Question
d) If the fadiun of the eurvature of the path was doubled the magnifude of the centripetal aeceleration of the eart would be (halved, doubled, quartered, quadrupled)
Ask by Colon Cox. in the United States
Feb 07,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
If the radius of curvature is doubled, the centripetal acceleration is halved.
Solution
The centripetal acceleration (\(a_c\)) is given by the formula:
\[
a_c = \frac{v^2}{r}
\]
where:
- \(v\) is the speed of the object (in this case, the Earth),
- \(r\) is the radius of curvature of the path.
If the radius of curvature (\(r\)) is **doubled**, the new radius becomes \(2r\). Substituting this into the formula:
\[
a_c' = \frac{v^2}{2r} = \frac{1}{2} \cdot \frac{v^2}{r} = \frac{a_c}{2}
\]
This shows that the centripetal acceleration is **halved** when the radius of curvature is doubled.
**Answer:** It would be halved.
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Simplify this solution Mind Expander
When the radius of curvature of a path is doubled, the centripetal acceleration is inversely proportional to the radius. This means if the radius increases, the centripetal acceleration decreases. Therefore, with a doubled radius of curvature, the magnitude of the centripetal acceleration would be halved. In a fun twist, think of it this way: if you're spinning round and round with a big radius, you feel slightly less of that dizzying acceleration compared to a tighter spin! So, more doughnut space means less whip around. Keep that in mind next time you're on a merry-go-round!
