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 = (mg)/(x)`

`k = (140 * 9.8)/(0.087)`

k = 15770 N/m

total mass = 140 + m_c

period of oscillation

`T = 2 \pi \sqrt{(total\ mass)/(k)}`

`1.66 = 2 \pi \sqrt{(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