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
Tom [10]
3 years ago
11

A particle of mass m moves under the influence of a force given by F = (−kx + kx3/α2) where k and α are positive constants. a) F

ind the potential energy function U(x) (Take U(x=0) = 0). b) Find any equilibrium points and determine if they are stable or unstable. c) Sketch the potential as a function of position. d)What is the maximum total energy, Emax a particle may have if its motion is to remain bounded? e) For the case of bounded motion with E
Physics
1 answer:
Romashka-Z-Leto [24]3 years ago
4 0

Answer:

Explanation:

a ) F = (-kx + kx³/a²)

intensity of field

I = F / m

=  (-kx + kx³/a²) / m

If U be potential function

- dU / dx =  (-kx + kx³/a²) / m

U(x)  = ∫  (kx - kx³/a²) / m dx

= k/m ( x²/2 - x⁴/4a²)

b )

For equilibrium points , U is either maximum or minimum .

dU / dx = x - 4x³/4a² = 0

x = ± a.

dU / dx = x - x³/a²

Again differentiating

d²U / dx² = 1 - 3x² / a²

Put the value of x = ± a.

we get

d²U / dx²  = -2 ( negative )

So at x = ± a , potential energy U is maximum.

c )

U =  k/m ( x²/2 - x⁴/4a²)

When x =0 , U = 0

When x=  ± a.

U is maximum

So the shape of the U-x curve is like a bowl centered at x = 0

d ) Maximum potential energy

put x = a or -a in

U(max)  =  k/m ( x²/2 - x⁴/4a²)

= k/m ( a² / 2 - a⁴/4a²)

= k/m ( a² / 2 - a²/4)

a²k / 4m

This is the maximum total energy where kinetic energy is zero.

You might be interested in
Starting from rest, a 68.0 kg woman jumps down to the floor from a height of 0.790 m, and immediately jumps back up into the air
Aleonysh [2.5K]

Answer:

a) I = 0 N s,  b)  v = -3.935 m / s, c) vf = 3.935 m / s,   d)   y = 0.790 m

Explanation:

a) Let's start by defining the upward direction (+ y) as positive. For this part of the exercise we must use the momentum relationship

          I = ∫F dt

The force of the woman on the floor is given and by action and rection the floor exerts on the woman a force of equal magnitude, but opposite direction

        I = ∫ (9200 t - 11500 t2) dt

        I = 9200 t² / 2 - 11500 t³ / 3

We evaluate between the lower limit t = 0 and upper limit t = 0.800 s

       I = 9200 (0.8² -0) - 11500 (0.8³ -0)

       I = 5888 -5888

       I = 0 N s

Directed from the floor to the woman

b) For this part we use kinematics

      v² = v₀² - 2g y

     v = √ (0 - 2 9.8 (-0.79))

     v = 3.935 m / s

The speed direction is down

c) for this we use the relationship between momentum and the amount of movement

      I = ΔP

      I = m vf - m v₀

     vf = (I + m v₀) / m

This is the impulse of women on the floor    

      vf = ( 0 + 68 (3.935)) / 68

      vf = 3.935 m / s

d) let's use kinematics

      v₂ = v₀² - 2gy

      0 = v₀² - 2gy

      y = v₀² / 2g

      y = 3.935²/2 9.8

      y = 0.790 m

8 0
3 years ago
What is the primary source of a sound?
brilliants [131]

Answer:

A vibration is the primary source of a sound.

8 0
3 years ago
A pendulum is constructed from a 6 kg mass attached to a strong cord of length 1.7 m also attached to a ceiling. Originally hang
valina [46]

Answer:

work done is -2.8  × 10⁻⁶ J

Explanation:

Given the data in the question;

mass of the pendulum m = 6 kg

Length of core = 1.7 m

Now, case1, mass is pulled aside a small distance of 7.6 cm and released from rest. so let θ₁ be the angle made by mass with vertical axis.

so, θ₁ = ( 7.6 × 10⁻² m / 1.7 m ) = 0.045 rad

In case2, mass is pulled aside a small distance of 8 cm and released from rest. so let θ₁ be the angle made by mass with vertical axis.

so, θ₂ = ( 8 × 10⁻² m / 1.7 m ) = 0.047 rad.

Now, the required work done will be;

W = \int\limits^{\theta_2} _{\theta_1} {r} \, d\theta

W = \int\limits^{\theta_2} _{\theta_1} {-mgl sin\theta } \, d\theta

W = -mgl  \int\limits^{0.047 } _{0.045 } {sin\theta } \, d\theta

W = -mgl[ -cosθ ]^{0.047}_{0.045 }

W = 6 × 9.8 × 1.7 × [ cos( 0.047 ) - cos( 0.045 ) ]

W = 6 × 9.8 × 1.7 × [ -2.8 × 10⁻⁸ ]

W = -2.8  × 10⁻⁶ J

Therefore, work done is -2.8  × 10⁻⁶ J

6 0
3 years ago
In a house, a circuit often includes multiple electrical outlets which are parallelconnected to a single voltage source. Each of
valkas [14]

Answer:

In parallel circuits, if one element has a problem, it can be eliminated and the rest of the elements continue to work.

Explanation:

There are two ways to connect electrical circuits, in series and in parallel.

Series circuits have the problem that when one element is damaged, the entire circuit is interrupted and runs out of power.

In parallel circuits, if one element has a problem, it can be eliminated and the rest of the elements continue to work.

In Breaker it is connected in series so that when some maintenance is needed, all the energy can be interrupted simultaneously and if some equipment tries to consume a lot of energy, the circuit prevents this action by interrupting the energy of the entire circuit

5 0
3 years ago
Which is an example of negative acceleration?
pshichka [43]

Answer:

A) a snowboarder who increases speed when traveling downhill

7 0
3 years ago
Read 2 more answers
Other questions:
  • Examples of increase in pressure due to increase in applied force<br>​
    14·1 answer
  • Prove that..<br>please help<br>​
    7·1 answer
  • While teaching about transistors, Mr. Mendoza shows a video of a hand pump being used to draw water from a well. He points out h
    7·2 answers
  • Which of the following can happen to solar energy after it enters the earths atmosphere?
    6·2 answers
  • You can carry a 50 N weight up a flight of stairs that is 3 m high in 10 s. Then you carry 40 N up two flights of stairs in 20 s
    14·1 answer
  • Please help me......
    8·1 answer
  • Search about non-ohmic devices in 3 pages​
    12·1 answer
  • A man on the moon with a mass of 90 kilograms weighs 146 newtons. The radius of the moon is 1.74 x 10^6
    7·1 answer
  • Simon's cat is evil and likes to knock his alarm clock off the night stand every morning. Simon's cat must apply a __________ to
    9·1 answer
  • What is the probability that time headway is at most 6 sec? (round your answer to three decimal places.)
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!