A 1200-kg car whose springs have an effective force constant of 2.66 × 10⁶ N/m is moving along the highway with its tires out of balance. The tires have a radius of 40.6 cm. At what speed will the driver experience large vibrations? A) 19.1 m/s B) 22.2 m/s C) 18.9 m/s D) 17.4 m/s E) 25.0 m/s

Question

Quizplus · Accepted Answer

The speed at which the driver will experience large vibrations is the speed at which the natural frequency of the car's suspension system matches the frequency of the tire imbalance. The natural frequency (f) can be calculated using the formula f = (1/2π) * √(k/m), where k is the spring constant and m is the mass. The frequency of the tire imbalance is v/(2πr), where v is the speed and r is the radius of the tire. Setting these equal gives the speed v = √(k/m) * r. Substituting the given values results in approximately 19.1 m/s.

A 1200-Kg Car Whose Springs Have an Effective Force Constant