Question About Forces Using Unit Vectors

[imapeiceofwod]

OK here's the problem. I am completely unsure how to solve it my teacher never even did an example like this before.

The total force exerted on the top of the mast B by the sailboat's forestay AB and backstay BC is 180i- 820j (N). What are the magnitudes of the forces exerted at B by the cables AB and BC?

A(0,1.2)
B(4,13)
C(9,1)

Any help please and thank you

 

[Andrew Mason]

OK here's the problem. I am completely unsure how to solve it my teacher never even did an example like this before.

The total force exerted on the top of the mast B by the sailboat's forestay AB and backstay BC is 180i- 820j (N). What are the magnitudes of the forces exerted at B by the cables AB and BC?

A(0,1.2)
B(4,13)
C(9,1)

Any help please and thank you

i represents the unit vector in the horizontal direction and j represents the unit vector in the vertical direction. So the force is 180 N in the + i direction and 820 N in -j (or downward) direction.

First of all, draw a diagram of the mast and cables. Then draw a vector diagram of the forces of the cables (this is not a free-body diagram because we are not concerned with all the forces - the forces exerted by the mast and boat and gravity, for example). Write out the equations for downward and lateral force. To do this you must resolve the components of the cable tensions in the i and j directions.

AM

 

[imapeiceofwod]

Question About Unit Vectors

OK here's the problem. I am completely unsure how to solve it my teacher never even did an example like this before.

The total force exerted on the top of the mast B by the sailboat's forestay AB and backstay BC is 180i- 820j (N). What are the magnitudes of the forces exerted at B by the cables AB and BC?

A(0,1.2)
B(4,13)
C(9,1)

Any help please and thank you

here's what i got so far. I drew i diagram of the situation drawing and drew the vectors. I figured out Fab=(4i,11.8j) and Fbc=(5i,-12j)

Then i found the total force in the i direction which is 9i and the total force in the j which is 0.2j .

I know that the total force in the i direction is suppose to be 180i but i got 9i for the total force. Any help?

 

[Andrew Mason]

OK here's the problem. I am completely unsure how to solve it my teacher never even did an example like this before.

The total force exerted on the top of the mast B by the sailboat's forestay AB and backstay BC is 180i- 820j (N). What are the magnitudes of the forces exerted at B by the cables AB and BC?

A(0,1.2)
B(4,13)
C(9,1)

Any help please and thank you

here's what i got so far. I drew i diagram of the situation drawing and drew the vectors. I figured out Fab=(4i,11.8j) and Fbc=(5i,-12j)

This is not correct.

Let the tension in AB be T_AB and the components in the directions of the unit vectors be $T_{ABi},T_{ABj}$. The following applies:

$$\vec{T_{AB}} = T_{ABi}\hat i + T_{ABj}\hat j$$

$$T_{AB}^2 = T_{ABi}^2 + T_{ABj}^2$$

AM