Calculating the Mechanical Advantage for an Axle Practice ... - Free Printable

Let’s go step by step to understand what this image is showing and how to use it.

The image displays six different simple machines, each with a formula for calculating its Ideal Mechanical Advantage (IMA). IMA tells us how much a machine multiplies your input force — basically, how much easier the machine makes the job.

We’ll go through each one briefly so you know what they are and how their IMA formulas work:

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1. Lever (top left)
- You push down on one end (effort force Fe), and it lifts something on the other end (resistance force Fr).
- The distances from the fulcrum (pivot point) are Le (effort arm) and Lr (resistance arm).
- Formula: IMA = Le / Lr
→ Longer effort arm = more advantage.

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2. Inclined Plane (top right)
- A ramp. You push an object up the slope instead of lifting it straight up.
- L = length of the ramp, h = height it rises.
- Formula: IMA = L / h
→ Longer, gentler ramp = less force needed.

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3. Wheel and Axle (middle left)
- Like a doorknob or steering wheel. You turn the big wheel (radius R), which turns the small axle (radius r).
- Formula: IMA = R / r
→ Bigger wheel compared to axle = more advantage.

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4. Wedge (middle right)
- Like a knife or axe blade. You push it in (Fe), and it splits things apart.
- L = length of wedge, t = thickness at the base.
- Formula: IMA = L / t
→ Longer, thinner wedge = more advantage.

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5. Pulley System (bottom left)
- Shows two setups: one pulley (N=1) and two pulleys (N=2).
- N = number of rope segments supporting the load.
- Formula: IMA = N
→ More ropes holding the weight = less force you need to pull.

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6. Screw (bottom right)
- A screw is like an inclined plane wrapped around a cylinder.
- L = length of the handle you turn, P = pitch (distance between threads).
- Formula: IMA = 2πL / P
→ Longer handle or finer threads (smaller P) = more advantage.

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Now, since there’s no specific question asked (like “calculate IMA for X”), but the user uploaded this as a task, we can assume the goal is to understand and recognize these machines and their IMA formulas.

But wait — maybe the real task is hidden? Let me check again...

Actually, looking closely — this looks like a reference sheet or study guide. There’s no actual problem to solve numerically. So perhaps the student is supposed to learn these formulas and be able to apply them later.

However, since the instruction says “Solve the problem accurately,” and there’s no explicit problem, I think the best approach is to summarize what each machine does and give the correct IMA formula for each — that way, if the student gets a question like “What’s the IMA of a lever with Le=60cm and Lr=20cm?” they’ll know how to plug in numbers.

But again — no numbers given. Hmm.

Wait — maybe the task is just to list all six machines and their IMA formulas correctly? That would make sense as a homework assignment.

Let me double-check each formula against standard physics knowledge:

✔ Lever: IMA = Le / Lr → Correct
✔ Inclined Plane: IMA = L / h → Correct
✔ Wheel & Axle: IMA = R / r → Correct
✔ Wedge: IMA = L / t → Correct
✔ Pulley: IMA = N → Correct (for ideal case)
✔ Screw: IMA = 2πL / P → Correct

All formulas match standard textbook definitions.

So if the task is to identify and write down the IMA formulas for each simple machine shown, then here’s the complete answer:

Final Answer:
Lever: IMA = Le / Lr
Inclined Plane: IMA = L / h
Wheel and Axle: IMA = R / r
Wedge: IMA = L / t
Pulley System: IMA = N
Screw: IMA = 2πL / P