Uniform circular motion of a particle problem

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Homework Help Overview

The problem involves a particle moving in uniform circular motion along a horizontal circular path, with specific positions, velocities, and accelerations given at two different times. The task is to determine the coordinates of the center of the circular path based on the provided information.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the implications of the particle's velocity and acceleration at specific points, considering how these relate to the center of the circular path. There is an exploration of the distance traveled in relation to time and speed, as well as the potential for different interpretations of the motion's direction.

Discussion Status

Some participants have offered reasoning regarding the relationship between the particle's position and its velocity components, while others have raised questions about the direction of motion and whether it is indeed clockwise. The discussion reflects a mix of interpretations and assumptions that are being examined.

Contextual Notes

There is uncertainty regarding the direction of the particle's motion, as it is not explicitly stated whether it is moving clockwise or counterclockwise. Participants are considering the implications of this assumption on the problem's setup.

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Homework Statement


A particle moves along a circular path over a horizontal xy coordinate system, at constant speed. At time t1 = 3.30 s, it is at point (5.10 m, 6.80 m) with velocity (3.90 m/s)## \hat j ## and acceleration in the positive x direction. At time t2 = 9.90 s, it has velocity (–3.90 m/s)## /hat i ##and acceleration in the positive y direction. What are the (a) x and (b) y coordinates of the center of the circular path? Assume at both times that the particle is on the same orbit.

Homework Equations


a=v2/r, v=2πr/T, [/B]

The Attempt at a Solution


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If all its speed is in j-hat while at (5.1, 6.8), then it is crossing the horizontal axis through the circle at that moment. Hence, the y-component of the center is the y-component of (5.1,6.8)

It’s tangential speed is 3.9 m/s. It takes 9.9-3.3 seconds to travel ¼ around its orbit. (I’m assuming it didn’t go 5/4, or 9/4 around, etc.). So now you have a speed and a time, so you can solve for distance (circumference). Then it’s easy to get radius. If you know the radius and you know its position when all its velocity in is the j hat direction, then your radius is the offset from you x-component of that position.
 
tony873004 said:
If all its speed is in j-hat while at (5.1, 6.8), then it is crossing the horizontal axis through the circle at that moment. Hence, the y-component of the center is the y-component of (5.1,6.8)

It’s tangential speed is 3.9 m/s. It takes 9.9-3.3 seconds to travel ¼ around its orbit. (I’m assuming it didn’t go 5/4, or 9/4 around, etc.). So now you have a speed and a time, so you can solve for distance (circumference). Then it’s easy to get radius. If you know the radius and you know its position when all its velocity in is the j hat direction, then your radius is the offset from you x-component of that position.
would'nt it travel 3/4 around the circle 3pi/2 if its velocity is positive jhat at the left side of the circle its moving clockwise?
 
Is it given that its moving clockwise?
 
tony873004 said:
Is it given that its moving clockwise?
no but both vectors are pointing in a direction that would indicate clockwise motion
 
You're right, it moves 3/4 around.
 

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