Question

A 10 kg mass is sliding at 8 m/s along a frictionless floor toward an ideal massless spring. When the mass hits the spring, they stick together without any loss of energy. The mass stops briefly at x = +4.2 m before moving back toward equilibrium. (Assume x = 0 at the point at which the mass sticks to the spring and t = 0 when the mass first makes contact with the spring.)a)What is the spring constant of the spring?b)What is the frequency, f, of the spring with the mass attached?c)At what time will the mass stop the second time?d)What is the equation to describe the position of the mass at time, t?e)How much will the spring have compressed when the mass stops moving?f)What is the period of the spring with the mass attached?g)How long will it take the mass to stop (the first time) once it hits the spring?h)When it stops, what is the magnitude of the acceleration of the mass?i)Three (3) seconds after the mass sticks to the spring, what is the mass's(a)Position, ⃗x?(b)Velocity, ⃗v?(c)Acceleration, ⃗a?After oscillating for a while, the mass breaks into two equal parts when it is at its maximum positive position. The piece which is broken off is pushed for a while.j)At what point does the broken piece separate from the part still attached to the spring?k)Under this new situation, what are the answers to parts a-c? (a)(b)(c)l)The half of the mass which breaks away will be going a constant 8 m/s, but the remaining half on the spring is varying in speed. Explain how energy is still conserved.

Answer 1