component Print of the force from cable AB in the direction of the chute must be 370 lb, determine the force Question in the cable for the position of the box given below. The chute is parallel to the x: plane. Report a P Neglect the size of the box and the winch. The box is the distance up the chute from point C.Explanation / Answer
coordinates of different points are:
C: (130,100,0) in
D: (0,100,55) in
B: (-45,0,130) in
distance CD=sqrt((130-0)^2+(100-100)^2+(0-55)^2)=141.16 in
distance AC=(1/4)*distance CD=35.289 in
angle made by CD with xy plane=arctan(55/130)=22.932 degrees
then coordinates of A=(130-35.289*cos(22.932), 100,35.289*sin(22.932))
=(97.5,100,13.75) in
direction of AB=(-45,0,130)-(97.5,100,13.75)=(-142.5,-100,116.25)
unit vector along AB=(-142.5,-100,116.25) / length of AB
=(-0.68073,-0.47771,0.55534)
vector along CD=(130,100,0)-(0,100,55)=(130,0,-55)
unit vector along CD=vector along CD/distance CD
=(0.92097,0,-0.38964)
if force in cable AB is F in magnitude,
vector notation force in AB=F*(-0.68073,-0.47771,0.55534)
component along CD=dot product of force vector and unit vector along CD
=0.84331*F
hence 0.84331*F=370
==>F=438.75 lb