Question

A 3.20-kilogram toy car is attached to a 125-centimeter string ofnegligible mass. The other end of the string is attached to a ringthat is slipped over a peg. The tensile strength of the string is144 newions. The car revolves about the peg in a circular path ona frictionless table. Find the maximum angular speed that the carcan travel in revolutions per minute without breaking the string.

Answer 1

Given data:

The tensile strength of the string is,

$F^{\prime}=144\text{ N}$

The mass of the car is,

$m=3.2\text{ kg}$

The length of the string is,

$\begin{gathered} r=125\text{ cm} \\ r=1.25\text{ m} \end{gathered}$

The force acting on the car is,

$F^{\prime}=\frac{mv}{r}^2$

where a is the linear acceleration and m is the mass of the car.

Substituting the known values,

$\begin{gathered} 144=\frac{3.2\times v^2}{1.25} \\ v^2=56.25 \\ v=7.5ms^{-1} \end{gathered}$

Thus, the angular speed of the car is,

$\begin{gathered} \omega=\frac{v}{r} \\ \omega=\frac{7.5}{1.25} \\ \omega=6 \end{gathered}$

Each distance of each revolution is,

$\begin{gathered} d=2\pi r \\ d=2\pi\times1.25 \\ d=7.85 \end{gathered}$

Thus, the value of angular speed in terms of revolution is,

$\begin{gathered} \omega=\frac{6}{7.85} \\ \omega=0.76\text{ revolution per second} \\ \omega=0.76\times60\text{ revolutions per minute} \\ \omega=45.6\text{ revolutions per minute} \end{gathered}$

Thus, the maximum angular speed of the toy car is 45.6 revolutions per minute.