Question

An object of mass MM = 3.00 kgkg is attached to a spring with spring constant kk = 33.0 N/mN/m whose unstretched length is LL = 0.140 mm , and whose far end is fixed to a shaft that is rotating with an angular speed of ωω = 1.00 radians/sradians/s . Neglect gravity and assume that the mass also rotates with an angular speed of 1.00 radians/sradians/s as shown. (Figure 1)When solving this problem use an inertial coordinate system, as drawn here.

Given the angular speed of ωω = 1.00 radians/sradians/s , find the radius R(ω)R(ω) at which the mass rotates without moving toward or away from the origin.

Express your answer in meters.

Answer #1

A block with mass 3.10 kgkg is attached
to a vertical spring that has negligible mass and force constant
895 N/mN/m . The spring initially is relaxed and in equilibrium.
The block is released from rest.
a) What is its speed after it has descended 0.0500 mm from its
initial position?
Express your answer with the appropriate units.
b) What is the maximum speed of the block as it descends?
Express your answer with the appropriate units.

A freight company uses a compressed spring to shoot 1.70 kgkg
packages up a 1.00-mm -high frictionless ramp into a truck, as the
figure(Figure 1) shows. The spring constant is 338 N/mN/m and the
spring is compressed 33.0 cmcm .
What is the speed of the package when it reaches the truck?
AND
A careless worker spills his soda on the ramp. This creates a
50.0-cmcm-long sticky spot with a coefficient of kinetic friction
0.43. How high up the ramp...

A 5 kg mass is
attached to a spring. The mass is compressed fully to the left and
released from rest. The mass displays simple harmonic motion with a
period of 3 s and a maximum speed of 0.4 m/s. Assume the spring is
massless and neglect friction and air resistance.
a. Determine ω
b. What is the
amplitude of the oscillations?
c. What is the initial
phase (in radians) of the oscillator?
d. What is the spring
constant?

A 0.454-kgkg block is attached to a horizontal spring that is at
its equilibrium length, and whose force constant is 22.0 N/mN/m.
The block rests on a frictionless surface. A
5.80×10−2-kgkg wad of putty is thrown horizontally at
the block, hitting it with a speed of 8.94 m/sm/s and sticking.
Part A
How far does the putty-block system compress the spring?

A uniform rod of mass 3.45×10−2 kgkg and length 0.360
mm rotates in a horizontal plane about a fixed axis through its
center and perpendicular to the rod. Two small rings, each with
mass 0.250 kgkg , are mounted so that they can slide along the rod.
They are initially held by catches at positions a distance
4.80×10−2 mm on each side from the center of the rod,
and the system is rotating at an angular velocity 28.0
rev/minrev/min ....

A 2.10 kgkg frictionless block is attached to an ideal spring
with force constant 317 N/mN/m . Initially the block has velocity
-4.00 m/sm/s and displacement 0.260 mm .
A.Find the amplitude of the motion.
B. Find the maximum acceleration of the block.
C. Find the maximum force the spring exerts on the block.

An object with mass 3.8 kg is executing simple harmonic motion,
attached to a spring with spring constant 260 N/mN/m . When the
object is 0.017 mm from its equilibrium position, it is moving with
a speed of 0.65 m/s .
Calculate the amplitude of the motion.
Calculate the maximum speed attained by the object.

An object of mass of 2.7 kg is attached to a spring with a force
constant of k = 280 N/m.
At t = 0, the object is observed to be 2.0 cm from its equilibrium
position with a speed of
55 cm/s in the -x direction. The object undergoes simple harmonic
motion “back and
forth motion” without any loss of energy.
(a) Sketch a diagram labeling all forces on the object and
calculate the maximum
displacement from equilibrium of...

1. A 0.45 kg object mass attached to a spring whose
spring constant is 600 n/m executes simple harmonic motion. its
maximum speed is 3.0 m/s the maximum acceleration is:

1. A mass 0.15 kg is attached to a horizontal spring with spring
constant k = 100 N/m moves on a horizontal surface. At the initial
moment in time, the mass is moving to the right at rate of 3.5 m/s
and displacement of 0.2 m to the right of equilibrium.
a) What is the angular frequency, period of oscillation, and
phase constant?
b) What is the amplitude of oscillation (Hint: Use energy.) and
maximum speed of the spring-mass system?

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