I keep getting the answer .599; however, it isincorrect. Any help is greatly app

Question

I keep getting the answer .599; however, it isincorrect. Any help is greatly appreciated.
A small 0.200-kg object moves on a frictionless horizontal table ina circular path of radius 5.00 m. The angular speed is 3.54 rad/s.The object is attached to a string of negligible mass that passesthrough a small hole in the table at the center of the circle.Someone under the table begins to pull the string downward to makethe circle smaller. If the string will tolerate a tension of nomore than 1310 N, what is the radius of the smallest possiblecircle on which the object can move? I keep getting the answer .599; however, it isincorrect. Any help is greatly appreciated.
A small 0.200-kg object moves on a frictionless horizontal table ina circular path of radius 5.00 m. The angular speed is 3.54 rad/s.The object is attached to a string of negligible mass that passesthrough a small hole in the table at the center of the circle.Someone under the table begins to pull the string downward to makethe circle smaller. If the string will tolerate a tension of nomore than 1310 N, what is the radius of the smallest possiblecircle on which the object can move?

Explanation / Answer

Given that
The object of mass (m) = 0.200kg
Circular path of the horizontal table is (ri) =5.00m
The angular speed is () = 3.54 rad/s.
The string will tolerate a tension of no more than (T) =1310N We know the initial speed of the object is                  vi = r                      = (3.54)(5.00)                       =17.7m/s Now the angular momentum for the object is conservedso              vi ri = vf rf So, if vf and rf are givenby                   vfrf = (17.7m/s)(5.00m)                        = 88.5 Also, we know that in the final state the tension provides thecentripetal force so      Tension = mv2 /r    or                 = m (30.826/r)2 / r           Or    Tension = m *7832.25 /r3     Solvinf for r, using the maximum tension and              r3 = 7832.25 * m /T                   = 7832.25 *0.200 / 1310                   =  1.1957 Thus the radius of the smallest possible circle on whichthe object can move is Thus the radius of the smallest possible circle on whichthe object can move is                r = 1.060m

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---