Find the Cutting Force Generated At A

In summary, the pruner uses a compound leverage mechanism to multiply blade-cutting power. When a force of 26 N is applied to the handles, the cutting force generated at point A is incorrectly determined to be 65 N due to incorrect assumptions about the blade's attachment to the upper handle. After correcting the free body diagrams, it is determined that the correct cutting force at point A is 169 N."
  • #1
gocats741
3
0

Homework Statement



The pruner multiplies blade-cutting power with the compound leverage mechanism.
If F = 26 is applied to the handles, determine the cutting force generated at A . Assume that the contact surface at is smooth.
Hibbler.ch6.p85.jpg

Homework Equations


M = F x d

The Attempt at a Solution



I drew the free body diagram of the upper handle. I took the moment at point B.

M_b = -26N (150 mm) + (Cutting Force) (60 mm) = 0 -> Cutting force = 65 N.
The answer is incorrect. I don't understand how that could be incorrect. There's no other force acting on the upper handle.

I tried looking at the lower handle, but there's point C and D which I can't figure out the FBD for. Please help! I really don't understand what is going on. I've been looking at that picture for half and hour and nothing. Dumb it down for me. I don't need an answer. I just need to know what is missing or going on. Please!
 
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  • #2
gocats741 said:
I drew the free body diagram of the upper handle. I took the moment at point B.

M_b = -26N (150 mm) + (Cutting Force) (60 mm) = 0 -> Cutting force = 65 N.
The answer is incorrect. I don't understand how that could be incorrect.

Hi gocats741, http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif [Broken]

The grey blade is not attached to the upper handle, apart from being free to pivot at point B. Apart from this pivot, the grey blade is acted on by the small grey arm exerting force at point E.
 
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  • #3
Thank you Oxygen. That was what cleared things up for me. I thought it was attached so it threw off all the FBD's. This is what happens when you get assigned problems with tiny pictures.

Here is the work I did to correct the situation:

FBD of the lower handle only including points C, D and G.

Take moments at C

M_c = (26N)(150mm) - Dsin45(25mm) = 0 --> D = 220.617

FBD of only the Gray Blade including only points A, B, and E

Force at E is the same as D but acting in the opposite direction for this FBD

Take moments at pin B

M_b = F_a(60mm) + Dsin45(55mm) +Dcos45(10mm) = 0

Plug in values for D and solve for F_a

F_a = 169 N.

Correct! Thanks!
 

1. What is "Find the Cutting Force Generated at A"?

"Find the Cutting Force Generated at A" is a scientific calculation used to determine the amount of force required to cut or shape a material at a specific point or location, known as point A.

2. Why is it important to know the cutting force at point A?

Knowing the cutting force at point A is crucial in order to properly design cutting tools and processes for specific materials. It helps ensure that the material is not damaged or that the cutting tool is not overloaded, which can lead to inefficient or ineffective cutting.

3. How is the cutting force at point A calculated?

The cutting force at point A is calculated by taking into account various factors such as the material properties, cutting tool geometry, and cutting conditions (e.g. speed, feed rate, depth of cut). These factors are used in mathematical equations to determine the force required to cut the material at point A.

4. What are the units of measurement for cutting force at point A?

The cutting force at point A is typically measured in units of force, such as Newtons (N) or pounds-force (lbf). However, the units may vary depending on the specific equations and units used in the calculation.

5. Can the cutting force at point A be accurately predicted?

Yes, with the proper tools and techniques, the cutting force at point A can be accurately predicted. However, there are many variables that can affect the accuracy of the prediction, such as material properties and cutting conditions, so it is important to use reliable data and methods for the calculation.

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