A car of mass 1000 kg moves at 20 m/s around a flat curve of radius 50 m. What is the required centripetal force?

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Multiple Choice

A car of mass 1000 kg moves at 20 m/s around a flat curve of radius 50 m. What is the required centripetal force?

Explanation:
Centripetal force comes from the need to provide inward acceleration for circular motion. The inward force equals F = m v^2 / r, since the centripetal acceleration is a_c = v^2 / r. Plugging in the values: m = 1000 kg, v = 20 m/s, r = 50 m gives v^2 = 400, m v^2 = 400,000, and F = 400,000 / 50 = 8,000 N. So the required centripetal force is 8.0 × 10^3 N toward the center of the curve. The other options don’t match this calculation.

Centripetal force comes from the need to provide inward acceleration for circular motion. The inward force equals F = m v^2 / r, since the centripetal acceleration is a_c = v^2 / r.

Plugging in the values: m = 1000 kg, v = 20 m/s, r = 50 m gives v^2 = 400, m v^2 = 400,000, and F = 400,000 / 50 = 8,000 N.

So the required centripetal force is 8.0 × 10^3 N toward the center of the curve. The other options don’t match this calculation.

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