A 4.00 kg mass is moving in a circular path with a constant angular speed of 5.00 rad/sec and with a linear speed of 5.00 m/sec. The magnitude of the radial force on the mass is
A) 90.0 N.
B) 100 N.
C) 125 N.
D) 169 N.
E) 200 N.

Question

Quizplus · Accepted Answer

The radial (centripetal) force $F$ required to keep an object moving in a circular path can be calculated using the formula $F = \frac{mv^2}{r}$, where $m$ is the mass of the object, $v$ is its linear speed, and $r$ is the radius of the circular path. Given that the linear speed $v = 5.00 \, \text{m/s}$ and the mass $m = 4.00 \, \text{kg}$, we need to find the radius $r$ to calculate the force. The radius can be found from the relationship between linear speed $v$, angular speed $\omega$, and radius $r$, which is $v = \omega r$. Given $v = 5.00 \, \text{m/s}$ and $\omega = 5.00 \, \text{rad/s}$, we find $r = \frac{v}{\omega} = \frac{5.00}{5.00} = 1.00 \, \text{m}$. Substituting $m$, $v$, and $r$ into the formula for $F$, we get $F = \frac{(4.00)(5.00)^2}{1.00} = 100 \, \text{N}$.

A 400 Kg Mass Is Moving in a Circular Path with with a Constant