To increase the centripetal acceleration to
, you can double the speed or decrease the radius by 1/4
Explanation:
An object is said to be in uniform circular motion when it is moving at a constant speed in a circular path.
The acceleration of an object in uniform circular motion is called centripetal acceleration, and it is given by
![a=\frac{v^2}{r}](https://tex.z-dn.net/?f=a%3D%5Cfrac%7Bv%5E2%7D%7Br%7D)
where
v is the speed of the object
r is the radius of the circular path
In the problem, the original centripetal acceleration is
![a=0.50 m/s^2](https://tex.z-dn.net/?f=a%3D0.50%20m%2Fs%5E2)
We want to increase it by a factor of 4, i.e. to
![a'=2.00 m/s^2](https://tex.z-dn.net/?f=a%27%3D2.00%20m%2Fs%5E2)
We notice that the centripetal acceleration is proportional to the square of the speed and inversely proportional to the radius, so we can do as follows:
- We can double the speed:
v' = 2v
This way, the new acceleration is
![a'=\frac{(2v)^2}{r}=4(\frac{v^2}{r})=4a](https://tex.z-dn.net/?f=a%27%3D%5Cfrac%7B%282v%29%5E2%7D%7Br%7D%3D4%28%5Cfrac%7Bv%5E2%7D%7Br%7D%29%3D4a)
so, 4 times the original acceleration
- We can decrease the radius to 1/4 of its original value:
![r'=\frac{1}{4}r](https://tex.z-dn.net/?f=r%27%3D%5Cfrac%7B1%7D%7B4%7Dr)
So the new acceleration is
![a'=\frac{v^2}{(r/4)}=4(\frac{v^2}{r})=4a](https://tex.z-dn.net/?f=a%27%3D%5Cfrac%7Bv%5E2%7D%7B%28r%2F4%29%7D%3D4%28%5Cfrac%7Bv%5E2%7D%7Br%7D%29%3D4a)
so, the acceleration has increased by a factor 4 again.
Learn more about centripetal acceleration:
brainly.com/question/2562955
brainly.com/question/6372960
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