In order to move a wrecked truck, two cables are attached at A and pulled by...
In order to move a wrecked truck, two cables are attached at A and pulled by winches B and C as shown. Knowing that the tension is 10 kN in cable AB and 7.5 kN in cable AC, determine the magnitude and direction of the resultant of the forces exerted at A by the two cables.
Fig. P2.135
Homework Answers
Draw the free body diagram.
Write the coordinates of the points.
Calculate the position vector of 
.
Calculate the unit vector of 
.
Substitute 
for 
.
Write the vector form for the tension in the cable 
.
Here, 
is the tension in the cable 
.
Substitute 
for 
and 
for 
.
Calculate the position vector of 
.
Calculate the unit vector of 
.
Substitute 
for 
.
Write the vector form for the tension in the cable 
.
Here, 
is the tension in the cable 
.
Substitute 
for 
and 
for 
.
Calculate the resultant force acting at point
by using the following relation: 
Substitute 
for 
and 
for 
.
Calculate the magnitude of the resultant by using the following relation:
Therefore, the magnitude of the resultant is 
.
Calculate the angle made by the resultant force with the 
axis.
Substitute 
for 
and 
for 
.
Therefore, the angle made by the resultant force with the 
axis is 
.
Calculate the angle made by the resultant force with the 
axis.
Substitute 
for 
and 
for 
.
Therefore, the angle made by the resultant force with the 
axis is 
.
Calculate the angle made by the resultant force with the 
axis.
Substitute 
for 
and 
for 
.
Therefore, the angle made by the resultant force with the 
axis is 
.
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