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
I have an algorithm that runs in O(N ), where N is the size of the problem. For N = 100, the time for the algorithm to run is 1
hodyreva [135]

Answer:

B) 10 minutes

Explanation:

When the size of the problem is 100 then it takes 1 minute to solve

100\ s=1\ min

So, when the size of the problem is 1 then it takes the following minutes

1\ s=\frac{1}{100}\ min

For when the size of the problem is 1000 we have

1000\ s=\frac{1000}{100}\ min=10\ min

So, it will take 10 minutes to solve the algorithm of size 1000

4 0
3 years ago
Aaron turns to walk back to the house. 4 m up the driveway, he
xxMikexx [17]

From the front door to his current position, Aaron's Distance is 4m. and his Displacement is 4m.

Distance is a measure of how far apart two objects or locations are using numbers. The distance can refer to a physical length in physics or to an estimate based on other factors in common usage. Sometimes, the symbol |AB| is used to represent the distance between two points.

A displacement is a vector in geometry and mechanics that have a length equal to the shortest distance between a point P's initial and final positions.

Given,

Length of path  = 4m

Distance  =?

Displacement  =?

Distance is the length of the path and it has magnitude but no direction. The distance covered is 4m Displacement is the length of the path and it has magnitude and direction. Displacement is 4m towards the mailbox.

To know more about Displacement  refer to:  brainly.com/question/11934397

#SPJ9

5 0
1 year ago
HELP!!!! PLEASE (and there will be more)
Alexus [3.1K]

Answer:

i wanna say tranverse if not surface

Explanation:

6 0
3 years ago
Read 2 more answers
A constant force of 45 N directed at angle θ to the horizontal pulls a crate of weight 100 N from one end of a room to another a
Rasek [7]

Answer:

W=173.48J

Explanation:

information we know:

Total force: F=45N

Weight: w=100N

distance: 4m

vertical component of the force: F_{y}=12N

-------------

In this case we need the formulas to calculate the components of the force (because to calculate the work we need the horizontal component of the force).

horizontal component: F_{x}=Fcos\theta

vertical component: F_{y}=Fsen\theta

but from the given information we know that F_{y}=12N

so, equation these two F_{y}=Fsen\theta and F_{y}=12N

Fsen\theta =12N

and we know the force F=45N, thus:

45sen\theta=12

now we clear for \theta

sen\theta =12/45\\\theta=sin^{-1}(12/45)\\\theta =15.466

the angle to the horizontal is 15.466°, with this information we can calculate the horizontal component of the force:

F_{x}=Fcos\theta

F_{x}=45cos(15.466)\\F_{x}=43.37N

whith this horizontal component we calculate the work to move the crate a distance of 4 m:

W=F_{x}*D\\W=(43.37N)(4m)\\W=173.48J

the work done is W=173.48J

7 0
3 years ago
The vibrations along a transverse wave move in a direction _________.
GrogVix [38]

Answer: perpendicular to it oscillations.

Explanation: A transverse wave is a wave whose oscillations is perpendicular to the direction of the wave.

By perpendicular, we mean that the wave is oscillating on the vertical axis (y) of a Cartesian plane and the vibration is along the horizontal axis (x) of the plane.

Examples of transverse waves includes wave in a string, water wave and light.

Let us take a wave in a string for example, you tie one end of a string to a fixed point and the other end is free with you holding it.

If you move the rope vertically ( that's up and down) you will notice a kind of wave traveling away from you ( horizontally) to the fixed point.

Since the oscillations is perpendicular to the direction of wave, it is a transverse wave

5 0
3 years ago
Other questions:
  • Get the lead out! That is really graphite in your pencil, not lead. Graphite is a form of carbon. Use the physical properties of
    8·2 answers
  • Match the correct term with each part of the wave
    7·1 answer
  • What type of evidence should be collected first ?
    13·1 answer
  • How to draw and label a diagram to show how you would separate each mixture
    9·1 answer
  • Assigned Media Question Help According to a random sample taken at 12​ A.M., body temperatures of healthy adults have a​ bell-sh
    5·1 answer
  • Which of the following are likely to form a covalent bond?
    15·2 answers
  • How are the Digestive system and the Circulatory system similar?
    14·1 answer
  • How is an image produced by a plane mirror different than an image produced by a convex mirror
    14·2 answers
  • How do the numbers of atoms of each element compare before and after the reaction? Why do you think this is?
    7·2 answers
  • A 2.00 kg mass is located at (4.00 m, 0.00 m, 0.00 m) and a 4.00 kg mass is located at (0.00 m, 3.00 m, 0.00 m). If this system
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!