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Zorluk: OrtaLevers and Fulcrums

A combat engineer uses a 120 cm120 \text{ cm} rigid steel pry bar to lift a 600 N600 \text{ N} concrete block. The pivot point (fulcrum) is placed exactly 30 cm30 \text{ cm} from the block. If the engineer applies a downward force at the far opposite end of the pry bar, what is the effort force required to balance the block?

  1. A
    150 N150 \text{ N}
  2. B
    1800 N1800 \text{ N}
  3. 200 N200 \text{ N}Cevap
  4. D
    2400 N2400 \text{ N}

Cevap

200 N200 \text{ N}
The pry bar acts as a first-class lever. The load arm (dLd_L) is the distance from the fulcrum to the concrete block, which is given as 30 cm30 \text{ cm}. The effort arm (dEd_E) is the distance from the fulcrum to the opposite end of the bar, calculated as the total length minus the load arm (120 cm−30 cm=90 cm120 \text{ cm} - 30 \text{ cm} = 90 \text{ cm}). According to the law of moments, the system is balanced when the effort torque equals the load torque (FE×dE=FL×dLF_E \times d_E = F_L \times d_L). Substituting the known values yields FE×90=600×30F_E \times 90 = 600 \times 30. Solving for FEF_E gives 200 N200 \text{ N}.

Adım Adım Çözüm

1
Identify the lever class and applicable formula.
This is a first-class lever. The principle of moments states FE×dE=FL×dLF_E \times d_E = F_L \times d_L.
To set up the torque equilibrium equation required to find the unknown force.
2
Determine the length of the load arm (dLd_L).
dL=30 cmd_L = 30 \text{ cm}
The load arm is defined as the distance from the fulcrum to the load.
3
Calculate the length of the effort arm (dEd_E).
dE=120 cm−30 cm=90 cmd_E = 120 \text{ cm} - 30 \text{ cm} = 90 \text{ cm}
The effort arm is the distance from the fulcrum to the point where the effort force is applied. Since the force is at the far opposite end, we subtract the load arm from the total length.
4
Calculate the required effort force (FEF_E).
FE×90=600×30⇒90FE=18000⇒FE=200 NF_E \times 90 = 600 \times 30 \Rightarrow 90 F_E = 18000 \Rightarrow F_E = 200 \text{ N}
Solving the equilibrium equation for the unknown variable.

Anahtar Kavram

First-class lever mechanical advantage and torque balance
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Konular

Levers and Fulcrums

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