A car goes around a flat circular curve of radius 50 m with a speed of 20 m/s. The centripetal force (provided by friction) is 1.2 × 104 N. What is the mass of the car?

Question

BlackTom AI · Accepted Answer

Centripetal force for uniform circular motion is Fc = m v^2 / r, so we can solve for the mass m by rearranging that equation.

1) Relevant knowledge points and concepts
- For an object moving in a circle of radius r at speed v, the net inward (centripetal) force required is Fc = m v^2 / r.
- Rearranging gives m = Fc r / v^2.
- Units: N·m / (m^2/s^2) = (kg·m/s^2)·m / (m^2/s^2) = kg, so the result is a mass.

2) Step-by-step reasoning
Given: Fc = 1.2 × 10^4 N, v = 20 m/s, r = 50 m.
Use m = Fc r / v^2.

3) Calculations with intermediate steps
- Compute v^2: v^2 = (20 m/s)^2 = 400 m^2/s^2.
- Multiply Fc by r: Fc × r = (1.2 × 10^4 N) × (50 m) = 1.2 × 10^4 × 50 = 6.0 × 10^5 N·m.
- Divide by v^2: m = (6.0 × 10^5) / 400 = (6.0 × 10^5) ÷ (4.0 × 10^2) = 1.5 × 10^3 kg = 1500 kg.

4) Why the correct answer is correct
The formula directly relates the known centripetal force to mass, speed, and radius. Substituting the given numbers and carrying out the arithmetic yields 1500 kg, so the car's mass must be 1500 kg to require the given centripetal force at that speed and radius.

5) Why the other options are incorrect
- 500 kg would give Fc = m v^2 / r = 500 × 400 / 50 = 4000 N (too small).
- 1000 kg would give Fc = 1000 × 400 / 50 = 8000 N (too small).
- 2000 kg would give Fc = 2000 × 400 / 50 = 16000 N (too large).
Only 1500 kg yields Fc = 1.2 × 10^4 N.

6) Conclusion
The calculated mass is 1500 kg, which matches the provided correct answer.

A car goes around a flat circular curve of radius 50 m with a speed of 20 m/s. The centripetal force (provided by friction) is 1.2 × 104 N. What is the mass of the car?单项选择题

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