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
What is the condition for an object experiencing free fall?
S_A_V [24]

Answer:

The body acts under the influence of gravity.

Explanation:

An object experiencing free fall is acting under the influence of gravitational force and the acceleration due gravity is positive for any falling object. The body is able to fall freely due to the effect of gravity on it. This gravity effect causes the body to get attracted to the earth's gravitational surface due to gravitational pull exerted on the body.

3 0
3 years ago
What is the relationship between stream and drainage basin
Sergeeva-Olga [200]
Each stream in a drainage system drains into a certain area. In a drainage basin the water falling in the basin drain will fall into the same stream. A drainage divides drawing basin from other drainage basins
5 0
3 years ago
Find the unit vector in the direction of vector B=4i+2j-5k​
solmaris [256]

Answer:

\frac{4}{\sqrt{45} } i\,+\frac{2}{\sqrt{45} } j-\frac{5}{\sqrt{45} } k

Explanation:

for the unit vector, we need to divide the given vector by its norm, because it should be in the SAME direction as the original vector, but of magnitude "1".

We notice that the norm of the given vector is:

\sqrt{4^2+2^2+(-5)^2} =\sqrt{45}

Then, the unit vector becomes:

\frac{4}{\sqrt{45} } i\,+\frac{2}{\sqrt{45} } j-\frac{5}{\sqrt{45} } k

7 0
2 years ago
What the unit of work?​
ra1l [238]

Answer:

yes

Explanation:

5 0
2 years ago
Would a measured force of (46.5 0.8 N  ) be in agreement with a theoretically calculated force of (48.4 0.6 N  ) ? Show your w
OverLord2011 [107]

Answer:

A measured force of (46.5 0.8 N  ) would not be in agreement with a theoretically calculated force of (48.4 0.6 N  )

Explanation:

From the question we are told that

  Measured force is  F_M  =  [46.5 \pm 0.8 \  N ]

   Calculated force is  F_c =  [48.4 \pm 0.6 \  N ]

Generally the measured force in interval form is

     46.5 - 0.8  < F_M  <  46.5 + 0.8

=>  45.7   < F_M  < 47.3

Generally the calculated  force in interval form is

     48.4 - 0.6  < F_c  <  48.4 + 0.6

=>  47.8   < F_M

Generally looking both interval we see that they do not intersect at any point Hence  

A measured force of (46.5 0.8 N  ) would not be in agreement with a theoretically calculated force of (48.4 0.6 N  )      

8 0
2 years ago
Other questions:
  • a. Of the three experiments that are used to confirm the Big Bang theory, which is the most interesting to you and why?
    7·1 answer
  • Select all the correct answers.
    12·1 answer
  • A 55 kg roller skater is at rest on a flat skating rink, a 198 N horizontal force is needed to set the skater in motion.
    9·1 answer
  • When thermal energy is added to an object what happens to the motion of the particles
    6·2 answers
  • Someone pls help mee
    10·1 answer
  • Three collisions are elastic and three are inelastic. Determine which collision type took place for each collision. Support your
    6·1 answer
  • А
    5·2 answers
  • 1. Compared to most other metals, what properties do the alkali metals have? А low melting points and high densities B low melti
    5·1 answer
  • A wave has frequency of 50 Hz and a wavelength of 10 m. What is the speed of the wave? Group of answer choices
    10·1 answer
  • 5.How do simple machines make work easier?(1 point)
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!