What effort will a machine of efficiency 90% apply to a load of 180N if its efforts arm is twice as long as its load arm?

Analyze the question

We have a lever with efficiency 90%, a load of 180 N, and an effort arm twice as long as the load arm. We need the effort applied.

Concept

• Velocity ratio (VR) of a lever = effort arm / load arm
• Mechanical advantage (MA) = Load / Effort
• Efficiency = MA / VR × 100%

Solution

1. VR = effort arm / load arm = 2

2. Efficiency = MA / VR, so 0.90 = MA / 2 MA = 1.8

3. MA = Load / Effort, so Effort = Load / MA = 180 / 1.8 = 100 N

Check: An ideal lever (100% efficient) would need 180 / 2 = 90 N. Because of friction and other losses, more effort is needed, so the answer must be greater than 90 N. 100 N fits. (Check: 90 / 0.9 = 100 N.)

Answer: A. 100 N

Exam tip: Remember the shortcut: Effort = Load / (VR × efficiency). Here that gives 180 / (2 × 0.9) = 100 N. Also, a real machine always needs more effort than the ideal one, so you can quickly eliminate any option below the ideal value (90 N here).