Tangential Acceleration Problem, UCM

AI Thread Summary
The discussion revolves around a physics problem involving a ball being swung in a horizontal plane with a constant tangential acceleration while the string length increases to maintain constant tension. Key equations include the relationship between tension, mass, and centripetal acceleration, specifically Tension = (mv^2)/r. Participants explore how to derive expressions for the string length and total acceleration over time using the initial conditions and tangential acceleration. There is uncertainty regarding the relationship between mass and tension in the context of the problem. The conversation emphasizes the need for clear connections between the variables to solve the problem effectively.
stark3000
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Homework Statement
A student is swinging a ball on a string overhead in a horizontal plane. The string initially has length š¯‘™0 and the ball is moving with an initial speed š¯‘£0 . The student decides to see how fast they
can spin the ball, so they begin moving it faster and faster with a constant tangential acceleration š¯‘ˇ_t. However, they know that the string is close to breaking, so they decide to keep letting the string get longer and longer in order to keep the tension in the string constant. Find expressions for the length of the string and the total acceleration (magnitude and direction) as a function of time, š¯‘™0 , š¯‘£0 , and š¯‘ˇ_t . You may ignore the effect of gravity on the ball.
Relevant Equations
F_R= m(a_R)
Tension = (mv^2)/r
Tension = m(a_R)
Homework Statement: A student is swinging a ball on a string overhead in a horizontal plane. The string initially has length š¯‘™0 and the ball is moving with an initial speed š¯‘£0 . The student decides to see how fast they
can spin the ball, so they begin moving it faster and faster with a constant tangential acceleration š¯‘ˇ_t. However, they know that the string is close to breaking, so they decide to keep letting the string get longer and longer in order to keep the tension in the string constant. Find expressions for the length of the string and the total acceleration (magnitude and direction) as a function of time, š¯‘™0 , š¯‘£0 , and š¯‘ˇ_t . You may ignore the effect of gravity on the ball.
Homework Equations: F_R= m(a_R)
Tension = (mv^2)/r
Tension = m(a_R)

I will need 2 F net equations.
F_R= m(a_R)
Tension = (mv^2)/r
Tension = m(a_R)
 
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Welcome to the PF. :smile:
stark3000 said:
Tension = (mv^2)/r
It seems like that is the key equation, no? Can you say more about how to use that one equation and the variables they mention to accomplish the goal?
 
berkeman said:
Welcome to the PF. :smile:

It seems like that is the key equation, no? Can you say more about how to use that one equation and the variables they mention to accomplish the goal?
Since I know F=ma, m=F/a. Then, can I plug in this m into the Tension equation to get Tension = (Fv^2/ar)? I am unsure about how to relate the length of the string though.
 

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