Final answer:
To prevent skidding when the radius of a turn is halved, the centripetal force must be doubled, as it is inversely proportional to the radius.
Step-by-step explanation:
The question of how the centripetal force must change when the radius of a curve is halved to prevent skidding involves understanding the relationship between centripetal force, radius, and velocity. The centripetal force needed for an object in circular motion can be calculated by the formula Fc = mv2/r, where Fc is the centripetal force, m is the mass of the object, v is the tangential velocity, and r is the radius of the circle.
If the radius is halved and speed remains the same, the centripetal force must be doubled to prevent skidding because the force is inversely proportional to the radius (Fc ∙ r = constant). This means that if the radius is reduced by half, the force must increase by a factor of two to maintain the same circular motion without skidding.