Final answer:
The single equation relating force, mass, speed, and radius in circular motion is F = kmr, where F is the force, m is the mass, r is the radius, and k is a constant.
Step-by-step explanation:
To develop the relationship among force, mass, speed, and radius in a circular motion, we can use the equation F = mra where F is the force, m is the mass, a is the acceleration, and r is the radius. Based on the given information:
The force is directly proportional to the mass of the car, so we can write F = km, where k is a constant.
The force is directly proportional to the car's speed squared, so we can write F = ks², where s is the speed and k is a constant.
The force is inversely proportional to the radius of the turn, so we can write F = k/r, where r is the radius and k is a constant.
Combining these equations, we get F = km = ks² = k/r. Rearranging the equation, we have F = k(mr²)/r, which simplifies to F = kmr, the single equation relating force, mass, speed, and radius.