# Solve Statics Problem for Bone Rongeur Machine Force at E

• cyberdeathreaper
In summary, the bone rongeur can be broken down into four free body diagrams, but the equations don't readily give a way to solve for the force at the center of the bone, E. The book indicates that the answer is 133.3 lb, but I was not able to find a way to calculate that using the equations.
cyberdeathreaper
Here's the problem:

"The bone rongeur shown [refer to attachment] is used in surgical procedures to cut small bones. Determine the magnitude of the forces exerted on the bone at E when two 25-lb forces are applied as shown."

I understand that this "machine" can be broken into 4 free-body diagrams, and then I can use the equilibrium equations on each one to supposedly find the answer. However, my equations don't readily give me a way to solve for the force at E. Any ideas?

Here's all the equilibrium equations I have come up with:
For the top left piece...
$$\sum F_x = 0 = D_x + B_x$$
$$\sum F_y = 0 = F_E + D_y - B_y$$
$$\sum M_D = 0 = -1.2 F_E - 1.6 B_y - 0.45 B_x$$
For the top right piece...
$$\sum F_x = 0 = -B_x + A_x$$
$$\sum F_y = 0 = B_y + A_y - 25$$
$$\sum M_A = 0 = -110 -1.1 B_y + 0.45 B_x$$

It should be obvious that the bottom pieces are symmetric with the top pieces, and similar in their equilibrium equations.

NOTE: The book indicates the answer is 133.3 lb.

#### Attachments

• machine2.jpg
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cyberdeathreaper said:
Here's the problem:

"The bone rongeur shown [refer to attachment] is used in surgical procedures to cut small bones. Determine the magnitude of the forces exerted on the bone at E when two 25-lb forces are applied as shown."

I understand that this "machine" can be broken into 4 free-body diagrams, and then I can use the equilibrium equations on each one to supposedly find the answer. However, my equations don't readily give me a way to solve for the force at E. Any ideas?

Here's all the equilibrium equations I have come up with:
For the top left piece...
$$\sum F_x = 0 = D_x + B_x$$
$$\sum F_y = 0 = F_E + D_y - B_y$$
$$\sum M_D = 0 = -1.2 F_E - 1.6 B_y - 0.45 B_x$$
For the top right piece...
$$\sum F_x = 0 = -B_x + A_x$$
$$\sum F_y = 0 = B_y + A_y - 25$$
$$\sum M_A = 0 = -110 -1.1 B_y + 0.45 B_x$$

It should be obvious that the bottom pieces are symmetric with the top pieces, and similar in their equilibrium equations.

NOTE: The book indicates the answer is 133.3 lb.

You are correct about the symmetry. For the upper and lower halves, each is just a coupled double lever. You can easily calculate the forces at B and C from the applied force and the distance ratios. Then do the same thing to find the force on each side of E.

Last edited:
Can u post a detailed description on how u arrived at the above equations?
You are correct, the four pieces of the instrument would give rise to four free body diagrams. However the final equations that u have got certainly have some components missing. So if u post how u analysed the free body diagrams (if possible do post the free body diagrams u have considered), it would be easier to point out the mistake (if any) u have made or possibly point out what u missed.

-- AI

Okay, I figured out how to get the answer via the couple ratios.
(25)(4.4)/(1.1) = By
(By)(1.6)/(1.2) = FE = 133.3 lb

However, I'm still not understanding how I could arrive at the via the equilibrium equations... attached is my free body diagrams for the top pieces. Any help?

#### Attachments

• machine3.jpg
8.8 KB · Views: 471

## 1. What is statics and why is it important for the bone rongeur machine?

Statics is a branch of mechanics that deals with the analysis of forces and their effects on rigid bodies at rest. It is important for the bone rongeur machine because it helps determine the forces acting on the machine and ensures its stability and efficiency.

## 2. How do you solve a statics problem for the bone rongeur machine at point E?

To solve a statics problem for the bone rongeur machine at point E, you will need to apply the principles of equilibrium, which state that the sum of all forces and moments acting on a body must be equal to zero. This involves identifying all the external forces acting on the machine, breaking them down into their components, and using equations of equilibrium to solve for the unknown forces at point E.

## 3. What are the common forces that act on the bone rongeur machine at point E?

The common forces that act on the bone rongeur machine at point E include the weight of the machine, the force exerted by the surgeon on the handle, and the reaction force from the bone being cut. Other forces to consider may include friction and tension in the cables or springs.

## 4. Can you determine the force at point E using a free body diagram?

Yes, a free body diagram is a useful tool in solving statics problems for the bone rongeur machine at point E. It involves drawing a simplified diagram of the machine, isolating it from its surroundings, and labeling all the external forces acting on it. This allows you to apply the principles of equilibrium and solve for the unknown force at point E.

## 5. How does the force at point E affect the performance of the bone rongeur machine?

The force at point E is an important factor in determining the cutting force and precision of the bone rongeur machine. If the force at point E is too high, it may result in excessive strain on the machine and affect its durability. On the other hand, if the force at point E is too low, it may result in insufficient cutting force, leading to ineffective performance. It is essential to find the optimal force at point E for the best performance of the machine.

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