A doorknob has an IMA equal to 8.5. If the diameter of the doorknob is 8.0 cm, what is the radius of the inner rod that connects the knob to the door?
Question
A doorknob has an IMA equal to 8.5.
If the diameter of the doorknob is 8.0 cm, what is the radius of the inner rod that connects the knob to the door?
Solution
To find the radius of the inner rod that connects the doorknob to the door, we can use the formula for Ideal Mechanical Advantage (IMA):
IMA = (radius of the doorknob) / (radius of the inner rod)
Given that the IMA is 8.5 and the diameter of the doorknob is 8.0 cm, we can calculate the radius of the doorknob:
radius of the doorknob = (diameter of the doorknob) / 2 = 8.0 cm / 2 = 4.0 cm
Now, we can rearrange the formula for IMA to solve for the radius of the inner rod:
IMA = (radius of the doorknob) / (radius of the inner rod)
8.5 = 4.0 cm / (radius of the inner rod)
To isolate the radius of the inner rod, we can rearrange the equation:
(radius of the inner rod) = (radius of the doorknob) / IMA = 4.0 cm / 8.5 ≈ 0.47 cm
Therefore, the radius of the inner rod that connects the doorknob to the door is approximately 0.47 cm.
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