Imagine designing an experiment to determine the mass of an unknown object by attaching it to a spring, setting it in motion, and observing how fast it vibrates. Assume that you know the spring constant k, and that you can ignore the effects of damping. Derive a formula for finding the mass of an object given the spring constant, k, and the oscillating frequency, f0. Explain how you derived your formula.

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.

earth's neighboring galaxy, the andromeda galaxy, is a distance of 2.54×107 light-years from earth. if the lifetime of a human is taken to be 70.0 years, a spaceship would need to achieve some minimum speed min to deliver a living human being to this galaxy.