Two protons are held a distance d apart. The electrostatic force and the gravitational force that one proton exerts on the other are Fe and Fg, respectively. Which of the following correctly compares the magnitude and direction of these forces?
Fe > Fg, opposite direction

a. Fe > Fg, same direction
b. Fe < Fg opposite direction
c. Fe < Fg same direction

Answer:

0.5 seconds

Explanation:

Work = Fdcos(theta) = 10*2*cos(0) = 20 J

Power = W/t

40 = 20/t

t = 0.5s

Answer:

Distance is a scalar quantity while displacement is a vector quantity

Explanation:

A scalar quantity represents only the magnitude and does not give any detail about the direction of the quantity for example distance. Distance can be any length measured in any direction (no specific direction)

However, a vector quality represents both the magnitude and direction. For instance displacement is a vector quantity. If direction is not defined then displacement becomes equal to distance.

Answer:

a)   v = [tex]\sqrt{G \frac{M_e}{(R+R_e)} }[/tex],   b)  Em = - ½ m [tex]G \frac{M_e}{(R+R_e)}[/tex], c)  T = 2π [tex]\sqrt{\frac{ (R+R_e)^3 }{G M_e } }[/tex]

Explanation:

a) For this exercise we must use Newton's second law with the gravitational force

          F = ma

          [tex]G \frac{m M_e}{(R+R_e)^2 }[/tex] = m a

the acceleration of the satellite is centripetal

          a = [tex]\frac{v^2}{(R+R_e)}[/tex]

we substitute

            [tex]G \frac{m M_e}{(R+R_e)^2 } = m \frac{v^2}{ (R+R_e)}[/tex]

          [tex]G \frac{M_e}{(R+R_e)}[/tex]  = v²

          v = [tex]\sqrt{G \frac{M_e}{(R+R_e)} }[/tex]

the distance is from the center of the earth

b) mechanical energy is the sum of kinetic energy plus potential energy

         Em = K + U

         Em = ½ m v² - G m M / (R + R_e)

we substitute the expression for the velocity

         Em = ½ m  [tex]G \frac{M_e}{(R+R_e)}[/tex]  - [tex]G \frac{M_e}{(R+R_e)}[/tex]  

         Em = - ½ m [tex]G \frac{M_e}{(R+R_e)}[/tex]  

c) as the orbit is circulating, the velocity modulus is constant

         v = d / t

in a complete orbit the distance traveled of the circle is

        d = 2π (R + R_e)

where time is called period

         v = 2π (R + R_e)

         T = 2π (R + R_e) / v

we substitute the speed value

        T = 2π (R + R_e) [tex]\sqrt{\frac{(R+R_e) }{G M_e } }[/tex]

        T = 2π [tex]\sqrt{\frac{ (R+R_e)^3 }{G M_e } }[/tex]

(a) An expression for the speed of the satellite in its orbit.

[tex]V=\sqrt{G\dfrac{M_e}{R+R_e}[/tex]

(b) An expression for the total mechanical energy of the satellite-Earth system in its orbit.

[tex]E_m =\dfrac{1}{2}mG\dfrac{M_e}{(R+R_e)}[/tex]

(c) An expression for the period of the satellite’s orbit.

[tex]T=2\pi\sqrt\dfrac{(R+R_e)^3}{GM_e}[/tex]

A satellite is a moon, planet or machine that orbits a planet or star. For example, Earth is a satellite because it orbits the sun

a) For this exercise we must use Newton's second law with the gravitational force

F = ma

[tex]ma =G\sqrt{\dfrac{mM_e}{(R+R_e)}[/tex]

the acceleration of the satellite is centripetal

[tex]a=\dfrac{v^2}{R+R_e}[/tex]

we substitute

[tex]G\dfrac{mM_e}{(R+R_e)}=m\dfrac{v^2}{(R+R_e)}[/tex]

[tex]G\dfrac{M_e}{(R+R_e)}=v^2[/tex]

[tex]v=\sqrt{G\dfrac{M_e}{(R+R_e)}[/tex]

b) mechanical energy is the sum of kinetic energy plus potential energy

        Em = K + U

[tex]Em =\dfrac{1}{2}m v^2 - \dfrac{G m M} {(R + R_e)}[/tex]

we substitute the expression for the velocity

[tex]E_m=\dfrac{1}{2}mG\dfrac{M_e}{(R+R_e)}-G\dfrac{M_e}{(R+R_e)}[/tex]

[tex]E_m=-\dfrac{1}{2}G\dfrac{M_e}{(R+R_e)}[/tex]

c) as the orbit is circulating, the velocity modulus is constant

[tex]v=\dfrac{d}{t}[/tex]  

in a complete orbit the distance traveled of the circle is

[tex]d = 2\pi (R + R_e)[/tex]

where time is called period

[tex]v = 2\pi (R + R_e)[/tex]

[tex]T = \dfrac{2\pi (R + R_e)} { v}[/tex]

we substitute the speed value

[tex]T = 2\pi (R + R_e) . \sqrt{\dfrac{(R+R_e)}{GM_e}[/tex]

[tex]T=2\pi\sqrt{\dfrac{(R+R_e)}{GM_e}[/tex]

(a) An expression for the speed of the satellite in its orbit.

[tex]V=\sqrt{G\dfrac{M_e}{R+R_e}[/tex]

(b) An expression for the total mechanical energy of the satellite-Earth system in its orbit.

[tex]E_m =\dfrac{1}{2}mG\dfrac{M_e}{(R+R_e)}[/tex]

(c) An expression for the period of the satellite’s orbit.

[tex]T=2\pi\sqrt\dfrac{(R+R_e)^3}{GM_e}[/tex]

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Answer:

a. 6000J or 6KJ

b. Force =600

To find the normal force, we can use the equation: normal force = weight + friction force * cos(incline angle).

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Answer:

v = 2 m/s

Explanation:

Here, we will use the law of conservation of momentum to solve this problem:

[tex]m_1u_1 + m_2u_2 = m_1v_1+m_2v_2[/tex]

where,

m₁ = mass of grandma = 80 kg

m₂ = mass of James = 40 kg

u₁ = initial speed of grandma = 3 m/s

u₂ = initial speed of James = 0 m/s

v₁ = v₂ = v = final speed of grandm and James = ?

Therefore,

[tex](80\ kg)(3\ m/s)+(40\ kg)(0\ m/s)=(80\ kg)(v)+(40\ kg)(v)\\\\(120\ kg)v = 240\ Ns\\\\v = \frac{240\ N.s}{120\ kg}\\[/tex]

v = 2 m/s

Answer:

Radioactive materials give off a form of energy called ionizing radiation.

Answer:

70.56 J

Explanation:

Gravitational Potential Energy= mass×gravitational pull× height

= 6×9.8×1.2= 70.56 J

The speed at which a clock would have to be moving in order to run at half the rate of a clock at rest depends on the theory of relativity that you are using.

In special relativity, time dilation is the phenomenon where time appears to pass differently for objects in motion relative to an observer at rest.

According to the theory, time appears to slow down for an object as it approaches the speed of light. The rate at which time appears to pass for an object is given by the equation:

T' = T / [tex]\sqrt{(1 - (v^2 / c^2))}[/tex]

Where T is the time as measured by an observer at rest, T' is the time as measured by an observer moving relative to the object, v is the velocity of the object, and c is the speed of light.

In addition, this is a theoretical scenario, practically in order to measure time dilation in a laboratory, it is required a very high precision of measurements, that are currently not possible.

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Answer:

did any of this help

Explanation:

y = (-2/3)x - 1

y-(-5)= -2/3(x-6)

y-y1=m(x-x1)

2x-3y=11

The displacement of the iguana between 3 s and 6 s  is 6.71 meters.

The distance traveled by the iguana between 3 s and 6 s is  8.08 meters.

Distance is the sum of an object's movements, regardless of direction.

The term "displacement" refers to a shift in an object's position.

According to the graph:

The displacement of the iguana between 3 s and 6 s

= √{ (3-6)²+(6-0)²} meters

= 6.71 meters.

The distance traveled by the iguana between 3 s and 6 s

= [ √{ (3-5)²+(6-6)²} +√{ (5-6)²+(6-0)²}] meters

= [2+ 6.08] meters

= 8.08 meters.

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Answer:

As a bat increases its forward speed, it should decrease the frequency of the emitted pulses to compensate.

decrease

Explanation:

Decreasing the frequency of the emitted pulse will help the bat reduce its frequency caused by its forward motion.  The forward motion shifts the bat's auditory frequency to a higher frequency; consequently, the bat should adjust downwards the frequency of the emitted pulse so the reflected pulse will be in the correct frequency range.

Answer:

Explanation:

Given that a centripetal force is a form of force that gives rise or causes a body to move in a curved path.

Hence;

1. When a car is being driven around a track, it is the FORCE OF FRICTION that is acting upon the turned wheels of the vehicle, which transforms into the centripetal force required for circular motion.

2. When a ball being is swung on the end of a string, TENSION FORCE acts upon the ball, which transforms the centripetal force required for circular motion.

3. When the moon is orbiting the earth, it is the FORCE OF GRAVITY acting upon the moon, which transforms the centripetal force required for circular motion.

4. A rotating wheel on the other hand has NO centripetal force because centripetal force is pull towards the center of a motion. However the speed of the object is tangent to the circle, while the direction of the force is also perpendicular to the direction of the rotating wheel.

The force that provides the centripetal force in each of the given situations are;

A) Friction Force

A) Friction ForceB) Tension Force

A) Friction ForceB) Tension ForceC) Force of gravity

A) Friction ForceB) Tension ForceC) Force of gravity D) No centripetal force

When an object is in circular motion, the force that keeps it moving round the circle while centrifugal force is the one that tries to pull the object away from the center.

A) When a car is driving around a track, there is a frictional force between the tires of the car and the track that acts on the vehicle to keep it in that circular motion. This frictional force is the centripetal force required to keep the vehicle in circular motion.

B) When a ball is swing on the end of a string, there is an upward force called tension force that acts on the ball to keep it swinging in circular motion. Thus, the centripetal force here is provided by the tension force.

C) When the moon is orbiting the earth, there is a force of gravity exerted by the earth on the moon that keeps the moon in a circular motion about Earth instead of moving in a straight line.

D) For a rotating wheel, the centripetal force does not do any work. The reason for that is because the centripetal force points toward the center of the circle, and as a result it means that the velocity of the rotating wheel is tangent to the circle.

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Answer:

Choice A. gamma rays

Explanation:

The bullet stops moving on hitting on a surface. Hence, the impulse here is equal to the momentum. Therefore, the mass of the bullet is 0.1 Kg.

Impulse in physics is the change in momentum. It is the product of the force and change in time.

hence, impulse = f. dt

When the bullet is travelling with  a velocity of 500 m/s it has a momentum. When it brought to rest, momentum become zero. Thus, the momentum is equal to the impulse here.

Therefore, f.dt = m. v

f.dt = 50 N s

v = 500 m/s

m = 50 N s/500 m/s = 0.1 Kg

Therefore, the mass of the bullet is 0.1 Kg.

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Answer:

v3 = 0 gm/s / 700g

Explanation:

To solve this problem, you need to use the principle of conservation of momentum, which states that the total momentum of a system remains constant unless acted upon by an external force. In this case, the total momentum of the system (the 2kg object before it explodes) is equal to the sum of the momenta of the three pieces after the explosion.

You can calculate the momentum of each piece by multiplying its mass by its velocity:

P1 = 800g * 30 m/s = 24,000 gm/s

P2 = 500g * 520 m/s = 260,000 gm/s

The total momentum of the system is the sum of these two momenta:

Ptotal = P1 + P2 = 24,000 gm/s + 260,000 gm/s = 284,000 g*m/s

The third piece has a mass of 2kg - 800g - 500g = 700g. We can use the conservation of momentum equation to find its velocity:

Ptotal = (700g * v3) + (800g * 30 m/s) + (500g * 520 m/s)

v3 = (Ptotal - (800g * 30 m/s) - (500g * 520 m/s)) / 700g

v3 = (284,000 gm/s - (800g * 30 m/s) - (500g * 520 m/s)) / 700g

v3 = (284,000 gm/s - 24,000 gm/s - 260,000 gm/s) / 700g

v3 = (284,000 - 24,000 - 260,000) gm/s / 700g

v3 = 0 gm/s / 700g

The velocity of the third mass is 0 m/s.

Hope this helps.

The displacement, acceleration, energy and velocity of the simple harmonic motion of the mass attached to the spring are as follows;

A) x(t) = 0.05·sin(10·t + π/2)

B) The acceleration is; a(t) = -2.5 m/s²

C) The total energy is 0.0625 J

D) The velocity is ±√3/4 m/s

The restoring force of a body in simple harmonic motion is directly proportional to the displacement of the body from its mean or central position.

Mass of the block, m = 2 kg

The spring constant, k = 200 N/m

The extension of the spring = 5 cm

Time at which the spring is released, t = 0

A. The motion of the spring with the mass is a Simple Harmonic Motion

The angular velocity can be obtained using the formula;

ω = √(k/m)

Therefore;
ω = √(200/2) = 10

The angular velocity of the block on the spring is, ω = 10 rad/s

The period, T = The time to complete 2·π rad

Therefore; T = 2·π rad/(10 rad/s) = π/5 s

The amplitude, A, is the cistance of the mass from the at rest position, which is 5 cm = 0.05 m

The equation of the extension of the spring is therefore;

x(t) = 0.05·sin(10·t + c)

At t = 0, x(t) = 0.05, therefore;

sin(10 × 0 + c) = sin(c) = 1

c = π/2

The equation for the displacement as a function of time is therefore;

B. The acceleration when x(t) = A/2 is obtained as follows;

x(t) = 0.05·sin(10·t + π/2)

A/2 = 0.05·sin(10·t + π/2)

A = 0.05

0.05/2 = 0.05·sin(10·t + π/2)

sin(10·t + π/2) = 1/2

10·t + π/2 = π/6

t = -π/30

cos(10×(-π/30) + π/2) = ±√3/2

v(t) = x'(t) = 0.05 × 10 × cos(10·t + π/2)

a(t) = v'(t) = -5·sin(10·t + π/2)

a(t) = v'(t) = -5·sin(10·t + π/2) = -5 × 1/2 = -2.5

C. The energy in a pring = (1/2)·k·x²

When x = A/2, we get;

E = (1/2) × 200 × (0.05/2)² = 0.0625

D) The velocity when x = A/2 is; v(t) = x'(t) = 0.05 × 10 × cos(10·t + π/2)

v(t) = 0.5 × cos(10·t + π/2)

When x = A/2, sin(10·t + π/2) = 1/2, therefore;

cos(10·t + π/2) = ±√3/2

v(t) = 0.5 × ±√3/2 = ±√3/4

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Answer:

800J

Explanation:

W = Fs, Work equals force times displacement

in this case, the force is 400N and the displacement is 2 meters.

The regular SI unit for work is joules

Answer:

(a) T = 2987.6 k

(b) T = 19986.2 k

Explanation:

The temperature of a star in terms of peak wavelength can be given by Wein's Displacement Law, which is as follows:

[tex]T = \frac{0.2898\ x\ 10^{-2}\ m.k}{\lambda_{max}}[/tex]

where,

T = Radiated surface temperature

[tex]\lambda_{max}[/tex] = peak wavelength

(a)

here,

[tex]\lambda_{max}[/tex] = 970 nm = 9.7 x 10⁻⁷ m

Therefore,

[tex]T = \frac{0.2898\ x\ 10^{-2}\ m.k}{9.7\ x\ 10^{-7}\ m}[/tex]

T = 2987.6 k

(b)

here,

[tex]\lambda_{max}[/tex] = 145 nm = 1.45 x 10⁻⁷ m

Therefore,

[tex]T = \frac{0.2898\ x\ 10^{-2}\ m.k}{1.45\ x\ 10^{-7}\ m}[/tex]

T = 19986.2 k

Answer:

Explanation:

The mass of the ball can be found by using the formula

[tex]m = \frac{f}{a} \\ [/tex]

f is the force

a is the acceleration

We have

[tex]m = \frac{15}{5} = 3 \\ [/tex]

We have the final answer as

Hope this helps you

The radius of the hydrogen-atom Bohr orbit shown in the figure is 5.3 nm.

The path that hypothetical electrons take around the nucleus is known as Bohr's orbit.

These orbits are described by Bohr in his hypothesis of the structure of an atom as energy levels or shells where electrons move in a fixed circle around the nucleus.

These orbits resemble solar system orbits, with the exception that they are attracted by electrical forces rather than gravity. The term "ground state" refers to the amount of energy that an electron typically occupies.

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Answer:

50 million years

Explanation:

light years is the distance light travels in one year given that the supercluster is 100 million light years across the the distance to the center will be half that amount therefore the answer is 50 million years

Answer:

Explanation:

We already know that Force is a vector. Weight being a force, is also a vector quantity. Displacement is distance in a specific direction, hence it is a vector quantity too. ... since energy, work done and time are scalar, Power is a scalar quantity

Answer:

  F = 3.6 10⁶ N

Explanation:

The expression for the electric force is

         F =  [tex]k \ \frac{q_1 q_2}{r^2}[/tex]

in this case it indicates that the charge q1 is doubled

       q₁ = 2   3 10⁻³ C

       q₁ = 6 10⁻³ C

let's reduce the magnitudes to the SI system

        q₂ = 6 10⁻³ C

        r = 0.3 m

let's calculate

       F = 9 10⁹ 6 10⁻³ 6 10⁻³ / 0.3²

       F = 3.6 10⁶ N

Capsule communicator or Capcom  is the only group in mission control that gets to communicate with the astronauts in space. Hence, option (B) is correct.

The capsule communicator, or Capcom, was the only voice that spoke to the astronauts during their trip to avoid any mistake. To ensure that the men in the capsule always had a familiar individual who understood their situation and could provide the information they required, Capcom was always manned by astronauts.

Both the technical control team on the ground and the astronauts in space are represented by Capcom.

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Answer:

Is at the pivot of the wheel

Answer:

1.66 m/s

Explanation:

Work or kinetic energy = [tex]\frac{1}{2} mv^{2}[/tex]

[tex]4864=\frac{1}{2} (3540)v^{2}[/tex]

v = 1.66 m/s