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

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In summary: I was able to solve for the x and y components of the force at C by using the fact that the net force must be normal to the rod. In summary, a 30 kg rod, one meter long, is supported by a hinge A attached to the ceiling. The rod rests on a peg C located at .7 meters along the rod away from the hinge. A vertical force of 1000 N is applied to the end of the rod, causing it to rest at a 30 degree angle from the vertical. To solve for the x and y components of the forces at the hinge and peg, equilibrium equations were set up. The net force at C must be normal to the rod, allowing for the solution of the unknowns in
  • #1
Menisto
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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.
 
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  • #2
Menisto said:
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.
 
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  • #3
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.)
 
  • #4
Menisto said:
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.
 
  • #5
Thank you! That works...
 

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

What is a statics problem?

A statics problem involves analyzing the forces acting on a stationary object or system. It typically involves finding the equilibrium of forces and moments in order to determine the unknown forces or reactions.

What is the purpose of finding forces on a rod at a hinge and peg?

The purpose of solving for the forces on a rod at a hinge and peg is to understand the stability and structural integrity of the system. It can also help in designing and optimizing the support structure for the rod.

What information is needed to solve a statics problem for a rod at a hinge and peg?

The information needed includes the dimensions and geometry of the rod, the location of the hinge and peg, the applied external forces, and any known forces or reactions at the hinge and peg.

What are the steps to solve a statics problem for a rod at a hinge and peg?

The steps to solve a statics problem for a rod at a hinge and peg are:

1. Draw a free-body diagram of the rod, showing all the known and unknown forces acting on it.

2. Apply the equations of equilibrium to the free-body diagram, setting the sum of forces and moments equal to zero.

3. Solve for the unknown forces and reactions using algebraic equations.

4. Check the solution by ensuring that the sum of forces and moments are still equal to zero.

What are some common mistakes when solving statics problems for a rod at a hinge and peg?

Some common mistakes include forgetting to include all the forces in the free-body diagram, using incorrect signs or directions for the forces, and neglecting to properly sum the forces and moments to zero. It is also important to consider the geometry and dimensions of the rod accurately, as well as the type of support at the hinge and peg.

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