Final answer:
The radius of the curve is 80 meters, which can be calculated using the centripetal force formula and the given values for mass, velocity, and force.
Step-by-step explanation:
To find the radius of the curve on which a car is moving with a centripetal force acting on it, the following formula is used:
F = (mv²)/r, where:
- F is the centripetal force,
- m is the mass of the car,
- v is the velocity,
- and r is the radius of the curve.
Given that F = 6000 N, m = 1200 kg, and v = 20 m/s, we can rearrange the formula to solve for r:
r = (mv²)/F = (1200 kg × (20 m/s)²) / 6000 N, which simplifies to:
r = 80 meters. Therefore, the radius of the curve is 80 meters.