A block and tackle pulley arrangement has 6 pulleys in which an effort of 50N supports a load of 200N, calculate the efficiency of the machine

1. Analyze the question

We are given a block and tackle system with:

• Number of pulleys ($n$) = 6
• Effort ($E$) = 50 N
• Load ($L$) = 200 N
• We need to find the Efficiency ($\eta$) of the machine.

2. Explain the concept

Efficiency ($\eta$) is the ratio of the Mechanical Advantage (MA) to the Velocity Ratio (VR), expressed as a percentage.

• Mechanical Advantage (MA) = $\frac{\text{Load}}{\text{Effort}}$
• Velocity Ratio (VR) = For a block and tackle system, the VR is equal to the total number of pulleys ($n$) in the system.
• Efficiency ($\eta$) = $\frac{\text{MA}}{\text{VR}} \times 100\%$

3. Show the solution

Step 1: Calculate the Mechanical Advantage (MA)

Step 2: Identify the Velocity Ratio (VR) In a block and tackle system, the velocity ratio is equal to the number of pulleys.

Step 3: Calculate the Efficiency ($\eta$)

4. Identify the answer

Comparing our result to the given options, 66.7% matches option C.

5. Exam Tip

Always remember that for any machine, the Mechanical Advantage is always less than the Velocity Ratio due to friction. If you calculate an efficiency greater than 100%, you know you have swapped your MA and VR! Also, for block and tackle systems, the number of pulleys is your best friend for finding the VR quickly.