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Zorluk: OrtaInclined Planes

Arrange the following inclined planes in order from the LEAST ideal mechanical advantage (IMA) to the GREATEST ideal mechanical advantage.

  1. 1A 10-foot long ramp reaching a 5-foot high dock
  2. 2A 12-foot long ramp reaching a 3-foot high van floor
  3. 3A 15-foot long ramp reaching a 3-foot high loading bay
  4. 4A 16-foot long ramp reaching a 2-foot high platform

Cevap

The correct order from least to greatest mechanical advantage is: the 10-foot ramp (IMA=2), the 12-foot ramp (IMA=4), the 15-foot ramp (IMA=5), and the 16-foot ramp (IMA=8).
The ideal mechanical advantage (IMA) of an inclined plane is calculated by dividing the length of the slope by its vertical height. A longer slope relative to its height yields a higher mechanical advantage, meaning less effort force is required. Ordering the ramps by their calculated IMA values gives 2 (least), 4, 5, and 8 (greatest).

Adım Adım Çözüm

1
Recall the formula for the ideal mechanical advantage (IMA) of an inclined plane.
IMA=Length of InclineVertical Height\text{IMA} = \frac{\text{Length of Incline}}{\text{Vertical Height}}
The mechanical advantage quantifies how much the inclined plane multiplies the input force or reduces the required effort.
2
Calculate the IMA for each given ramp.
10-foot ramp: 10÷5=210 \div 5 = 2. 12-foot ramp: 12÷3=412 \div 3 = 4. 16-foot ramp: 16÷2=816 \div 2 = 8. 15-foot ramp: 15÷3=515 \div 3 = 5.
Calculating the individual values allows for direct comparison.
3
Order the calculated values from least to greatest.
The values in ascending order are 2, 4, 5, and 8.
The question specifically asks for the arrangement starting from the lowest mechanical advantage to the highest.

Anahtar Kavram

The ideal mechanical advantage of a ramp is determined by the ratio of its length to its vertical height.
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Konular

Inclined Planes

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