Let’s solve each problem one by one using the formula for Ideal Mechanical Advantage (IMA):
IMA = Effort Distance ÷ Resistance Distance
Or, when dealing with pulleys or inclined planes, we can use other forms like:
- For pulleys: IMA = number of rope segments supporting the load
- For inclined plane: IMA = length of slope ÷ height
- For wheel and axle: IMA = radius of wheel ÷ radius of axle (or diameter if both are given)
- For screw: IMA = circumference of handle ÷ pitch (but here it’s simplified as distance moved by effort ÷ distance moved by load)
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Problem 1:
A man pulls 10 m of rope to raise a package 2 m.
→ Effort Distance = 10 m
→ Resistance Distance = 2 m
→ IMA = 10 ÷ 2 =
5
✔ Answer:
5
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Problem 2:
Wheelchair goes up ramp 9 m long, rises 3 m high.
→ This is an inclined plane.
→ IMA = length of ramp ÷ height = 9 ÷ 3 =
3
✔ Answer:
3
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Problem 3:
Barber pushes wheelchair up 6 m long ramp to top of 1.5 m high step.
→ Again, inclined plane.
→ IMA = 6 ÷ 1.5 =
4
✔ Answer:
4
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Problem 4:
Pulley system — count number of ropes supporting the load.
Looking at the diagram (even though not visible, based on standard problems), if it says “simply counting the number of pulleys” and answer is written as “2 pulleys = 2”, that likely means 2 rope segments support the load → IMA = 2.
But wait — sometimes people confuse number of pulleys with number of supporting ropes. In many basic diagrams, if there are 2 pulleys arranged so that 2 ropes hold the load, then IMA = 2.
Given the handwritten note says “2 pulleys = 2”, we’ll go with that.
✔ Answer:
2
*(Note: If this were a more complex setup, we’d need to see the diagram, but based on context, 2 is correct.)*
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Problem 5:
Man jacks car — moves jack handle 30 cm, total lift is 1 cm.
→ Effort Distance = 30 cm
→ Resistance Distance = 1 cm
→ IMA = 30 ÷ 1 =
30
✔ Answer:
30
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Problem 6:
Wedge driven into log — wedge moves 0.2 m, log splits 0.05 m.
→ Effort Distance = 0.2 m
→ Resistance Distance = 0.05 m
→ IMA = 0.2 ÷ 0.05 =
4
Wait — the handwritten answer says “20/5 = 4”. That’s correct too: 0.2 / 0.05 = 20/5 = 4.
✔ Answer:
4
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Problem 7:
Block and tackle with 4 pulleys — count supporting ropes.
In a typical block and tackle with 4 pulleys, if it’s set up so that 4 rope segments support the load, then IMA = 4.
Handwritten note says “4 pulleys x 4” — probably meaning IMA = 4.
✔ Answer:
4
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Problem 8:
Jackwhew (probably typo for “jack” or “screw”) with 20 cm handle, side of compound is 2 cm.
This seems to be a screw or lever system. The note says “20/2 = 10”.
If the handle moves in a circle (circumference), but they’re simplifying it as effort distance = 20 cm, resistance distance = 2 cm → IMA = 20 ÷ 2 =
10
✔ Answer:
10
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Now let’s compile all answers:
1. 5
2. 3
3. 4
4. 2
5. 30
6. 4
7. 4
8. 10
Final Answer:
1. 5
2. 3
3. 4
4. 2
5. 30
6. 4
7. 4
8. 10
Parent Tip: Review the logic above to help your child master the concept of mechanical advantage worksheet.
