Ghazala Khan, Teacher at Aga Khan Education Service, Pakistan, Numerade Educator

02:07

Physics 101 Mechanics

A 200 -g object is tied to the end of a cord and whirled in a horizontal circle of radius $1.20 \mathrm{~m}$ at a constant $3.0 \mathrm{rev} / \mathrm{s}$. Assume that the cord is horizontal- that is, that gravity can be neglected. Determine $(a)$ the centripetal acceleration of the object and $(b)$ the tension in the cord.
(a) The object is not accelerating tangentially to the circle but is undergoing a radial, or centripetal, acceleration given by
$$a_{C}=\frac{v^{2}}{r}=r \omega^{2}$$
where $\omega$ must be in rad/s. Since $3.0 \mathrm{rev} / \mathrm{s}=6.0 \pi \mathrm{rad} / \mathrm{s}$,
$a_{C}=(1.20 \mathrm{~m})(6.0 \pi \mathrm{rad} / \mathrm{s})^{2}=426 \mathrm{~m} / \mathrm{s}^{2}=0.43 \mathrm{~km} / \mathrm{s}^{2}$
(b) To cause the acceleration found in $(a)$, the cord must pull on the $0.200$ -kg mass with a centripetal force given by
$$F_{C}=m a_{C}=(0.200 \mathrm{~kg})\left(426 \mathrm{~m} / \mathrm{s}^{2}\right)=85 \mathrm{~N}$$
This is the tension in the cord.