A car with mass 1000 kg turns around a flat curve of radius 40 m at 20 m/s. What is the required centripetal force?

A car with mass 1000 kg turns around a flat curve of radius 40 m at 20 m/s. What is the required centripetal force?

• A. 1,000 N
• B. 10,000 N
• C. 40,000 N
• D. 2,000 N

Answer: (B)

To keep the car moving in a circle, the inward force must equal the centripetal force needed for circular motion. That force is F = m v^2 / r, where m is mass, v is speed, and r is the radius of the path. For this car: m = 1000 kg, v = 20 m/s, r = 40 m. Calculate v^2 = 400, then m v^2 = 1000 × 400 = 400,000. Dividing by r gives F = 400,000 / 40 = 10,000 N. So the required centripetal force is 10,000 newtons directed toward the center of the curve. On a flat curve, this inward force comes from friction between the tires and the road (up to the available friction), and the value is set by F = m v^2 / r. Other numerical choices don’t satisfy this relationship with the given values.

To keep the car moving in a circle, the inward force must equal the centripetal force needed for circular motion. That force is F = m v^2 / r, where m is mass, v is speed, and r is the radius of the path.

For this car: m = 1000 kg, v = 20 m/s, r = 40 m. Calculate v^2 = 400, then m v^2 = 1000 × 400 = 400,000. Dividing by r gives F = 400,000 / 40 = 10,000 N.

So the required centripetal force is 10,000 newtons directed toward the center of the curve. On a flat curve, this inward force comes from friction between the tires and the road (up to the available friction), and the value is set by F = m v^2 / r. Other numerical choices don’t satisfy this relationship with the given values.