Solve Statics Problem: Find Forces on Rod at Hinge & Peg

[Menisto]

A 30 kg rod one meter long is supported by a hinge A hanging from the ceiling. The rod rests on a peg "C" at a point .7 meters along the rod away. A vertical force of 1000 N is applied to the end of the rod. The rod rests at an angle of 30 degress from the vertical.

Find the x and y components of the forces on the rod at the hinge point A and the peg C.

To solve this I set up equilibrium equations.

A(x) + C(x) = 0 (force of hinge in x direction, force of peg in x direction)

A(y) + C(y) -Mg - 1000 = 0

With an axis through the peg and counting counterclockwise as positive:

.7[A(x) sin 60 -A(y) sin 30] + .2(Mg sin 30) - .3(1000 sin 30) = 0

But there are 4 unknowns here and only three equations to solve them. I don't see any way I could get a relation between two of the quantities for the forth equation.

 

[OlderDan]

A 30 kg rod one meter long is supported by a hinge A hanging from the ceiling. The rod rests on a peg "C" at a point .7 meters along the rod away. A vertical force of 1000 N is applied to the end of the rod. The rod rests at an angle of 30 degress from the vertical.

Find the x and y components of the forces on the rod at the hinge point A and the peg C.

To solve this I set up equilibrium equations.

A(x) + C(x) = 0 (force of hinge in x direction, force of peg in x direction)

A(y) + C(y) -Mg - 1000 = 0

With an axis through the peg and counting counterclockwise as positive:

.7[A(x) sin 60 -A(y) sin 30] + .2(Mg sin 30) - .3(1000 sin 30) = 0

But there are 4 unknowns here and only three equations to solve them. I don't see any way I could get a relation between two of the quantities for the forth equation.

It would be helpful if you would provide a more accurate description of the problem. For example, where is point A? For C, ".7 meters along the rod away" away from what? Is the 1000N vertical force upward or downward?

How about something like this (based on a pure guess of the situation):
The rod is tilted at 30 degrees to the vertical. The 1000N force is applied downward at the lower end of the rod. The rod is suspended by a hinge at point A in the center of the rod. The rod rests on a peg C located 0.7 meters from the high end of the rod, etc. Be specific and be accurate.

 

[Menisto]

Sorry, I tried to upload a picture but it was too large.

The 1000 N force is directed downward at the end of the rod. The hinge is located at the opposite end, attached to the ceiling. The rod is hanging 30 degrees to the right of the vertical and sitting on a peg located at point C. Point C is .7 m from the hinge point A (.3 m from the applied force B on the right, .2 meters from the center of the rod on the left.)

 

[OlderDan]

Sorry, I tried to upload a picture but it was too large.

The 1000 N force is directed downward at the end of the rod. The hinge is located at the opposite end, attached to the ceiling. The rod is hanging 30 degrees to the right of the vertical and sitting on a peg located at point C. Point C is .7 m from the hinge point A (.3 m from the applied force B on the right, .2 meters from the center of the rod on the left.)

Much better. Thank you. Perhaps you are only missing the fact that since the peg is not connected to the rod, the net force acting on the rod at C must be normal to the rod. If that solves your problem, then you have the other things correct. If not, I (or someone else) will take a closer look at your equations.

 

[Menisto]

Thank you! That works...