This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Step 1: Calculate the total mass (m) of the car and its occupants. The mass of the car is 1300 kg. The combined mass of two people is 160 kg. m = m_car + m_people m = 1300 kg + 160 kg m = 1460 kg Step 2: Calculate the total effective spring constant (k_total). The car is supported by four springs, and each spring has a force constant of 20,000 N/m. Since the springs act in parallel to support the car, their effective spring constant is the sum of their individual constants. k_total = 4 × k_each k_total = 4 × 20,000 N/m k_total = 80,000 N/m Step 3: Calculate the frequency of vibration (f). The frequency of vibration for a mass-spring system is given by the formula: f = (1)/(2) sqrt(k_total)m Substitute the calculated values for m and k_total: f = (1)/(2) sqrt(80,000 N/m)1460 kg f = (1)/(2) sqrt(54.7945 s)^-2 f = (1)/(2) × 7.4023 s^-1 f ≈ (7.4023)/(6.28318) Hz f ≈ 1.178 Hz Rounding to three significant figures: f ≈ 1.18 Hz The frequency of vibration of the car is 1.18 Hz.