arch 207 (plate 1)\nsolve the following problems. write your final answer in the space provided. good…

arch 207 (plate 1)\nsolve the following problems. write your final answer in the space provided. good luck.\nnote: use 3 decimal places in rounding off decimals if necessary.\nsituation 1. if the magnitude of the resultant force is to be 500 n, directed along the positive y - axis, determine the magnitude of force f and its direction θ.\nsituation 2. if the resultant force acting on the support is to be 1200 lb, directed horizontally to the right, determine the force f in rope a and the corresponding angle θ.\nsituation 3. if the mass of cylinder c is 40 kg, determine the mass of cylinder a in order to hold the assembly in the position shown.\nsituation 3. the members of a truss are pin - connected at joint o. determine the magnitude of f1 and its angle θ for equilibrium. set f2 = 6 kn.\nsituation 4. determine the reactions at the supports.\nsituation 5. determine the force in each member of the truss. state if the members are in tension or compression.

arch 207 (plate 1)\nsolve the following problems. write your final answer in the space provided. good luck.\nnote: use 3 decimal places in rounding off decimals if necessary.\nsituation 1. if the magnitude of the resultant force is to be 500 n, directed along the positive y - axis, determine the magnitude of force f and its direction θ.\nsituation 2. if the resultant force acting on the support is to be 1200 lb, directed horizontally to the right, determine the force f in rope a and the corresponding angle θ.\nsituation 3. if the mass of cylinder c is 40 kg, determine the mass of cylinder a in order to hold the assembly in the position shown.\nsituation 3. the members of a truss are pin - connected at joint o. determine the magnitude of f1 and its angle θ for equilibrium. set f2 = 6 kn.\nsituation 4. determine the reactions at the supports.\nsituation 5. determine the force in each member of the truss. state if the members are in tension or compression.

Answer

Explanation:

Situation 1:

Step1: Resolve forces in x - direction

For equilibrium in x - direction, $\sum F_x=0$. The 700 N force has an x - component of $700\cos15^{\circ}$ and the force $F$ has an x - component of $-F\sin\theta$. So, $700\cos15^{\circ}-F\sin\theta = 0$.

Step2: Resolve forces in y - direction

For equilibrium in y - direction, $\sum F_y = 500$. The 700 N force has a y - component of $- 700\sin15^{\circ}$ and the force $F$ has a y - component of $F\cos\theta$. So, $F\cos\theta-700\sin15^{\circ}=500$. From the first equation $F\sin\theta=700\cos15^{\circ}\approx700\times0.966 = 676.2$. From the second equation $F\cos\theta=500 + 700\sin15^{\circ}\approx500+700\times0.259=500 + 181.3=681.3$. Dividing the first by the second: $\tan\theta=\frac{676.2}{681.3}\approx0.9925$, so $\theta=\arctan(0.9925)\approx44.7^{\circ}$. $F=\frac{676.2}{\sin\theta}=\frac{676.2}{\sin(44.7^{\circ})}\approx960.997$ N.

Situation 2:

Step1: Resolve forces in x - direction

For equilibrium in x - direction, $\sum F_x = 1200$. The 900 lb force has an x - component of $900\cos60^{\circ}$ and the force $F$ has an x - component of $F\cos\theta$. So, $F\cos\theta+9[Client Connection Error]