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.

Explanation:

Mass of car = 1400 kg

T = Time period = 0.371 s

k = Spring constant =

Time period is given by

The 4 in the numerator is because there are 4 springs

Mass of car with people is 1687.46 kg.

Mass of people

Mass of each person

Mass of each person is .

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.