How Far Can a Spider Safely Cling to a Spinning Ceiling Fan Blade?

In summary, centripetal acceleration is the acceleration that occurs when an object moves in a circular motion, always directed towards the center of the circle. It can be calculated using the formula a = v²/r, where "a" is the centripetal acceleration, "v" is the velocity of the object, and "r" is the radius of the circular path. It differs from tangential acceleration, which is directed along the tangent to the circle and is responsible for changes in velocity magnitude. Centripetal acceleration constantly changes the direction of an object's velocity, but not its speed, as it moves in a circular path, and can be seen in various real-life examples such as the motion of satellites, Ferris wheels, and
  • #1
Masafi
65
0
A ceiling fan is turning at a rate of 100 revolutions per minute. A spider is clinging to a blade. If he experiences a centripetal acc greater than 0.3g, he wil lose his grip and be flung off. How far from the centre can he safely go?

I used: T = 60/100 = 0.6

angular velocity = 2pi/T = 10pi/3

a = (10pi/3)^2 * radius

using a = 0.3g

i get radius = 0.0268...

But the answer is 1.05m?
 
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  • #2
Your answer looks right to me.
 
  • #3


Based on the given information, it appears that there may be a discrepancy in the calculations used to determine the safe distance from the center for the spider on the ceiling fan blade. It is possible that the formula used to calculate the centripetal acceleration, a = (10pi/3)^2 * radius, may not be the correct one to use in this scenario. It would be helpful to have more information, such as the mass of the spider and the dimensions of the blades, to accurately determine the centripetal acceleration and the safe distance from the center. Additionally, it is important to note that the centripetal acceleration may vary depending on the speed of the fan and the position of the spider on the blade. Further analysis and experimentation may be needed to accurately determine the safe distance for the spider on the ceiling fan.
 

Related to How Far Can a Spider Safely Cling to a Spinning Ceiling Fan Blade?

1. What is centripetal acceleration?

Centripetal acceleration is the acceleration that occurs when an object moves in a circular motion. It is always directed towards the center of the circle and is responsible for keeping the object in its circular path.

2. How is centripetal acceleration calculated?

The formula for calculating centripetal acceleration is a = v²/r, where "a" is the centripetal acceleration, "v" is the velocity of the object, and "r" is the radius of the circular path.

3. What is the difference between centripetal acceleration and tangential acceleration?

Centripetal acceleration is directed towards the center of the circle, while tangential acceleration is directed along the tangent to the circle. Centripetal acceleration is responsible for the change in direction of the object's velocity, while tangential acceleration is responsible for the change in magnitude of the object's velocity.

4. How does centripetal acceleration affect the motion of an object?

Centripetal acceleration causes an object to constantly change direction, but not speed, as it moves in a circular path. This means that the object is constantly accelerating, even if its speed remains constant.

5. What are some real-life examples of centripetal acceleration?

Some real-life examples of centripetal acceleration include the motion of a satellite orbiting the Earth, the rotation of a Ferris wheel, and the swinging of a pendulum. Any time an object moves in a circular path, centripetal acceleration is at play.

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