Question

A massless spring of spring constant *k* = 4872 N/m is
connected to a mass *m* = 210 kg at rest on a horizontal,
frictionless surface.

**Part (a)** The mass is displaced from equilibrium
by *A* = 0.73 m along the spring’s axis. How much potential
energy, in joules, is stored in the spring as a result?

**Part (b)** When the mass is released from rest at
the displacement *A*= 0.73 m, how much time, in seconds, is
required for it to reach its maximum kinetic energy for the first
time?

**Part (c)** The typical amount of energy released
when burning one barrel of crude oil is called the barrel of oil
equivalent (BOE) and is equal to 1 BOE = 6.1178362 GJ. Calculate
the number, *N*, of springs with spring constant *k*
= 4872 N/m displaced to *A* = 0.73 m you would need to store
1 BOE of potential energy.

**Part (d)** Imagine that the *N* springs
from part (c) are released from rest simultaneously. If the
potential energy stored in the springs is fully converted to
kinetic energy and thereby “released” when the attached masses pass
through equilibrium, what would be the average rate at which the
energy is released? That is, what would be the average power, in
watts, released by the Nspring system?

**Part (e)** Though not a practical system for
energy storage, how many million buildings, *B*, each using
10^{5} W, could the spring system temporarily power?

Answer #1

Problem 2: (a) In this exercise a massless spring with a spring
constant k = 6 N/m is stretched from its equilibrium position with
a mass m attached on the end. The distance the spring is stretched
is x = 0.3 m. What is the force exerted by the spring on the mass?
(5 points)
(b) If we were to stretch the spring-mass system as in part (a)
and hold it there, there will be some initial potential energy
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