Question

Two people with a combined mass of 140 kg hop into an old car with worn-out shock absorbers. This causes the springs to compress by 8.70 cm. When the car hits a bump in the road, it oscillates up and down with a period of 1.66 s.

a) Find the total load supported by the springs.

b) Find the mass of the car.

Answer 1

Answe

given,

combined mass of two people = 140 Kg

compression of spring = 8.70 cm

time period = 1.66 s

we know,

F = k x

where k is spring constant

and also

F = mg

equating both the force equation

k x  = mg

$k = \dfrac{mg}{x}$

$k = \dfrac{140 \times 9.8}{0.087}$

k = 15770 N/m

total mass = 140 + m_c

period of oscillation

$T = 2 \pi \sqrt{\dfrac{total\ mass}{k}}$

$1.66 = 2 \pi \sqrt{\dfrac{140 + m_c}{15770}}$

140 + m_c = 1100

m_c = 960 Kg

a) total load supported by the car

  P  = 1100 Kg

b) mass of car = 960 Kg