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
inysia [295]
3 years ago
11

A potential energy function is given by u(x)=(3.00n)xâ(1.00n/m2)x3. at what position or positions is the force equal to zero?

Physics
1 answer:
qwelly [4]3 years ago
5 0

I believe the correct form of the energy function is:

u (x) = (3.00 N) x + (1.00 N / m^2) x^3

or in simpler terms without the units:

u (x) = 3 x + x^3

Since the highest degree is power of 3, therefore there are two roots or solutions of the equation.

 

Since we are to find for the positions x in which the force equal to zero, u (x) = 0, therefore:

3 x + x^3 = u (x)

3 x + x^3 = 0

Taking out x:

x (3 + x^2) = 0

So one of the factors is x = 0.

 

Finding for the other two factors, we divide the two sides by x and giving us:

x^2 + 3 = 0

x^2 = - 3

x = sqrt (- 3)

x = - 1.732 i, 1.732 i

 

The other two roots are imaginary therefore the force is only equal to zero when the position is also zero.

 

Answer:

x = 0

You might be interested in
Atomic physicists usually ignore the effect of gravity within an atom. To see why, we may calculate and compare the magnitude of
STatiana [176]

Answer:

2.27\cdot 10^{49}

Explanation:

The gravitational force between the proton and the electron is given by

F_G=G\frac{m_p m_e}{r^2}

where

G is the gravitational constant

m_p is the proton mass

m_e is the electron mass

r = 3 m is the distance between the proton and the electron

Substituting numbers into the equation,

F_G=(6.67259\cdot 10^{-11} m^3 kg s^{-2})\frac{(1.67262\cdot 10^{-27}kg) (9.10939\cdot 10^{-31}kg)}{(3 m)^2}=1.13\cdot 10^{-68}N

The electrical force between the proton and the electron is given by

F_E=k\frac{q_p q_e}{r^2}

where

k is the Coulomb constant

q_p = q_e = q is the elementary charge (charge of the proton and of the electron)

r = 3 m is the distance between the proton and the electron

Substituting numbers into the equation,

F_E=(8.98755\cdot 10^9 Nm^2 C^{-2})\frac{(1.602\cdot 10^{-19}C)^2}{(3 m)^2}=2.56\cdot 10^{-19}N

So, the ratio of the electrical force to the gravitational force is

\frac{F_E}{F_G}=\frac{2.56\cdot 10^{-19} N}{1.13\cdot 10^{-68}N}=2.27\cdot 10^{49}

So, we see that the electrical force is much larger than the gravitational force.

5 0
3 years ago
What is the kinetic theory of matter? How does it relate to the motion of molecules?
navik [9.2K]
The Kinetic<span> Molecular </span>Theory<span> explains the forces between </span>molecules<span> and the energy that </span>they<span> possess.

</span>
3 0
3 years ago
The heat capacity of object B is twice that of object A. Initially A is at 300 K and B at 450 K. They are placed in thermal cont
ivann1987 [24]

Answer:

The final temperature of both objects is 400 K

Explanation:

The quantity of heat transferred per unit mass is given by;

Q = cΔT

where;

c is the specific heat capacity

ΔT is the change in temperature

The heat transferred by the  object A per unit mass is given by;

Q(A) = caΔT

where;

ca is the specific heat capacity of object A

The heat transferred by the  object B per unit mass is given by;

Q(B) = cbΔT

where;

cb is the specific heat capacity of object B

The heat lost by object B is equal to heat gained by object A

Q(A) = -Q(B)

But heat capacity of object B is twice that of object A

The final temperature of the two objects is given by

T_2 = \frac{C_aT_a + C_bT_b}{C_a + C_b}

But heat capacity of object B is twice that of object A

T_2 = \frac{C_aT_a + C_bT_b}{C_a + C_b} \\\\T_2 = \frac{C_aT_a + 2C_aT_b}{C_a + 2C_a}\\\\T_2 = \frac{c_a(T_a + 2T_b)}{3C_a} \\\\T_2 = \frac{T_a + 2T_b}{3}\\\\T_2 = \frac{300 + (2*450)}{3}\\\\T_2 = 400 \ K

Therefore, the final temperature of both objects is 400 K.

4 0
2 years ago
Where can you find your carotid pulse to take your heart rate?
Nesterboy [21]

Answer: In your right wrist

Explanation:

6 0
3 years ago
An RC circuit is connected across an ideal DC voltage source through an open switch. The switch is closed at time t = 0 s. Which
steposvetlana [31]

Answer:

e)

Explanation:

In an RC series circuit, at any time, the sum of the voltages through the resistor and the capacitor must be constant and equal to the voltage of the DC voltage source, in order to be compliant with KVL.

At= 0, as the voltage through the capacitor can't change instantaneously, all the voltage appears through the resistor, which means that a current flows, that begins to charge the capacitor, up to a point that the voltage through the capacitor is exactly equal to the DC voltage, so no current flows in the circuit anymore, and the charge in the capacitor reaches to its maximum value.

5 0
2 years ago
Other questions:
  • 3. A crew team rows a boat at a rate of 20 km/h in still water. Beginning at time = 0 minutes, the team rows for 30 minutes up a
    14·2 answers
  • What adaptation in frogs enables them to swim​
    13·2 answers
  • A lunar lander is making its descent to moon base i. the lander descends slowly under the retro-thrust of its descent engine. th
    5·2 answers
  • If two objects are in thermal equilibrium, do they have the same thermal or internal energy?
    12·1 answer
  • Two equal quantities of water, of mass m and at temperatures T1 and T2, (T1 &gt; T2) are mixed together with the pressure kept c
    15·1 answer
  • Describe the relationship between the length and period of a pendulum in the language of direct proportions
    12·1 answer
  • 1. Which one of the following physical quantities is formed after dividing<br>mass by volume?​
    8·1 answer
  • HELP ASAPP!!!! WILL GIVE BRAINLIEST!<br> Describe the chemical structure of a cell membrane
    13·2 answers
  • so no body wants to help me:((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((
    5·1 answer
  • When a guitar string is plucked, what part of the standing wave is found at the fixed ends of the string?(1 point)
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!