RaySix

Post

Calculating Centripetal Force in a Horizontal Circle

Created by @nathanedwards

at November 1st 2023, 2:19:33 am.

AP_Physics_1-Questions

#physics

#circular-motion

#centripetal-force

Question:

A 0.5 kg object is attached to a string and is being swung in a horizontal circle with a radius of 2 meters. The angular speed of the object is 3 rad/s. Determine the centripetal force acting on the object.

Answer:

To find the centripetal force acting on the object, we need to use the formula for centripetal force:

F_{\text{c}} = \frac{m \cdot v^2}{r}

First, let's find the linear velocity of the object. The linear velocity can be calculated using the formula:

v = \omega \cdot r

Here, $\omega$ is the angular speed in rad/s and $r$ is the radius of the circular path.

Substituting the given values:

v = 3 \, \text{rad/s} \times 2 \, \text{m} = 6 \, \text{m/s}

Next, substitute the given values and the obtained linear velocity into the formula for centripetal force:

F_{\text{c}} = \frac{0.5 \, \text{kg} \times (6 \, \text{m/s})^2}{2 \, \text{m}}

Simplifying the equation:

F_{\text{c}} = \frac{0.5 \, \text{kg} \times 36 \, \text{m}^2/\text{s}^2}{2 \, \text{m}}

F_{\text{c}} = 9 \, \text{N}

Therefore, the centripetal force acting on the object is 9 N.