Question

A toy cart at the end of a string 0.70 m long moves in a circle on a table. The cart has a mass of 2.0 kg, and the string has a breaking strength of 40N. (a) What is the centripetal acceleration of the car? (b) What is the maximum speed of the car?

Answer 1

Centripetal acceleration is given as follows for tangential velocity \(v\).\[\boxed{\displaystyle a_c = \frac{v^2}{r}}\]Centripetal force is given by \(F_c =ma_c= \frac{mv^2}{r}\). The maximum speed of the car \(v_{max}\) is when the centripetal force required is just at the breaking strength of the string \(F_{max}\).\[F_{max}=\frac{mv_{max}^2}{r} \Rightarrow \boxed{\displaystyle v_{max} = \sqrt{\frac{rF_{max}}{m}}}\]