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
Paraphin [41]
2 years ago
14

A 10 g particle undergoes SHM with an amplitude of 2.0 mm and a maximum acceleration of magnitude 8.0 multiplied by 103 m/s2, an

d an unknown phase constant ?.(a) What is the period of the motion?1 s(b) What is the maximum speed of the particle?2 m/s(c) What is the total mechanical energy of the oscillator?3 J(d) What is the magnitude of the force on the particle when the particle is at its maximum displacement?4 N(e) What is this force when the particle is at half its maximum displacement?5 N
Physics
1 answer:
Nat2105 [25]2 years ago
8 0

Answer:

a)T=0.0031416s

b)v_{max}=6.283\frac{m}{s}

c) E=0.1974J

d)F=80N

e)F=40N

Explanation:

1) Important concepts

Simple harmonic motion is defined as "the motion of a mass on a spring when it is subject to the linear elastic restoring force given by Hooke's Law (F=-Kx). The motion experimented by the particle is sinusoidal in time and demonstrates a single resonant frequency".

2) Part a

The equation that describes the simple armonic motion is given by X=Acos(\omega t +\phi)    (1)

And taking the first and second derivate of the equation (1) we obtain the velocity and acceleration function respectively.

For the velocity:

\frac{dX}{dt}=v(t)=-A\omega sin(\omega t +\phi)   (2)

For the acceleration

\frac{d^2 X}{dt}=a(t)=-A\omega^2 cos(\omega t+\phi)   (3)

As we can see in equation (3) the acceleration would be maximum when the cosine term would be -1 and on this case:

A\omega^2=8x10^{3}\frac{m}{s^2}

Since we know the amplitude A=0.002m  we can solve for \omega like this:

\omega =\sqrt{\frac{8000\frac{m}{s^2}}{0.002m}}=2000\frac{rad}{s}

And we with this value we can find the period with the following formula

T=\frac{2\pi}{\omega}=\frac{2 \pi}{2000\frac{rad}{s}}=0.0031416s

3) Part b

From equation (2) we see that the maximum velocity occurs when the sine function is euqal to -1 and on this case we have that:

v_{max}=A\omega =0.002mx2000\frac{rad}{s}=4\frac{m rad}{s}=4\frac{m}{s}

4) Part c

In order to find the total mechanical energy of the oscillator we can use this formula:

E=\frac{1}{2}mv^2_{max}=\frac{1}{2}(0.01kg)(6.283\frac{m}{s})^2=0.1974J

5) Part d

When we want to find the force from the 2nd Law of Newton we know that F=ma.

At the maximum displacement we know that X=A, and in order to that happens cos(\omega t +\phi)=1, and we also know that the maximum acceleration is given by::

|\frac{d^2X}{dt^2}|=A\omega^2

So then we have that:

F=ma=mA\omega^2

And since we have everything we can find the force

F=ma=0.01Kg(0.002m)(2000\frac{rad}{s})^2 =80N

6) Part e

When the mass it's at the half of it's maximum displacement the term cos(\omega t +\phi)=1/2 and on this case the acceleration would be given by;

|\frac{d^2X}{dt^2}|=A\omega^2 cos(\omega t +\phi)=A\omega^2 \frac{1}{2}

And the force would be given by:

F=ma=\frac{1}{2}mA\omega^2

And replacing we have:

F=\frac{1}{2}(0.01Kg)(0.002m)(2000\frac{rad}{s})^2 =40N

You might be interested in
AYUDA!!!!!
ZanzabumX [31]

Answer:

a) El valor de la densidad es 0.79 \frac{g}{cm^{3} } o 790 \frac{g}{cm^{3} }

b) El peso especifico es 7749.9\frac{N}{m^{3} }

Explanation:

a) La densidad se define como la propiedad que tiene la materia, ya sean sólidos, líquidos o gases, para comprimirse en un espacio determinado. En otras palabras, la densidad es una magnitud que permite medir la cantidad de masa que hay en determinado volumen de una sustancia. Entonces, la expresión para el cálculo de la densidad es el cociente entre la masa de un cuerpo y el volumen que ocupa:

d=\frac{m}{V}

En este caso:

  • masa= 237 g= 0,237 kg (siendo 1000 g= 1 kg)
  • volumen= 300 cm³= 0,0003 m³ (siendo 1 cm³= 0,000001 m³)

Reemplazando:

d=\frac{237 g}{300cm^{3} } →  d=0.79 \frac{g}{cm^{3} }

d=\frac{0,237 kg}{0,0003m^{3} }→  d=790 \frac{g}{cm^{3} }

<u><em>El valor de la densidad es 0.79 </em></u>\frac{g}{cm^{3} }<u><em> o 790 </em></u>\frac{g}{cm^{3} }<u><em></em></u>

b) El peso específico es la relación existente entre el peso y el volumen que ocupa una sustancia en el espacio.

Entonces, en este caso, siendo el peso:

P= m*g= 0,237 kg* 9,81 \frac{m}{s^{2} }= 2,32497 N

el peso especifico es calculado como:

Pe=\frac{Peso}{Volumen}= \frac{2,32497N}{0,0003 m^{3} }

Pe= 7749.9\frac{N}{m^{3} }

<u><em>El peso especifico es 7749.9</em></u>\frac{N}{m^{3} }<u><em></em></u>

8 0
3 years ago
Calculate the heat energy required to increase the temperature of 3 kg of water by 20ºC. The specific heat capacity of water is
Marina86 [1]

Answer:

Heat energy required = 252000J or 252KJ.

Explanation:

<u>Given the following data;</u>

Mass = 3kg

Temperature = 20ºC

Specific heat capacity of water = 4200 J/kg°C

To find the heat energy required;

Heat capacity is given by the formula;

Q = mct

Where;

  • Q represents the heat capacity or quantity of heat.
  • m represents the mass of an object.
  • c represents the specific heat capacity of water.
  • t represents the temperature.

Substituting into the equation, we have;

Q = 3*4200*20

Q = 252000 Joules or 252 Kilojoules.

6 0
2 years ago
What is the kinetic energy of a 400kg house that is racing around a track at 17 meters per second?
nasty-shy [4]

Kinetic energy = (1/2) (mass) (speed squared)

Kinetic energy = (1/2) (400 kg) (17 m/s)²

Kinetic energy = (1/2) (400 kg) (289 m²/s²)

<em>Kinetic energy = 57,800 Joules</em>

<em></em>

(That's some amazing house.  I'd like to be there to see it.)

5 0
3 years ago
1. A base-ball of mass 0.3kg approaches the bat at a speed of 30 miles/hour and when the ball hits the bat for 0.5 s, it started
andre [41]

Answer:

I = 27kg.mi/h

Explanation:

In order to calculate the impulse of the ball, you use the following formula:

I=m\Delta v  =m(v-v_o)      (1)

m: mass of the ball = 0.3kg

v: speed of the ball after the bat hit it = 60mi/h

vo: speed of the ball before the bat hit it = 30mi/h

You replace the values of all parameters in the equation (1):

I=(0.3kg)(60mi/h-(-30mi/h))=27kg\frac{mi}{h}

where the minus sign of the initial velocity means that the motion of the ball is opposite to the final direction of such a motion.

The imulpse of the ball is 27 kg.miles/hour

5 0
3 years ago
Acceleration Practice
Trava [24]

Answer:

0.85 m/s²

Explanation:

Acceleration is change in velocity over change in time. In mathematically, it can be expressed as:

\displaystyle{\vec{a} = \dfrac{\Delta \vec{v}}{\Delta t} = \dfrac{\vec v_2 - \vec v_1}{t_2-t_1}}

Our final velocity is given to be 17 m/s in 20 seconds. Initial velocity is at starting point which is 0 m/s in 0 second. Therefore:

\displaystyle{\vec{a} = \dfrac{\Delta \vec{v}}{\Delta t} = \dfrac{17-0}{20-0}}\\\\\displaystyle{\vec{a} = \dfrac{\Delta \vec{v}}{\Delta t} = \dfrac{17}{20}}\\\\\displaystyle{\vec{a} = \dfrac{\Delta \vec{v}}{\Delta t} = 0.85 \ \, \sf{m/s^2}}

Therefore, the acceleration of a horse from starting point to 17 m/s in 20 seconds is 0.85 m/s²

8 0
1 year ago
Read 2 more answers
Other questions:
  • If an object has a kinetic energy of 30 j and mass of 34kg how fast is the object moving ?
    8·1 answer
  • A horse gallops along a racecourse at a speed of 40km/h. It takes the horse 3 minutes to run the length of the track. Convert 3
    7·1 answer
  • An astronaut notices that a pendulum which took 2.45 s for a complete cycle of swing when the rocket was waiting on the launch p
    6·1 answer
  • A net force of 25.0 N causes an object to accelerate at 4.00 m/s2. What is the mass of the object?
    15·2 answers
  • What best explains why a wood burning fire place represents an open system
    13·2 answers
  • When you graph the motion of an object, you put ____ on the horizontal axis and ____ on the axis.
    10·1 answer
  • "A positively-charged particle is held at point A between two parallel metal plates. The plate on the left has a net positive ch
    7·1 answer
  • Which statement should he place in the region marked X?
    7·1 answer
  • HEEEEEEELLLLLPPPPPPP 20 points and Brainliest
    6·1 answer
  • S Four identical particles, each having charge q and mass m, are released from rest at the vertices of a square of side L. How f
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!