Finding Lever Lengths With Overall Mechanical Advantage

  • Thread starter Wolfowitz
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  • #1
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Homework Statement


If the mechanical advantage of a lever is, lets say, 10; the forces pushing down on the effort arm equate to 100kg and the forces pushing down on the load arm equate to 1000kg and the lever itself is 5 meters, how do we go about finding the individual arm lengths (i.e. the length of the effort/lever arm).


Homework Equations





The Attempt at a Solution


Here's what I'm thinking.
MA = 10
Simultaneously,
MA = Effort Arm / Load Arm
10 = Effort Arm / Load Arm
Load Arm * 10 = Effort Arm
Load Arm + Load Arm * 10 = Effort Arm + Load Arm
2Load Arm * 10 = 5
2Load Arm = 5/10
Load Arm = 0.5

True or false?
 
Last edited:

Answers and Replies

  • #2
ehild
Homework Helper
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The Attempt at a Solution


Here's what I'm thinking.
MA = 10
Simultaneously,
MA = Effort Arm / Load Arm
10 = Effort Arm / Load Arm
Load Arm * 10 = Effort Arm
Load Arm + Load Arm * 10 = Effort Arm + Load Arm
It is correct up to here, but how did you get the following?
2Load Arm * 10 = 5
1(load arm)+10 (load arm) = ? (load arm) ?

If you add one apple to 10 apples will you get 2*10 =20 apples?

ehild
 
  • #3
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Then how would you isolate the load arm?
 
  • #4
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11 * load arm = effort arm + load arm?
load arm = effort arm + load arm / 11?
 
  • #5
ehild
Homework Helper
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1,901
11 * load arm = effort arm + load arm?
load arm = effort arm + load arm / 11?
No, it is wrong. Division by 11 in your formula refers to the load arm only.
Use parentheses: length of load arm =(length of effort arm+length of load arm)/11, that is, 5/11 m.

Remember the hierarchy of operations: First perform everything in the parentheses. Otherwise perform multiplication/division first then the addition/subtraction.

ehild
 

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