1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
bearhunter [10]
3 years ago
15

A 0.50-kg block attached to an ideal spring with a spring constant of 80 N/m oscillates on a horizontal frictionless surface. Th

e total mechanical energy is 0.12 J. What is the greatest extension of the spring from its equilibrium length? What is the maximum speed of the block?
Physics
1 answer:
Taya2010 [7]3 years ago
8 0

Answer:

The greatest extension of the spring is \bf{0.055~m} and the maximum speed of the block is \bf{0.695~m/s}.

Explanation:

Given:

The mass of the block is, m = 0.50~kg

The spring constant of the spring is, k = 80~N/m

The mechanical energy of the block is, E = 0.12~J

When a particle is oscillating in a simple harmonic way, its total energy is given by

E = \dfrac{1}{2}m\omega^{2}a^{2}~~~~~~~~~~~~~~~~~~~~~~~~~~~(1)

where \omega is the angular velocity of the mass and a is the amplitude of its motion.

The relation between angular velocity and spring constant is given by

\omega = \sqrt{\dfrac{k}{m}}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(2)

Substituting equation (2) in equation (1), we have

~~~~~~&& E = \dfrac{1}{2}ka^{2}\\&or,& a = \sqrt{\dfrac{2E}{k}}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(3)

Substituting 0.12~J for E and 80~N/m for k in equation (3), we can write

a &=& \sqrt{\dfrac{2(0.12~J)}{80~N/m}}\\~~~&=& 0.055~m

The relation between the maximum velocity and the amplitude is given by

v_{m} &=& \omega a\\~~~~&=& \sqrt{\dfrac{k}{m}}a~~~~~~~~~~~~~~~~~~~~~~~~~~~~(4)

Substituting 80~N/m for k , 0.50~kg for m and 0.055~m for a in equation (4), we have

v_{m} &=& \sqrt{\dfrac{80~N/m}{0.50~kg}}(0.055~m)\\~~~&=& 0.695~m/s

You might be interested in
A waitperson carrying a tray with a platter on it tips the tray at an angle of 12° below the horizontal. If the gravitational fo
Nadusha1986 [10]

Answer:

The answer is 1.0 N

Explanation:

inclination of tray=12^{\circ}

gravitational Force=5 N

Now this gravitational force has two component i.e.

5\sin \theta  is parallel to the tray =1.039 N

5\cos \theta  is perpendicular to the tray =4.890 N

7 0
2 years ago
Five scientist who travelled to space​
Masja [62]

Answer:

The Most Famous Astronomers of All Time. Karl Tate, SPACE.com. ...

Claudius Ptolemy. Bartolomeu Velho, Public Domain. ...

Nicolaus Copernicus. Public Domain. ...

Johannes Kepler. NASA Goddard Space Flight Center Sun-Earth Day. ...

Galileo Galilei. NASA

6 0
3 years ago
How to hope with challeges of today,&how to veaw our current​
mel-nik [20]

Answer:

hey how are you

are these points for free or something

5 0
2 years ago
Is the world flat or round?
Arisa [49]

Answer:

round

Explanation:

science explained it alot

7 0
3 years ago
Read 2 more answers
Your friend's car is stuck in the snow. You push very hard and become very 1 tired but the car won't move. Did you do work?
crimeas [40]

Answer:

Yes you  worked

Explanation:

You may have not seen a good outcome but you did put effort in.

7 0
3 years ago
Other questions:
  • An object acted on by three forces moves with constant velocity. one force acting on the object is in the positive x direction a
    8·1 answer
  • Why do you think it is so important that all evidence be identified (such as marking the bullets and tagging firearms)? What con
    15·1 answer
  • The driver of a car slams on the brakes when he sees a tree blocking the road. The car slows uniformly with acceleration of -5.7
    13·1 answer
  • In separate experiments, a large number of particles (all with the same charge, but with a wide variety of masses and speeds) ar
    9·1 answer
  • Matter and energy cycle around our ecosystem, are never being created or destroyed.
    6·2 answers
  • A hair dryer is a pump for air. Do a battery and a Genecon act like pumps for charge?
    8·2 answers
  • A ball on the end of a rope is moving in a vertical circle near the surface of the earth. Point A is at the top of the circle; C
    10·1 answer
  • After the box comes to rest at position x1, a person starts pushing the box, giving it a speed v1. When the box reaches position
    11·1 answer
  • A tennis player serves a tennis ball such that it is moving horizontally when it leaves the racquet. When the ball travels a hor
    12·1 answer
  • After a projectile is fired into the air, what is the magnitude of the acceleration
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!