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What's the shortest length?

A certain cord will break if its tension exceeds 360 N. Suppose the cord is attached to a 0.40 kg ball. If the ball is to be swung with a speed of 25 m/s, what's the shortest length of cord that can be used?

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John M. | John - Algebra TutorJohn - Algebra Tutor
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Check Marked as Best Answer
Sun, just as in the cornering problem this is a rotational acceleration and force problem. 
 
F= m v2/r, but this time we want to solve for r given a mass, velocity and maximum force.
 
rearranging the equation:
 
r= mv2/F , given the values in the problem
 
rmin= (.4)(252)/360 = .6944 meters
Robert J. | Certified High School AP Calculus and Physics TeacherCertified High School AP Calculus and Ph...
4.6 4.6 (13 lesson ratings) (13)
0
T = mv^2/r
Plug in the maximum tension force to get the shortest length of the cord.
360 = 0.40(25^2)/r
Solve for r,
r = 25/36 = .69 m <==Answer