Question

Two geekie physics students with a combined mass of 131 kg jump into their old car to run out for some late night pizza. The distance between the front and back axles of the car is 2.9 m. When they get in the car, the springs compress a total of 9.3 cm. On their way to the Pizza Hut, when they go over a bump, the car oscillates up and down with a period of 1.6 seconds.

(a) What is mass of the car?




Can you guys figure it out??
i got 2020.185 for K constant and then i used the formula m=kt^2/4pi^2 but that is wrong and it's giving me the same mass help or guide me please.

Answer 1

From the compression deltaX of the springs when they get in, you know that the spring constant of the suspension system is
k = F/deltaX = 131*g*/0.093 = 13800 N/m

The oscillation period is 2 pi sqrt [(M+m)/k] = 1.6
where M is the car weight and m is the additional weight of the passengers.

Solve for M+m and them subtract m

(M+m)/k = 6.48*10^-2 s^2

M+m = 895 kg
m = 764 kg