Question

Multiple-Concept Example 6 presents a model for solving this problem. As far as vertical oscillations are concerned, a certain automobile can be considered to be mounted on four identical springs, each having a spring constant of 1.21 x 105 N/m. Then, four identical passengers are seated in the car, and it is set into a vertical oscillation that has a period of 0.371 s. If the mass of the empty car is 1400 kg, determine the mass of each passenger. Assume that the mass of the car and its passengers is distributed evenly over the springs.

Answer 1

Answer:

$71.865\ \text{kg}$

Explanation:

Mass of car = 1400 kg

T = Time period = 0.371 s

k = Spring constant = $1.21\times 10^{5}\ \text{N/m}$

Time period is given by

$\dfrac{1}{T}=\dfrac{1}{2\pi}\sqrt{\dfrac{k}{m}}\\\Rightarrow m=4\dfrac{kT^2}{4\pi^2}\\\Rightarrow m=\dfrac{4\times 1.21\times 10^5\times (0.371)^2}{4\pi^2}\\\Rightarrow m=1687.46\ \text{kg}$

The 4 in the numerator is because there are 4 springs

Mass of car with people is 1687.46 kg.

Mass of people

$1687.46-1400=287.46\ \text{kg}$

Mass of each person

$\dfrac{287.46}{4}=71.865\ \text{kg}$

Mass of each person is $71.865\ \text{kg}$.