Centripetal merry-go-round problem

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In summary, a man standing on the edge of a carnival merry-go-round with a constant speed of 3.43 m/s and a centripetal acceleration of magnitude 1.87 m/s2 has a radius of 6.29 meters from the center of the merry-go-round. The equation used is Ac= v^2/r, where Ac is the centripetal acceleration, v is the speed, and r is the radius. The wording "centripetal acceleration of magnitude 1.87 m/s2" means that the magnitude of the centripetal acceleration vector is 1.87 m/s2.
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wegman14
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Homework Statement


A carnival merry-go-round rotates about a vertical axis at a constant rate. A man standing on the edge has a constant speed of 3.43 m/s and a centripetal acceleration of magnitude 1.87 m/s2. How far is the man from the center of the merry-go-round?


Homework Equations


Ac= v^2/r


The Attempt at a Solution


I understand I am looking for the radius in the equation, I am just not sure about the other aspects of it. I get a radius of 6.29 the way i do it by: (3.43^2/1.87). Not confident though.
 
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  • #2
Looks fine to me.
 
  • #3
alright, so the constant speed of 3.43 m/s can be plugged in as the velocity? and I am confused on the wording "centripetal acceleration of magnitude... "
 
  • #4
"...centripetal acceleration of magnitude 1.87 m/s2" means that the magnitude of the centripetal acceleration vector is 1.87.
 
  • #5
Similarly the speed is the magnitude of the velocity vector, so yes you use the speed for v in the equation.
 

FAQ: Centripetal merry-go-round problem

What is the centripetal merry-go-round problem?

The centripetal merry-go-round problem is a physics problem that involves finding the centripetal force required to keep a person or object moving in a circular motion on a rotating platform, such as a merry-go-round.

What are the main factors that affect the centripetal force in this problem?

The main factors that affect the centripetal force in the centripetal merry-go-round problem are the mass of the object, the speed of its motion, and the radius of the circular path it is following.

How can I calculate the centripetal force in this problem?

The centripetal force can be calculated using the formula F = mv²/r, where F is the centripetal force, m is the mass of the object, v is the speed of motion, and r is the radius of the circular path.

What is the relationship between centripetal force and centripetal acceleration?

The centripetal force and centripetal acceleration are directly proportional to each other. This means that as the centripetal force increases, the centripetal acceleration also increases, and vice versa.

What are some real-world applications of the centripetal merry-go-round problem?

The centripetal merry-go-round problem has many real-world applications, such as designing amusement park rides, analyzing the forces acting on cars and motorcycles around curves, and understanding the motion of planets and satellites in orbit.

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