An insect is moving on a circular track with speed 2m/s in radius 2m i...
Introduction:
The problem states that an insect is moving on a circular track with a speed of 2 m/s and a radius of 2 m. We are required to find the magnitude of its acceleration. To solve this problem, we need to understand the concepts of centripetal acceleration and centripetal force.
Centripetal Acceleration:
Centripetal acceleration is the acceleration experienced by an object moving in a circular path. It is always directed towards the center of the circle. The formula for centripetal acceleration is given by:
\[a_c = \frac{v^2}{r}\]
where \(a_c\) is the centripetal acceleration, \(v\) is the velocity of the object, and \(r\) is the radius of the circular path.
Given Values:
- Velocity (v) = 2 m/s
- Radius (r) = 2 m
Calculating Centripetal Acceleration:
Substituting the given values into the formula, we can calculate the centripetal acceleration:
\[a_c = \frac{(2 \, \text{m/s})^2}{2 \, \text{m}}\]
\[a_c = \frac{4 \, \text{m}^2/\text{s}^2}{2 \, \text{m}}\]
\[a_c = 2 \, \text{m/s}^2\]
Explanation:
The magnitude of the acceleration of the insect moving on the circular track is 2 m/s². This means that the insect is accelerating towards the center of the circular path with an acceleration of 2 m/s². The acceleration is necessary to keep the insect moving in a circular path, as it constantly changes direction. The insect experiences a constant inward force called centripetal force that causes its acceleration towards the center of the circle.
Conclusion:
In summary, the insect moving on the circular track with a speed of 2 m/s and a radius of 2 m has a magnitude of acceleration equal to 2 m/s². The acceleration is directed towards the center of the circular path and is necessary to maintain the insect's motion in the circular track.
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