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Zorluk: OrtaLevers and Fulcrums

Match each operational adjustment made to a mechanical lever system with its correct effect on the system's mechanical advantage.

  • Grasping a first-class pry bar further away from the fulcrumIncreases the effort arm, increasing the mechanical advantage and reducing the required force
  • Shifting a heavy load closer to the wheel of a wheelbarrowDecreases the load arm, increasing the mechanical advantage and reducing the required force
  • Pinching a pair of tweezers closer to their joined, pivoting endDecreases the effort arm, reducing the mechanical advantage but increasing the load's travel distance
  • Replacing a lever with one that has both its effort and load arms doubled in lengthResults in no change to the mechanical advantage, as the ratio of the lever arms remains constant

Cevap

Grasping the pry bar further out increases the effort arm. Shifting the wheelbarrow load closer to the wheel decreases the load arm. Pinching tweezers closer to the hinge decreases the effort arm. Doubling all proportions maintains the original ratio.
Mechanical advantage for any lever is calculated by dividing the length of the effort arm by the length of the load arm (MA=dedlMA = \frac{d_e}{d_l}). Any adjustment that increases the effort arm or decreases the load arm will result in a higher mechanical advantage, making the work feel easier. Conversely, reducing the effort arm or increasing the load arm lowers the mechanical advantage. Proportional changes to both arms maintain the exact same ratio.

Adım Adım Çözüm

1
Recall the formula for Mechanical Advantage (MA) of a lever.
MA=Effort ArmLoad ArmMA = \frac{\text{Effort Arm}}{\text{Load Arm}}.
This fundamental relationship determines how any physical adjustment to the lever's dimensions will affect the required force.
2
Analyze the pry bar adjustment.
Grasping the tool further from the fulcrum increases the numerator (Effort Arm), which increases the overall MA.
A higher MA means less force is required to move the same load.
3
Analyze the wheelbarrow adjustment.
The wheel is the fulcrum. Moving the load closer to the wheel decreases the denominator (Load Arm), which increases the overall MA.
A smaller denominator results in a larger ratio, requiring less lifting force at the handles.
4
Analyze the tweezers adjustment.
Tweezers are a third-class lever with the fulcrum at the joined end. Pinching closer to the joined end decreases the Effort Arm.
Decreasing the numerator lowers the MA, meaning more pinch force is required, though the tips will close faster and over a larger distance.
5
Analyze the proportional scaling adjustment.
If both the effort arm and load arm are multiplied by 2, the new MA is 2×Effort Arm2×Load Arm\frac{2 \times \text{Effort Arm}}{2 \times \text{Load Arm}}.
The factor of 2 cancels out, leaving the mechanical advantage exactly the same as the original lever.

Anahtar Kavram

Mechanical Advantage Ratio and Lever Adjustments
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Konular

Levers and Fulcrums

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