Efficiency Equation Rearrangement & Calculation Examples

Learn how to rearrange and calculate efficiency using the efficiency equation in machines. Understand the concept of efficiency, its limits, related equations, and work output calculations with step-by-step examples.

• Efficiency
• Equation
• Calculation
• Machines
• Examples

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Uploaded on Feb 19, 2025 | 0 Views

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Presentation Transcript

1. Rearranging Efficiency Equation and teach examples

2. Learning Objectives I can mathematically rearrange the efficiency equation. I can calculate efficiency using the formula.

3. Efficiency The percentage of the work input that becomes work output in a machine. ???? ?????? (??) ???? ????? (??)x 100% ??? = Efficiency can never be greater than 100 %. Why? - Some work is always needed to overcome friction.

4. Formula Representation Formula Eff = ?? ?? Represents Units x 100%Eff = Efficiency Wo= Work output Joules (J) Wi= work input Percent Joules (J)

5. Solve for Work Output (W Solve for Work Output (Wo o) ) Step 1 Multiply both sides by Wi- work input Eff = ?? (Wi) (Wi) ?? Wo= Wi(Eff)

6. Solve for Work Input (W Solve for Work Input (Wi i) ) Step 1 Multiply both sides by Wi - work input (Wi) Eff = ?? (Wi) ?? WiEff = Wo Step 2 Divide by Eff - efficiency on both sides. __ Eff __ Eff Wi = ?? ???

7. Efficiency Related Equations Efficiency Eff = ?? Work Output Work Input Wi = ?? ?? x 100% Wo = Wi(Eff) ???

8. Calculation Example #1 1. You have just designed a machine that uses 1000J of work from a motor for every 800J of useful work the machine supplies. What is the efficiency of your machine? Given/ Unknown Eff = Wo = Wi = Work ? 800J 1000J 800J 1000Jx 100 Eff =Wo Eff = 80% Eff = Wix 100

9. Calculation Example #2 2. If a machine has a efficiency of 40%, and you do 1000J of work on the machine, what will be the work output of the machine? 1st take efficiency percent and put into a decimal. Given/ Unknown Eff = Wo = Wi = Work To convert percent to decimal move the decimal 2 places to the left. So 40% will be .4 40% or .4 ? 1000J Wo = Eff x Wi Wo = (.4)(1000J) Wo = 400J

10. Calculation Example #3 3. Using a lever, a person applies 40 newtons of force and moves the lever 1 meter. This moves a 200 newton boulder at the other end by .1 meters. What is the efficiency of the lever? Given/ Unknown Eff = Fr = Dr = Fe = De = 1m 1st calculate the work output and work input. Work ? Wo = (200N)(.1m) Wi = (40N)(1m) Wo = 20J Wi = 40J Wo = Fr x Dr Wi = Fe x De 200N .1m 40N 20J 40Jx 100 Eff =Wo Eff = 50% Eff = Wix 100