The members of a truss are pin connected at joint O. (Figure 1) ** If you can ex

Question

The members of a truss are pin connected at joint O. (Figure 1)

**If you can explain the forces in the x and the y direction using trig functions, can you please do so. This is the part that confuses me the most. Thanks**

Part A Determine the magnitude of F1 for equilibrium. Set F2 = 5.8 kN .

Express your answer to three significant figures and include the appropriate units.

F1 =

Part B Determine the angle ? for equilibrium.

Express your answer to three significant figures and include the appropriate units.

? =

Explanation / Answer

Resolve all forces into components.

Always remeber, Component on to any axis is the magnitude times cosine of the angle it makes with axis

So if it makes theta with x axis then component will be F cos(theta). So angle with y axis will be 90 - theta.

So component in y is F cos( 90 -theta) = F sin (theta). That is how sin (theta) came in to picture. It is always cos of angle with axis.

Now in this problem.

For equilibrium in components. Resolve all components.

F1 Cos( -theta) + F2 Cos(20) + 5 * cos( 150) - 7 * (3/5)   [ this is because force resolved on to negative x axis) with cos ( angle of 7KN) force is 3/5

So F1 Cos( -theta) +5.8* Cos(20) + 5 * cos( 150) - 7 * (3/5) = 0 implies F1 cos(-theta) = 3.08

Similarly Y component we have , - F1 Sin(theta) - 7(4/5) + 5 Sin(30) + 5.8 Sin(20) = 0 implies +F1 sin(-theta) = 1.116

So Tan (-theta) = 1.116/3.08

So theta = -19.92 degrees.

Now F1 * cos( 19.92) = 3.08

So F1 = 3.276KN

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