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allsm [11]
2 years ago
11

Suppose your friend claims to have discovered a mysterious force in nature that acts on all particles in some region of space. H

e tells you that the force is always pointed away a definite point in space, which we can call the force center. The magnitude of the force turns out to be proportional to B/r3, where r is the distance from the force center to any other point. Your friend says that it has been determined that the constant of proportionality has been determined to be B= 2 (in units to be determined later), so that the magnitude of the force on a particle (in newtons) can be written as 2r^3, when the particle is at a distance r from the force center.
Required:
Write an expression of potential energy.
Physics
1 answer:
kirill [66]2 years ago
5 0

Answer:

             U = 1 / r²

Explanation:

In this exercise they do not ask for potential energy giving the expression of force, since these two quantities are related

             

         F = - dU / dr

this derivative is a gradient, that is, a directional derivative, so we must have

          dU = - F. dr

the esxresion for strength is

         F = B / r³

let's replace

          ∫ dU = - ∫ B / r³  dr

in this case the force and the displacement are parallel, therefore the scalar product is reduced to the algebraic product

let's evaluate the integrals

            U - Uo = -B (- / 2r² + 1 / 2r₀²)

To complete the calculation we must fix the energy at a point, in general the most common choice is to make the potential energy zero (Uo = 0) for when the distance is infinite (r = ∞)

             U = B / 2r²

we substitute the value of B = 2

             U = 1 / r²

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Peter is a middle-aged, overweight man who is trying to decrease his body circumference. How could the serving size on a nutriti
gregori [183]
One simple way to losing weight is by calorie counting. Peter can go to his nutritionist and learn just how much calories he can have as intake per day to lose weight. The nutrition label on any food item lists the calories and their serving sizes. This can be used to keep track of how much calories Peter has taken each day, so as to not go over his daily limit.
3 0
2 years ago
Air "breaks down" when the electric field strength reaches 3×106n/c, causing a spark. a parallel-plate capacitor is made from tw
aalyn [17]
Ok, I think this is right but I am not sure:
 Q = ϵ
 0AE
A= π π
 r^2

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( π π (0.02m)^2)
(3x10^6 N/C) =3.3x10^-8 C = 33nC N = Q/e = (3.3x10^-8 C)/(1.60x10^-19 C/electron) = 2.1x10^11 electrons


4 0
2 years ago
Suppose that the current in the solenoid is i(t). The self-inductance L is related to the self-induced EMF E(t) by the equation
Artemon [7]

Answer:

L =   μ₀ n r / 2I

Explanation:

This exercise we must relate several equations, let's start writing the voltage in a coil

        E_{L} = - L dI / dt

 

Let's use Faraday's law

       E = - d Ф_B / dt

in the case of the coil this voltage is the same, so we can equal the two relationships

        - d Ф_B / dt = - L dI / dt

The magnetic flux is the sum of the flux in each turn, if there are n turns in the coil

        n d Ф_B = L dI

we can remove the differentials

      n Ф_B = L I

magnetic flux is defined by

     Ф_B = B . A

in this case the direction of the magnetic field is along the coil and the normal direction to the area as well, therefore the scalar product is reduced to the algebraic product

      n B A = L I

the loop area is

      A = π R²

     

we substitute

       n B π R² = L I                    (1)

To find the magnetic field in the coil let's use Ampere's law

        ∫ B. ds = μ₀ I

where B is the magnetic field and s is the current circulation, in the coil the current circulates along the length of the coil

           s = 2π R

we solve

              B 2ππ R =  μ₀ I

              B =  μ₀ I / 2πR

we substitute in

       n ( μ₀ I / 2πR) π R² = L I

       n  μ₀ R / 2 = L I

       L =   μ₀ n r / 2I

4 0
3 years ago
Two identical bullets are used. Both are released at the same height - one fired out of a gun, the other is dropped. Ignoring ai
irina [24]

Answer:

Both bullets will hit the ground at the same time.

Explanation:

Let's only analyze the vertical problem.

Any object that is not in the floor or resting in some site is being affected by the gravitational force (remember that we are ignoring air resistance)

Then the acceleration of this object will be equal to the gravitational acceleration:

a = -9.8m/s^2

Where the minus sign is because this acceleration goes down.

To get the velocity equation we need to integrate over time, we will get:

v(t) = ( -9.8m/s^2)*t + v0

Where v0 is the initial vertical velocity.

To get the position equation we need to integrate over time again, we will get:

p(t) = (1/2)*( -9.8m/s^2)*t^2 + v0*t + H

Where H is the initial height.

p(t) = (-4.9 m/s^2)*t^2 + v0*t + H

The object will hit the ground when p(t) = 0

Then we need to solve for t the next equation:

(-4.9 m/s^2)*t^2 + v0*t + H = 0

Notice that the only things we need to know are:

H = initial height (we know that is the same for both bullets)

v0 = initial vertical velocity (also is the same for both bullets)

Notice that the horizontal velocity does not affect this equation, then we will get the same value of t for the dropped bullet and for the fired bullet.

This means that both bullets will hit the ground at the same time.

8 0
2 years ago
Suppose that the inverse market demand for silicone replacement tips for Sony earbud headphones is p ​= pN ​- 0.1Q, where p is t
lbvjy [14]

Complete Question

The complete question is shown on the first uploaded image

Answer:

a

   The effect of a change in the price of a new pair of headphones on the equilibrium price of replacement tips​ ( ​dp/dpN​) is

                   \frac{\delta p}{\delta p_N} =1

b

 The value of Q and p at equilibruim is

          Q_e = 250    and    p_d = 5

The consumer surplus is  C= 3125

The producer surplus  is   P = 375

Explanation:

      From the question we are told that

           The inverse market demand is  p_d = p_N -0.1Q

                The inverse supply function is     p_s = 2+ 0.012Q

a

The effect of change in the price  is mathematically given as

                  \frac{\delta p}{\delta p_N}

Now differntiating the inverse market demand function with respect to p_N

We get that  

                   \frac{\delta p}{\delta p_N} =1

b

   We are told that p_N =$30

        Therefore the inverse market demand becomes

                             p_d = 30 -0.1Q

At  equilibrium

                  p_d = p_s

So we have

               30 -0.1Q_e = 2+ 0.012Q_e

Where Q_e is the quantity at equilibrium

                    28 = 0.112Q_e

                     Q_e = \frac{28}{0.112}

                    Q_e = 250

Substituting the value of  Q into the equation for the inverse market demand function

                p_d = 30 - 0.1 (250 )

                    p_d = 5

Looking at the equation for p_d \ and \ p_s we see that

     For  Q =  0

             p_d = 30

             p_s =2

 And  for Q =  250

                 p_d = 5

                 p_s = 5

Hence the consumer surplus is mathematically evaluated as

           C = \frac{1}{2} * Q_e * (30 -5)

Substituting value

        C = \frac{1}{2} * 250 (30-5)

           C= 3125

And

  The  producer surplus is mathematically evaluated as

                    P = \frac{1}{2} *250 * (5-2)

                    P = 375

     

         

           

                     

4 0
3 years ago
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