Question

Determine the centripetal force acting on a \(1000\,\text{kg}\) car moving at \(20\,\text{m/s}\) around a curve of radius \(50\,\text{m}\).

• A. \(4000\,\text{N}\)
• B. \(8000\,\text{N}\)
• C. \(10000\,\text{N}\)
• D. \(20000\,\text{N}\)

Hint:

For circular motion problems, remember the centripetal force formula \(F = \frac{mv^2}{r}\). Always square the velocity before substitution.

Answer 1

The Correct Option is B

Concept: The centripetal force required to keep an object moving in a circular path is given by \[ F = \frac{mv^2}{r} \] where \(m\) = mass, \(v\) = velocity, \(r\) = radius of the circular path.

Step 1: Substitute the given values. \[ m = 1000\,\text{kg}, \quad v = 20\,\text{m/s}, \quad r = 50\,\text{m} \] \[ F = \frac{1000 \times (20)^2}{50} \]

Step 2: Simplify the expression. \[ F = \frac{1000 \times 400}{50} \] \[ F = \frac{400000}{50} \] \[ F = 8000\,\text{N} \]