Question

6. A 5.00 kg object is suspended vertically by a spring that is attached to a ceiling at the other end. The object is held at rest such that the spring is initially in its relaxed (unstretched/uncompressed) state. The spring constant of the spring is 50.0 N/m. Determine: a) The lowest point below the spring’s equilibrium position the object will go if it is slowly lowered by hand (5 points) b) The lowest point below the spring’s equilibrium position the object will go if it is released from its initial position (5 points) c) Using work and/or force arguments, explain the difference in numerical values between a) and b) (5 points)

Answer #1

An object is attached to a hanging unstretched ideal
and massless spring and slowly lowered to its equilibrium position,
a distance of 6.4 cm below the starting point. If instead of having
been lowered slowly the object was dropped from rest, how far then
would it then stretch the spring at maximum elongation (in cm)?

1 A massless spring with spring constant ? hangs from the
ceiling with a small object of mass ? attached to its lower end.
The object is initially held at the spring’s rest position. The
object is then released oscillates up and down, with its lowest
position being 10 ?? below the point from which it was released. a)
What is the value of the ratio of the spring constant of the spring
over the mass attached? That is, what...

A small object of mass 1 kg is attached to a spring with spring
constant 2 N/m. This spring mass system is immersed in a viscous
medium with damping constant 3 N· s/m. At time t = 0, the mass is
lowered 1/2 m below its equilibrium position, and released. Show
that the mass will creep back to its equilibrium position as t
approaches infinity.

A 2.3 kg object oscillates at the end of a vertically hanging
light spring once every 0.40 s .
Write down the equation giving its position y (+
upward) as a function of time t. Assume the object started
by being compressed 19 cm from the equilibrium position (where
y = 0), and released. Note: the equilibrium position is
defined here as that location of the mass at rest when it is freely
hung from the spring, not the unstretched...

A particle of mass 5.00 kg is attached to a spring with a force
constant of 100 N/m. It is oscillating on a horizontal frictionless
surface with an amplitude of 2.00 m. A 7.00 kg object is dropped
vertically on top of the 5.00 kg object as it passes through its
equilibrium point. The two objects stick together.
(a) By how much does the amplitude of the vibrating system
change as a result of collision?
(b) By how much does...

A 50-cm-long spring is suspended from the ceiling. A 330 gmass
is connected to the end and held at rest with the spring
unstretched. The mass is released and falls, stretching the spring
by 20 cm before coming to rest at its lowest point. It then
continues to oscillate vertically.
a. What is the spring constant?
b. What is the amplitude of the oscillation?
c. What is the frequency of the oscillation?

Chapter 15, Problem 037
A massless spring hangs from the ceiling with a small object
attached to its lower end. The object is initially held at rest in
a position yi such that the spring is at its
rest length. The object is then released from
yi and oscillates up and down, with its lowest
position being 21 cm below yi.
(a) What is the frequency of the oscillation?
(b) What is the speed of the object when it is...

A 99-kg box hangs from the ceiling of a room suspended from a
spring with a force constant of 525 N/m. the unstressed length of
the spring is 0.450 m.
a) Find the equilibrium position of the box.
b) An identical spring is stretched and attached to the ceiling
and the box, and its parallel with the first spring. Find the
frequency of the oscillations when the box is released.
c) What is the new equilibrium position of the box...

A spring with constant k1 is attached vertically to the ceiling
and a sphere of mass m1 hangs from the other end of the spring.
Another spring, this one with constant k2 is attached vertically to
the first sphere. Finally a second sphere (mass m2) is attached to
the lower end of the second spring. Assuming that the spheres can
only move vertically and using y1 and y2 as coordinates measured
from the equilibrium position of each sphere, show that...

A 5.00 kg object on a hor-
izontal frictionless surface is at-
tached to a spring with
k
1000 N/m. The object is dis-
placed from equilibrium 50.0
cm horizontally and given an initial velocity of 10.0 m/s
back
toward the equilibrium position. What are (a) the motion’s
frequency, (b) the initial potential energy of the block –
spring
system, (c) the initial kinetic energy, and (d) the motion’s
am-
plitude?

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