8th Grade Science Mechanical Advantage Worksheet featuring problems on calculating mechanical advantage of various simple machines.

Let's solve each problem step by step using the mechanical advantage (MA) formula:

Mechanical Advantage Formula:

$$
\text{MA} = \frac{\text{Resistance Force (R)}}{\text{Effort Force (E)}}
$$

Alternatively, for levers when distances are given:
$$
\text{MA} = \frac{\text{Distance to Effort}}{\text{Distance to Resistance}}
$$

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1. Screwdriver Problem

- Effort Force (E) = 30 N
- Resistance Force (R) = 90 N

$$
\text{MA} = \frac{90}{30} = 3
$$

✔ Answer: MA = 3

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2. Lever Lifting Rock

- Mass of rock = 800 N → This is the resistance force (R)
- Effort Force (E) = 200 N

$$
\text{MA} = \frac{800}{200} = 4
$$

✔ Answer: MA = 4

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3. Bottle Opener

- Effort Force (E) = 55 N
- Resistance Force (R) = 675 N

$$
\text{MA} = \frac{675}{55} \approx 12.27
$$

(We can leave it as a decimal or fraction.)

✔ Answer: MA ≈ 12.27

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4. Pulley System

- Effort Force (E) = 250 N
- Resistance Force (R) = 1250 N (mass of box in newtons)

$$
\text{MA} = \frac{1250}{250} = 5
$$

✔ Answer: MA = 5

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5. Nutcracker – Given MA, Find Output Force

- Effort Force (E) = 75 N
- MA = 5
- We need to find the Resistance Force (R)

Use:
$$
\text{MA} = \frac{R}{E} \Rightarrow R = \text{MA} \times E = 5 \times 75 = 375 \text{ N}
$$

✔ Answer: Force = 375 N

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6. Lever with MA = 6, Output Force = 1800 N

- MA = 6
- Resistance Force (R) = 1800 N
- Find Effort Force (E)

$$
\text{MA} = \frac{R}{E} \Rightarrow E = \frac{R}{\text{MA}} = \frac{1800}{6} = 300 \text{ N}
$$

✔ Answer: Force = 300 N

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7. Lever with Distances

From diagram:
- Distance from fulcrum to effort = 9 m
- Distance from fulcrum to resistance = 3 m

$$
\text{MA} = \frac{\text{Distance to Effort}}{\text{Distance to Resistance}} = \frac{9}{3} = 3
$$

✔ Answer: MA = 3

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8. Lever with Distances

From diagram:
- Distance from fulcrum to resistance = 5 m
- Distance from fulcrum to effort = 20 m (total length), but wait — let's interpret carefully.

The object is placed 5 m from the fulcrum, and the effort is applied at the end of a 20 m lever. So:

- Distance to resistance = 5 m
- Distance to effort = 20 m

$$
\text{MA} = \frac{20}{5} = 4
$$

✔ Answer: MA = 4

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✔ Final Answers:

1. MA = 3
2. MA = 4
3. MA ≈ 12.27
4. MA = 5
5. Force = 375 N
6. Force = 300 N
7. MA = 3
8. MA = 4

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