The radius of the path of an object in uniform circular motion is halved. The centripetal acceleration needed if its speed remains the same is _____.
-half as great,
-the same as before,
-twice as great as before, or
-four times as great as before?
could somebody explain the answer for me?
im unsure about what the answer is.
a = v^2/r
a' = v^2/(r/2) = 2 v^2/r = 2 a
Twice as great before is the answer
DANGGG THIS WAS IN 2015??
To determine the answer, let's recall the relationship between the centripetal acceleration, speed, and radius in uniform circular motion.
The centripetal acceleration (a) is given by the formula:
a = (v^2) / r
where:
- v is the velocity/speed of the object
- r is the radius of the circular path
In this scenario, the radius is halved, but the speed remains the same. Let's consider the effect of this change on the centripetal acceleration.
If the radius is halved, let's denote the new radius as r_new and the original radius as r_old.
Given that the speed (v) remains the same, we have:
r_new = (1/2) * r_old
Now, let's substitute these values into the centripetal acceleration formula:
a_new = (v^2) / r_new
= (v^2) / [(1/2) * r_old]
= 2 * (v^2) / r_old
Comparing this with the original centripetal acceleration (a_old), we can see that:
a_new / a_old = [2 * (v^2) / r_old] / [(v^2) / r_old]
= 2
Therefore, the centripetal acceleration needed if the radius is halved, with the speed remaining the same, is twice as great as before.
So, the answer to the question is: The centripetal acceleration needed is twice as great as before.