A 0.50-kg toy is attached to the end of a 1.0-m very light string.The toy is whirled in a horizontal circular path on a frictionless tabletop.If the maximum tension force that the string can exert on an object without breaking is 350 N,what is the maximum speed the toy can have without breaking the string?
A)700 m/s
B)26 m/s
C)19 m/s
D)13 m/s

Question

Quizplus · Accepted Answer

The maximum tension force that the string can exert on the toy is 350 N. The centripetal force required to keep the toy moving in a circle is given by:$$F_c = mv^2/r$$where m is the mass of the toy, v is its speed, and r is the radius of the circle.Setting the centripetal force equal to the maximum tension force, we get:$$mv^2/r = 350 N$$Solving for v, we get:$$v = \sqrt{350 N * r/m}$$Substituting the given values, we get:$$v = \sqrt{350 N * 1.0 m / 0.50 kg} = 26 m/s$$

A 050-Kg Toy Is Attached to the End of a 1