Ch - Simple Machines. Numericals

⚙️ Lever Numericals - Questions & Solutions

📌 Useful Formulas:

1. Mechanical Advantage (M.A) = Effort Arm ÷ Load Arm
2. M.A = Load ÷ Effort
3. Effort = Load ÷ M.A
4. Load = Effort × M.A

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1. A lever used to lift a heavy box has an effort arm of 2 m and a load arm of 0.5 m. What is the mechanical advantage of the lever? What will be the effort required to overcome the load of 8 N?

Step 1: Formula → M.A = Effort Arm ÷ Load Arm
M.A = 2 ÷ 0.5 = 4

Step 2: Effort = Load ÷ M.A
Effort = 8 ÷ 4 = 2 N

✅ Answer: M.A = 4; Effort = 2 N

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2. A worker uses a crowbar to lift a manhole cover weighing 45 N. The effort arm of the lever is 50 cm long and the load arm is 10 cm long. What is the mechanical advantage of the bar? How much effort is applied?

Step 1: Formula → M.A = Effort Arm ÷ Load Arm
M.A = 50 ÷ 10 = 5

Step 2: Effort = Load ÷ M.A
Effort = 45 ÷ 5 = 9 N

✅ Answer: M.A = 5; Effort = 9 N

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3. A lever has an effort arm of 3 m and a load arm of 2 m. What is the M.A? How much load can be lifted if the input force is 3 N?

Step 1: Formula → M.A = Effort Arm ÷ Load Arm
M.A = 3 ÷ 2 = 1.5

Step 2: Load = Effort × M.A
Load = 3 × 1.5 = 4.5 N

✅ Answer: M.A = 1.5; Load = 4.5 N

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4. If an output force is double the input force, what is the mechanical advantage?

Step 1: Formula → M.A = Load ÷ Effort
Here, Load = 2 × Effort
M.A = 2E ÷ E = 2

✅ Answer: M.A = 2

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5. The M.A of a lever is 0.4. If the load is 2 N, calculate the effort needed.

Step 1: Formula → Effort = Load ÷ M.A
Effort = 2 ÷ 0.4
Effort = 5 N

✅ Answer: Effort = 5 N