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Centripetal Force Calculation in Circular Motion

Created by @nathanedwards

at October 31st 2023, 8:57:44 pm.

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#circular-motion

#centripetal-force

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AP Physics 1 Exam Question: Centripetal Force

A small object of mass 0.1 kg is attached to a string and is swung in a horizontal circular path of radius 0.5 m. The object completes one full revolution in 2 seconds. Determine the centripetal force acting on the object.

Answer:

To determine the centripetal force acting on the object, we can use the formula for centripetal force:

F_c = \frac{mv^2}{r}

where:

$F_c$ is the centripetal force in Newtons (N),
$m$ is the mass of the object in kilograms (kg),
$v$ is the velocity of the object in meters per second (m/s),
$r$ is the radius of the circular path in meters (m).

Step 1: Calculate the velocity of the object. Since the object completes one full revolution in 2 seconds, we can find the velocity using the formula:

v = \frac{2\pi r}{t}

where $t$ is the time taken for one full revolution. Substituting the given values into the equation:

v = \frac{2 \pi \times 0.5 \, \text{m}}{2\, \text{s}}

Simplifying:

v = \pi \, \text{m/s}

Step 2: Substitute the values into the formula for centripetal force. Now we can substitute the known values into the formula:

F_c = \frac{0.1 \, \text{kg} \times (\pi \, \text{m/s})^2}{0.5 \, \text{m}}

Simplifying:

F_c = \frac{0.1 \, \text{kg} \times \pi^2 \, \text{m}^2/\text{s}^2}{0.5 \, \text{m}}

F_c = 0.2 \pi^2 \, \text{N}

Hence, the centripetal force acting on the object is $0.2 \pi^2 \, \text{N}$ .