Final answer:
For a 1700 kg car navigating a 43.0 m radius unbanked curve at 15.5 m/s, a vital coefficient of friction, approximately 0.590, is necessary. This coefficient ensures that the friction between the car's tires and the road supplies the needed centripetal force, preventing sliding during the turn.
Step-by-step explanation:
To navigate a 43.0 m radius unbanked curve at 15.5 m/s, a 1700 kg car requires a coefficient of friction of approximately 0.590. This coefficient is essential to ensure that the frictional force between the car's tires and the road provides the necessary centripetal force for a smooth turn without sliding. The calculation involves comparing the centripetal force required for circular motion to the frictional force, which is influenced by the weight of the car and the friction coefficient. A coefficient of friction below 0.590 would mean insufficient friction to keep the car on the curve, risking skidding or loss of control. Thus, this coefficient acts as a crucial factor for the car's successful negotiation of the unbanked curve.