Solving a Truss: Methodial of Joints

[NoobeAtPhysics]

Homework Statement

The truss is suspended by two pin joints. Each segment is 3 m wide and 4 m high. The applied force is F = 6 N. What is the force in member 10? Include the sign for tension (positive) or compression (negative).

Homework Equations

T=rf
sum of forces = 0

The Attempt at a Solution

On the far end joint for the Y direction

0=-6-F_seven * sin(53.13) [53.13 becaue arctan(4/3)
F_seven = -21.9344

joint on right of 10 in x direction

0=F_seven*cos(90-53.13)-F_ten
=> F_ten =-17.5 N


Please help me solve this..

 

[haruspex]

You can get there by writing out equations for every joint, but there's an easier way here.
Just consider the truss as three components: the rigid triangle of 6, 7, and 14; the member 10; and everything else as a rigid assembly. Draw that and see what equations you can find.

Spoiler

(Hint: considering moments about a certain joint will help.)

 

[PhanthomJay]

Homework Statement

The truss is suspended by two pin joints. Each segment is 3 m wide and 4 m high. The applied force is F = 6 N. What is the force in member 10? Include the sign for tension (positive) or compression (negative).

Homework Equations

T=rf
sum of forces = 0

The Attempt at a Solution

On the far end joint for the Y direction

0=-6-F_seven * sin(53.13) [53.13 becaue arctan(4/3)
F_seven = -21.9344

Your equation is correct but your Math is way off.

joint on right of 10 in x direction

0=F_seven*cos(90-53.13)-F_ten
=> F_ten =-17.5 N

looks like you cosined when you should have sined.
Do you understand the minus sign? It is easier to use method of sections to find force in member 10, as haruspex pointed out. If using method of joints, you should take advantage of the 3-4-5 right triangle to get member forces and components instead of getting bogged down in the trig.







Please help me solve this..[/QUOTE]

 

[NoobeAtPhysics]

Thank you for the responses. I ended up just asking my teacher because I was confused.

 

[Nickie]

I would approach this problem by first identifying the known values and variables, and then using the principles of statics and the method of joints to solve for the unknown force in member 10. The given information states that the truss is suspended by two pin joints, and each segment is 3 m wide and 4 m high. The applied force, F, is 6 N.

Using the method of joints, we can start by analyzing the forces acting on the far end joint in the Y direction. We know that the sum of forces in the Y direction must equal 0, since the truss is in equilibrium. Therefore, we can set up the equation:

0 = -6 - F_seven * sin(53.13)

We use the negative sign for the applied force, F, because it is acting downwards in the negative Y direction. We also use the sine function because the angle between the applied force and the vertical segment is 53.13 degrees (as calculated using arctan(4/3)). Solving for F_seven, we get -21.9344 N.

Next, we can analyze the forces acting on the joint to the right of member 10 in the X direction. Again, the sum of forces in the X direction must equal 0. Therefore, we can set up the equation:

0 = F_seven * cos(90-53.13) - F_ten

We use the cosine function because the angle between F_seven and the horizontal segment is 90-53.13 degrees. Solving for F_ten, we get -17.5 N.

Therefore, the force in member 10 is -17.5 N, indicating that it is in compression. This means that the member is being pushed inward, towards the joint. It is important to include the negative sign to indicate the direction of the force and whether it is in tension (positive) or compression (negative).

In summary, the force in member 10 is -17.5 N, indicating that it is in compression. The method of joints is a useful tool for solving truss problems and can be applied to more complex truss structures as well.