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Eddi Din [679]
3 years ago
10

Two circular coils are concentric and lie in the same plane. The inner coil contains 120 turns of wire, has a radius of 0.012 m,

and carries a current of 5.0 A. The outer coil contains 165 turns and has a radius of 0.017 m. What must be the magnitude and direction (relative to the current in the inner coil) of the current in the outer coil, such that the net magnetic field at the common center of the two coils is zero
Physics
1 answer:
RUDIKE [14]3 years ago
4 0

Answer:

5.152 A

Opposite to the inner coil

Explanation:

\mu_0 = Vacuum permeability = 4\pi \times 10^{-7}\ H/m

I_o = Outer coil current

I_i = Inner coil current = 5 A

N_i = Turns in inner coil = 120

N_o = Turns in outer coil = 165

R_i = Inner radius = 0.012 m

R_o = Outer radius = 0.017 m

Putting the magnetic field as equal we have

\dfrac{\mu_0I_iN_i}{2R_i}=\dfrac{\mu_0I_oN_o}{2R_o}\\\Rightarrow I_o=I_i\dfrac{N_i}{N_o}\dfrac{R_o}{R_i}\\\Rightarrow I_o=5\times \dfrac{120}{165}\times \dfrac{0.017}{0.012}\\\Rightarrow I_o=5.152\ A

The magnitude of current is 5.152 A,

The direction of the current is opposite to that of the inner coil as they have opposing magnetic fields

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Two identical bodies are sliding toward each other on a frictionless surface. One moves at 1 m/s and the other at 2 m/s. They co
mario62 [17]

Answer:

V=\dfrac{3}{2}\ m/s

Explanation:

Two identical bodies are sliding toward each other on a frictionless surface.

Initial speed of body 1, m₁ = 1 m/s

Initial speed of body 2, m₂ = 2 m/s

They collide and stick.

We need to find the speed of the combined mass. Let V is the speed of the combined mass.

Using the conservation of momentum.

m_1u_1+m_2u_2=V(m_1+m_2)

We have, m₁ = m₂ = m

m\times 1+m\times 2=(m+m)V\\\\m+2m=2m\times V\\\\3m=2mV\\\\V=\dfrac{3}{2}\ m/s

So, the speed of the combined mass is \dfrac{3}{2}\ m/s.

6 0
2 years ago
Three bullets are fired simultaneously by three guns aimed toward the center of a circle where they mash into a stationary lump.
earnstyle [38]

Answer:

2,87 * 10^{-3}

Explanation:

When the bullets meet at the center and collide, since momentum is a vectoral quantity, their momentum vectors even up and are sumof zero. Formula of momentum is P = m.v , where m is mass and v is velocity. Let’s name the first two bullets as x,y and the one which mass is unknown as z. Then calculate momentum of x and y:

Px= 5,30 * 10^{-3} * 301 = 1,5953 kg*m/s

Py= 5,30 * 10^{-3} * 301 = 1,5953 kg*m/s

The angle between x and y bullets is 120°, and we know that if the angle between two equal magnitude vectors is 120°, the magnitude of the resultant vector will be equal to first two and placed in exact middle of two vectors. So we can say total momentum of x and y (Px+Py) equals to 1,5953 kg*m/s as well (Shown in the figure).  

For z bullet to equalize the total momentum of x and y bullets, it needs to have the same amount of momentum in the opposite way.

Pz = 1,5953 = m * 554

m = 2,87 * 10^{-3} kg

8 0
3 years ago
An atom containing 16 protons, 31 neutrons, and 16 electrons would have an atomic mass of
Eddi Din [679]
<span>47 amu is the correct answer</span>
7 0
3 years ago
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You walk 45 m to the north, then turn 90° to your right and walk another 45 m How far are you from where you originally started?
docker41 [41]
C^2=a^2+b^2
c^2=45^2+45^2
c^2=4050
c=63.64
c=64
The answer is D.
3 0
3 years ago
Suppose a car approaches a hill and has an initial speed of 108 km/h at the bottom of the hill. The driver takes her foot off of
Aleks04 [339]

Answer:

a) The car will reach a height of 45.9 m.

b) The amount of thermal energy generated is 173382 J.

c) The magnitude of the force of friction is 417.8 N.  

Explanation:

Hi there!

a) In this problem, we have to use the conservation of energy. The energy conservation theorem states that the energy of a system remains constant. Energy can´t be created nor destroyed, only transformed. In the case of the car, the initial kinetic energy is transformed into potential energy as the car´s height increases while coasting up the hill.

Then, all the initial kinetic energy (KE) will be transformed into potential energy (PE) (only if there is no friction).

The equation of KE is the following:

KE = 1/2 · m · v²

Where:

m = mass of the car.

v = speed of the car.

The equation of PE is the following:

PE = m · g · h

Where:

m = mass of the car.

g = acceleration due to gravity.

h = height at which the car is located.

Since work done by friction is negligible, we can assume that all the initial kinetic energy will be transformed into potential energy. Then:

KE at the bottom of the hill = PE at the top of the hill

1/2 · m · v² = m · g · h

Solving for h:

1/2 · v² / g = h

Let´s convert the speed unit into m/s:

108 km/h · 1000 m/ 1 km · 1 h / 3600 s = 30 m/s

Now, let´s calculate h:

h = 1/2 · (30 m/s)² / 9.8 m/s²

h = 45.9 m

The car will reach a height of 45.9 m.

b) In this case, all the kinetic energy is not transformed into potential energy because some energy is transformed into thermal energy due to friction. The thermal energy generated is equal to the work done by friction. Then:

KE at the bottom of the hill = PE + work done by friction

KE = PE + Wfr  (where Wfr is the work done by friction).

1/2 · m · v² = m · g · h + Wfr

1/2 · m · v² - m · g · h = Wfr

1/2 · 710 kg · (30 m/s)² - 710 kg · 9.8 m/s² · 21 m = Wfr

Wfr = 173382 J

The amount of thermal energy generated is 173382 J.

c) The work done by friction is calculated as follows:

Wfr = Ffr · Δx

Where:

Ffr = friction force.

Δx = traveled distance

Please, see the attached figure to notice that the traveled distance can be calculated by trigonometry using this trigonometric rule of right triangles:

sin angle = opposite side / hypotenuse

In our case:

sin 2.9° = h / Δx

Δx = h / sin 2.9°

Δx = 21 m / sin 2.9° = 415 m

Then, solving for the friction force using the equation of the work done by friction:

Wfr = Ffr · Δx

Wfr / Δx = Ffr

173382 J / 415 m = Ffr

Ffr = 417.8 N

The magnitude of the force of friction is 417.8 N

6 0
3 years ago
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