Question

A lever acts like a fulcrum to help lift heavy objects. The formula for the placement of the fulcrum is f1 · d1 = f2 · d2 where f1 = force applied at one end, d1 = distance of the first force from the fulcrum, f2 = force applied at the other end, and d2 = distance of the second force from the fulcrum. Rewrite this formula to solve for d1. Show all steps in your work.

Answer 1

f1 · d1 = f2 · d2
Divide both sides by f1:
\( f1 · d1 /f1= f2 · d2/f1\)
\( \cancel{f1} · d1 /\cancel{f1}= f2 · d2/f1\)

Answer 2

So then the answer would be D1=F2*D2?

Answer 3

Divide the right side by f1 and you're done.

Answer 4

So D1=D2?
I'm super confused

Answer 5

So my last step above was:
$$
\cancel{f1} · d1 /\cancel{f1}= f2 · d2/f1
$$
After cancellations, we have:
$$
d1 =\cfrac{ f2 \times d2}{f1}
$$

Answer 6

Okay
So is that my answer or do I need to simplify it down... even though I'm not really sure how I would do that in this equation...

Answer 7

If you know the numbers for f1,f2 and d2 you can plug them in to get d1; otherwise, no further simplification is possible. The only step required here is isolation of the variable d1, which we did above by dividing both sides by f1. We divide BOTH sides by f1 because, whatever you do to one side, you MUST do to the other.

Answer 8

Okay. The question never gave any numbers to plug in so thanks! :) I really appreciate it!

Answer 9

Not a problem. I'm happy that you asked further questions, I appreciate that. Take care.

Answer 10

You too! :)

Answer 11

Can you help me on another question as well?

Answer 12

sure