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
artcher [175]
3 years ago
6

A block with mass M attached to a horizontal spring with force constant k is moving with simple harmonic motion having amplitude

A1. At the instant when the block passes through its equilibrium position, a lump of putty with mass m is dropped vertically onto the block from a very small height and sticks to it. Part APart complete What should be the value of the putty mass m so that the amplitude after the collision is one-half the original amplitude? Express your answer in terms of the variables M, A1, and k. m = 3M Previous Answers Correct Part B For this value of m, what fraction of the original mechanical energy is converted into heat? Express your answer in terms of the variables M, A1, and k.
Physics
1 answer:
NeX [460]3 years ago
3 0

Answer:

Explanation:

Given

Mass of block is M

spring constant =k

Amplitude is A_1

when putty is placed then amplitude decreases to \frac{A_1}{2}

Initially \frac{1}{2}kA^2=\frac{1}{2}Mv^2\quad \ldots(i)

Conserving momentum

Mv_o=(m+M)v

where v_o=initial velocity

v=\frac{M}{M+m}v_o

Now

\frac{1}{2}k(\frac{A_1}{2})^2=\frac{1}{2}(M+m)v^2

\frac{1}{2}k(\frac{A_1}{2})^2=\frac{1}{2}(M+m)(\frac{M}{M+m}v_o)^2\quad \ldots(ii)

divide (i) and (ii) we get

\frac{4}{1}=\frac{M}{M+m}\times (\frac{m+M}{m})^2

4=\frac{m+M}{M}

m=3M

Fraction of energy converted into heat=\frac{1}{2}kA_1^2-\frac{1}{2}k(\frac{A_1}{2})^2

=\frac{1}{2}kA_1^2[1-\frac{1}{4}]

=\frac{1}{2}kA_1^2[0.75]

So, \frac{3}{4} fraction is converted into heat energy

You might be interested in
A uniform stick 1.5 m long with a total mass of 250 g is pivoted at its center. A 3.3-g bullet is shot through the stick midway
Andru [333]

Answer:

<em>63.44 rad/s</em>

<em></em>

Explanation:

mass of bullet = 3.3 g = 0.0033 kg

initial velocity of bullet v_{1} = 250 m/s

final velocity of bullet v_{2} = 140 m/s

loss of kinetic energy of the bullet = \frac{1}{2}m(v^{2} _{1} - v^{2} _{2})

==> \frac{1}{2}*0.0033*(250^{2}  - 140^{2} ) = 70.785 J

this energy is given to the stick

The stick has mass = 250 g =0.25 kg

its kinetic energy = 70.785 J

from

KE = \frac{1}{2} mv^{2}

70.785 = \frac{1}{2}*0.25*v^{2}

566.28 = v^{2}

v= \sqrt{566.28} = 23.79 m/s

the stick is 1.5 m long

this energy is impacted midway between the pivot and one end of the stick, which leaves it with a radius of 1.5/4 = 0.375 m

The angular speed will be

Ω = v/r = 23.79/0.375 =<em> 63.44 rad/s</em>

5 0
2 years ago
A 120-V rms voltage at 1000 Hz is applied to an inductor, a 2.00-μF capacitor and a 100-Ω resistor, all in series. If the rms va
natima [27]

Answer:

The inductance of the inductor is 35.8 mH

Explanation:

Given that,

Voltage = 120-V

Frequency = 1000 Hz

Capacitor C= 2.00\mu F

Current = 0.680 A

We need to calculate the inductance of the inductor

Using formula of current

I = \dfrac{V}{Z}

Z=\sqrt{R^2+(L\omega-\dfrac{1}{C\omega})^2}

Put the value of Z into the formula

I=\dfrac{V}{\sqrt{R^2+(L\omega-\dfrac{1}{C\omega})^2}}

Put the value into the formula

0.680=\dfrac{120}{\sqrt{(100)^2+(L\times2\pi\times1000-\dfrac{1}{2\times10^{-6}\times2\pi\times1000})^2}}

L=35.8\ mH

Hence, The inductance of the inductor is 35.8 mH

4 0
3 years ago
Read 2 more answers
HELP! What are some examples of energy transformations?????
Fittoniya [83]

hydro: water pushing turbines to create electricity

wind: wind pushing wind turbines to create electricity

geothermal: heat from earth core creating steam which moves turbines and creates heat and electricity

5 0
3 years ago
The first-order decomposition of cyclopropane has a rate constant of 6.7 × 10–4 s–1. If the initial concentration of cyclopropan
Ket [755]

Answer:

.864 M

Explanation:

For first order decomposition,

rate constant k = 1/t x ln a / (a - x )

given , a = 1.33 M , t = 644 s , k = 6.7 x 10⁻⁴ , a - x  = ? = b( let )

6.7 x 10 ⁻⁴ = 1/644 x ln 1.33/b

ln 1.33/b = 6.7 x 10⁻⁴ x 644 = .4315

1.33 / b = e⁰ ⁴³¹⁵ = 1.5395

b = 1.33 / 1.5395 = .864 M.

7 0
3 years ago
What are magnetic forces produced by?
babymother [125]
The magnetic force is a consequence of the electromagnetic force, one of the four fundamental forces of nature, and is caused by the motion of charges.
3 0
3 years ago
Other questions:
  • What is empirical evidence and what is it not
    8·1 answer
  • When an object is solely under the influence of conservative forces, the sum of its kinetic and potential energies does not chan
    8·1 answer
  • How do the tension of the cord and the force of gravity affect a pendulum
    14·1 answer
  • Fill in the blank-There is very little precipitation in the Taiga, however when moisture does fall, it is typically in the form
    13·1 answer
  • What is meant by the term fitness​
    6·1 answer
  • We can model a lightning bolt as a very long, straight wire. If a lightning bolt carries a current of 30 kA, and you are unfortu
    7·1 answer
  • What is the mass of 5 moles of gold
    8·2 answers
  • How does no light affect the plants?
    10·1 answer
  • At an amusement park, a roller coaster carrying nine homosexuals, moving at 18 m/s, jumps its track at a point that is 20 meters
    13·1 answer
  • 5.00-kg particle starts from the origin at time zero. Its velocity as a function of time is given by v =6t^2 i + 2t j where v is
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!