Based on the detailed analysis of the pulley system diagram, here is the solution to find the "FINAL EFFORT" required to lift the 100N load.
Solution
The "FINAL EFFORT" required is
25 Newtons (N).
---
Explanation
To solve this problem, we need to determine the
mechanical advantage (MA) of the pulley system. The mechanical advantage tells us how much the system multiplies the input force. It is calculated by counting the number of rope segments that are actively supporting the movable block (the part that holds the load).
The formula for mechanical advantage in an ideal pulley system is:
`MA = Number of supporting rope segments`
The relationship between the load, effort, and mechanical advantage is:
`Effort = Load / MA`
Step 1: Counting the Supporting Rope Segments
By carefully tracing the path of the rope in the image, we can identify all the segments that are pulling up on the movable block assembly:
1.
Segment 1: The rope comes down from the fixed block and goes around the top pulley of the movable block.
2.
Segment 2: After going around the top pulley, the rope goes down and around the middle pulley of the movable block.
3.
Segment 3: After going around the middle pulley, the rope goes down and around the bottom pulley of the movable block.
4.
Segment 4: After going around the bottom pulley, the rope goes back up and is anchored to the frame of the *movable* block itself (this is a common configuration). This final segment also pulls up on the movable block.
This gives us a total of
four (4) rope segments supporting the movable block.
Step 2: Calculating the Mechanical Advantage
Since there are 4 supporting rope segments, the mechanical advantage is:
`MA = 4`
Step 3: Calculating the Final Effort
We are given that the load is 100N. Using the formula:
`Effort = Load / MA`
`Effort = 100 N / 4`
`Effort = 25 N`
Therefore, the "FINAL EFFORT" required to lift the 100N load is
25 N.
The labels (e1), (e2), (e3), and (e4) in the diagram likely correspond to these four supporting segments, confirming our count.
Parent Tip: Review the logic above to help your child master the concept of mechanical advantage of a pulley worksheet.
