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

Step 1: Understanding the Question:
The question asks for the inward force required to maintain circular motion for a vehicle.
The topic is Circular Motion.
Step 2: Key Formula or Approach:
The centripetal force is given by:
\[ F_c = \frac{mv^2}{r} \]
Step 3: Detailed Explanation:
Identify given parameters:
Mass \( m = 1000\,\text{kg} \).
Velocity \( v = 20\,\text{m/s} \).
Radius \( r = 50\,\text{m} \).
Plug the values into the force equation:
\[ F_c = \frac{1000 \times (20)^2}{50} \]
\[ F_c = \frac{1000 \times 400}{50} \]
\[ F_c = 20 \times 400 \]
Step 4: Final Answer:
\[ F_c = 8000\,\text{N} \]