Question

You are watching an object that is moving in SHM. When the object is displaced 0.580 m to the right of its equilibrium position, it has a velocity of 2.50 m/sto the right and an acceleration of 8.30 m/s2 to the left.

How much farther from this point will the object move before it stops momentarily and then starts to move back to the left?

Answer #1

Solution-:

Given data ,

Velocity = 2.50 m/s (towards right ) Acceleration = 8.30
m/s^{2} (towards left)

x = 0 580 meter

Force = Mass * Acceleration = Ma

Kx = Ma

So,

0.580 K = 8.3 M

or K/M = 8.3 / 0.580

= 14.31

Fron Using Energy Conservation ,

Total mechanical energy = constant

Then Energy conservation between point x= 0.580 and the extreme point i.e x = A at this point the velocity becomes is 0 .

So ,

1/2 M (2.5)^2 + 1/2 K(0.580)^2 = 1/2 KA^2

3.125 M = 0.5K(A^2 - 0.3364 )

So,

6.25 = (K/M) (A^2 - 0.3364) (K/M) = 14.31 from previous equation is ,

6.25 = 14.31(A^2 - 0.3364)

So find A ,

A^2-0.3364 = 6.25 / 14.31

A^2-0.3364 = 0.43675

A^2 = 0.4367 + 0.3364

A^2 = 0.7731 m

A = 0.879 m

Then , A - x

0.879 - 0.580 = 0.299 meter (Answer)

I hope help you !!

You are watching an object that is moving in SHM. When the
object is displaced 0.570 m to the right of its equilibrium
position, it has a velocity of 2.25 m/s to the right and an
acceleration of 8.15 m/s2 to the left. How much farther from this
point will the object move before it stops momentarily and then
starts to move back to the left?

You are watching an object that is moving in SHM. When the
object is displaced 0.620 m to the right of its equilibrium
position, it has a velocity of 2.10 m/s to the right and an
acceleration of 8.60 m/s2to the left.
How much farther from this point will the object move before it
stops momentarily and then starts to move back to the left?

You are watching an object that is moving in SHM. When the
object is displaced 0.640 m to the right of its equilibrium
position, it has a velocity of 2.50 m/s to the right and an
acceleration of 8.15 m/s2 to the left.

A 0.580-kg object attached to a spring with a force constant of
8.00 N/m vibrates in simple harmonic motion with an amplitude of
13.0 cm. (Assume the position of the object is at the origin at
t = 0.)
(a) Calculate the maximum value of its speed.
cm/s
(b) Calculate the maximum value of its acceleration.
cm/s2
(c) Calculate the value of its speed when the object is 11.00 cm
from the equilibrium position.
cm/s
(d) Calculate the value of...

The position of an object moving horizontally after t seconds is
given by the function s =12t-t^3 , for t > 0, where s is
measured in feet, with s g> 0 corresponding to positions right
of the origin.
a. When is the object stationary, moving to the right, and
moving to the left?
b. Determine the velocity and acceleration of the object at
t=4.
c. Determine the acceleration of the object when its velocity is
zero.
d. On what...

An object of mass m = 0.25 kg has a horizontal spring attached
to its left side, and slides along a frictionless surface. The
spring constant is κ = 0.4 N m . At t = 0 s, the object is
displaced 0.1m to the right of its equilibrium position. Its
initial velocity is 0.4 m s , toward the right.
a) Calculate the period T of the motion. b) Calculate the
angular frequency ω. c) Calculate the frequency ν....

A small object with mass 4.10 kg moves counterclockwise with
constant speed 1.35 rad/s in a circle of radius 3.05 m centered at
the origin. It starts at the point with position vector
3.05î m. Then it undergoes an angular displacement
of 8.65 rad.
(a) What is its new position vector?
m
(b) In what quadrant is the particle located and what angle does
its position vector make with the positive x-axis?
Second at ??°
(c) What is its velocity?
m/s...

1. An object-spring system moving with simple harmonic motion
(SHM) has an amplitude A.
(a) What is the total energy of the system in terms of k and A
only?
(b) Suppose at a certain instant the kinetic energy is twice the
elastic potential energy, KE = 2PE. Re-write this equation by using
only the variables for the mass, m, velocity, v, spring constant,
k, and position, x.
(c) Using the results of (a) and (b) and conservation of energy,...

15. Describe the energy transfers taking place when a spring SHM
system is moving.
Draw a diagram, pick 5 points, and describe the energy present at
each.
16. Start with Ebefore = Eafter to derive the maximum velocity
in a spring SHM
system.
17. A 2.0 kg mass is pulled 10. cm away from its equilibrium
point, on a spring with a
15 N/m constant. Show all steps.
a) Determine its maximum velocity as it passes through
equilibrium.
b) Determine...

A 2.80 kg box is moving to the right with speed 8.50 m/s on a
horizontal, frictionless surface. At t= 0 a horizontal
force is applied to the box. The force is directed to the left and
has magnitudeF(t)=( 6.00 N/s2 )t^2
a. What distance does the box move from its position at
t=0 before its speed is reduced to zero?
b. If the force continues to be applied, what is the velocity of
the box at 3.00 s ?

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 23 minutes ago

asked 31 minutes ago

asked 39 minutes ago

asked 46 minutes ago

asked 51 minutes ago

asked 51 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago