An object with a mass of #12 kg# is revolving around a point at a distance of #12 m#. If the object is making revolutions at a frequency of #1 Hz#, what is the centripetal force acting on the object?

Question

An object with a mass of #12   kg# is revolving around a point at a distance of #12  m#. If the object is making revolutions at a frequency of #1 Hz#, what is the centripetal force acting on the object?

Elena Albarran · Accepted Answer

#F_c =576pi^2 N#
#approx 5684.89 N# For Circular Motion, Centripetal Force #F_c= - mr omega^2# Where #m# is the mass of the body in circular motion. #r# is the radius of the circle and #omega# is angular velocity. #-# sign means that the force is opposite to the radius vector and is directed towards the center. Now #omega=(2pi) /T=2pif# Therefore, magnitude of the force #|F_c|=4pi^2 f^2mr# Assuming it to be a point mass object and substituting the given values, #|F_c|=4pi^2. 1^2 .12 times 12 N#

Isabella Alvarez · Answer

undefined The centripetal force acting on the object can be calculated using the formula:

$F = m \cdot r \cdot \omega^2$

Where:
$F$ = centripetal force,
$m$ = mass of the object,
$r$ = radius of the circular path,
$\omega$ = angular velocity.

Given:
$m = 12 \text{ kg}$,
$r = 12 \text{ m}$,
Frequency $f = 1 \text{ Hz}$.

Angular velocity ($\omega$) can be calculated as $2\pi f$.

Substituting the values:

$\omega = 2\pi \cdot 1 = 2\pi \text{ rad/s}$

$F = 12 \text{ kg} \cdot 12 \text{ m} \cdot (2\pi)^2 \text{ rad/s}^2$

$F \approx 144 \pi^2 \text{ N} \approx 1423.72 \text{ N}$

Therefore, the centripetal force acting on the object is approximately $1423.72 \text{ N}$.

Elena Albarran · Answer

undefined The centripetal force acting on the object can be calculated using the formula:

$$ F = m \times r \times \omega^2 $$

Where:
- $ F $ is the centripetal force,
- $ m $ is the mass of the object,
- $ r $ is the distance from the object to the center of rotation,
- $ \omega $ is the angular velocity, which is $ 2\pi $ times the frequency ($ f $).

Given that $ m = 12 $ kg, $ r = 12 $ m, and $ f = 1 $ Hz, we can calculate $ \omega $:

$$ \omega = 2\pi \times f = 2\pi \times 1 = 2\pi \, \text{rad/s} $$

Now, substituting the values into the formula:

$$ F = 12 \times 12 \times (2\pi)^2 = 288 \pi^2 \, \text{N} $$

Therefore, the centripetal force acting on the object is $ 288 \pi^2 $ N.