A hydrogen atom contains a single electron that moves in a circular orbit about a single proton. Assume the proton is stationary, and the electron has a speed of 7.5 105 m/s. Find the radius between the stationary proton and the electron orbit within the hydrogen atom.

Answer:

Net force= 14 units

The object is unbalanced

Explanation:

The net force refers to the sum of all forces applied to an object. However, the direction of force applied determine the net force. In this question, a boy and girl is pulling a heavy crate at the same time.

This means that the force is in the same direction, hence, the net force will be:

F(N) = 7 + 7 = 14 unit

However, since the pull is occuring at the same direction. This means that the object has a net force, therefore, will move in a particular direction. This means that the OBJECT IS UNBALANCED

Answer:

Fundamental frequency= 174.5 hz

Explanation:

We know

fundamental frequency=

velocity =

mass per unit length==0.00427

Now calculating velocity v=

                                           =244.3

Distance between two nodes is 0.7 m.

Plugging these values into to calculate frequency

f = =174.5 hz

Answer:

5.831 m/s

Explanation:

According to the work-energy law,

Work done between two points = Change in kinetic energy between the two points.

Since the plastic ball is initially at rest, its initial kinetic energy is 0 since the initial velocity = 0

Work done by the spring = ∫ F.dx

The spring is compressed by 10 cm, so, we integrate from -0.1 m to 0 m

Fₓ(x) = (-30.0 N/m)x+ (60.0 N/m²)x²

F = -30x + 60x²

W = ∫ F.dx = ∫ (-30x + 60x²) dx

W = [- 15x² + 20x³]⁰₋₀.₁ = 0 - [- 15(0.01) + 20(-0.001)] = 0.17 J

W = ΔKE

ΔKE = (mv²/2) - 0

mv²/2 = 0.17

m = 10 g = 0.01 kg

0.01 v² = 0.34

v² = 34

v = 5.831 m/s

To solve this problem we will start from the definition of Force, as the product between the electric field and the proton charge. Once the force is found, it will be possible to apply Newton's second law, and find the proton acceleration, knowing its mass. Finally, through the linear motion kinematic equation we will find the speed of the proton.

PART A ) For the electrostatic force we have that is equal to

Here

q= Charge

E = Electric Force

PART B) Rearrange the expression F=ma for the acceleration

Here,

a = Acceleration

F = Force

m = Mass

Replacing,

PART C) Acceleration can be described as the speed change in an instant of time,

There is not then

Rearranging to find the velocity,

Final answer:

The magnitude of the electric force felt by the proton is 4.4 x 10^-16 N. The proton's acceleration is 2.64 x 10^11 m/s^2. The proton's speed after 1.40 μs in the field is 3.70 x 10^5 m/s.

Explanation:

The charge of a proton is 1.6 x 10-19 coulombs and the electric field strength is 2750 N/C. Therefore, the magnitude of the electric force felt by the proton is (1.6 x 10-19 C)(2750 N/C) = 4.4 x 10-16 N. The mass of a proton is approximately 1.67 x 10-27 kilograms. Therefore, the proton's acceleration is (4.4 x 10-16 N)/(1.67 x 10-27 kg) = 2.64 x 1011 m/s2. Since the proton starts from rest, its initial velocity (u) is 0. Therefore, the proton's speed after 1.40 μs is v = (2.64 x 1011 m/s2)(1.40 x 10-6 s) = 3.70 x 105 m/s.

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Answer:

Explanation:

The average speed of a body is defined as the ratio between total distance and total time

    v = dx / dt

    v = 162.0 / 2.95

    v = 54.9 m / s

The absolute errors (uncertainties) of the distance and time measurements as measured with instruments are the errors of the instruments

     Δx = 0.1 cm

     Δt = 0.01 s

Relative errors (uncertainties) are the absolute errors between the measured value

     Er = Δx /x

     Er = 0.1 / 162.0

     Er = 6.2 10⁻⁴        length

     Er = 0.01 / 2.95

     Er = 3.4 10⁻³        time

The most uncertain measure is the time to have a greater relative error

Let's calculate the relative speed error

     Δv / v = dv / dx dx + dv / dt dt

     dv / dx = 1 / t

     dv / dt = x (-1 / t²)

     Er = Δv / v = 1 / t Δx + x / t² Δt

     Er = 0.1 / 2.95 + 162.0/2.95²  0.01

     Er = 0.034 + 0.19

     Er = 0.22

We can observe that the relative error of time is much higher than the relative error of distance, so to reduce the speed error, time must be measured with much more precision

Absolut mistake

   Er = Δv / v

   Δv = Er v

   Δv = 0.22 54.9

   Δv = 12 cm / s

    v± Δv = (5 ±1 ) 10 cm/s

When calculating the relative uncertainty, it is known which magnitude should be more precisely medical to reduce the total error of a derived magnitude

Answer:

W = ½ m v²

Explanation:

In this exercise we must solve it in parts, in a first part we use the conservation of the moment to find the speed after the separation

We define the system formed by the two parts of the rocket, therefore the forces during internal separation and the moment are conserved

initial instant. before separation

        p₀ = m v

final attempt. after separation

        = m /2  0 + m /2 v_{f}

       p₀ = p_{f}

       m v = m /2

       v_{f}= 2 v

this is the speed of the second part of the ship

now we can use the relation of work and energy, which establishes that the work is initial to the variation of the kinetic energy of the body

initial energy

         K₀ = ½ m v²

final energy

        = ½ m/2  0 + ½ m/2 v_{f}²

        K_{f} = ¼ m (2v)²

        K_{f} = m v²

the expression for work is

         W = ΔK = K_{f} - K₀

         W = m v² - ½ m v²

         W = ½ m v²

Final answer:

The principle of conservation of momentum implies that no work is performed by the internal forces during the separation of the space vehicle. This is granted that external forces are ignored and the total momentum and kinetic energy of the closed system remain constant.

Explanation:

The subject you're asking about centers around the principle of conservation of momentum. In the case of this space vehicle, before separation, the momentum of the whole system is given by the product of the mass and velocity, mv. After separation, one piece is at rest, leaving the other piece with momentum mv. As there is no external force, the total momentum does not change, so no work is performed by the internal forces causing the separation.

In more detail, the principle of conservation of momentum states that the total linear momentum of a closed system remains constant, regardless of any interactions happening within the system. The system is 'closed' meaning that no external forces are acting upon it. In this case, the space vehicle and the two smaller pieces it separates into form a closed system. This is consistent with your question's stipulation to ignore external forces, such as gravitational forces.

This can also be understood from the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy. If we consider the vehicle before and after the separation, the kinetic energy of the system remains the same: initially all the energy is concentrated in the moving vehicle, and after the separation, all the kinetic energy is transferred to the moving piece while the at-rest piece has none. Therefore, the work done by the internal forces - which would change the kinetic energy - must be zero.

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