Finding Lever Lengths With Overall Mechanical Advantage

[Wolfowitz]

Homework Statement

If the mechanical advantage of a lever is, let's 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?

 

[ehild]

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

 

[Wolfowitz]

Then how would you isolate the load arm?

 

[Wolfowitz]

11 * load arm = effort arm + load arm?
load arm = effort arm + load arm / 11?

 

[ehild]

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