Question

A 7 kg object attached to a horizontal string moves with constant speed in a circle on a frictionless horizontal surface. The kinetic energy of the object is 36 J and the tension in the string is 326 N. Find the radius of the circle. Answer in units of m.

Answer 1

Answer:

Explanation:

Given

mass of object $m=7 kg$

kinetic Energy $k=36\ J$

Tension in string $T=326\ N$

mass is moving in a horizontal circle so tension is providing the centripetal acceleration

therefore $T=\frac{mv^2}{r}----1$

where r=radius of circle

kinetic energy of particle $k=\frac{1}{2}mv^2----2$

divide 1 and 2 we get

$\frac{T}{k}=\frac{\frac{mv^2}{r}}{\frac{1}{2}mv^2}$

$\frac{T}{k}=\frac{2}{r}$

$r=\frac{2k}{T}=\frac{2\times 36}{326}$

$r=0.2208\ m$