The voltage across the terminals of an ac power supply varies with time according to V=V0cos(t). The voltage amplitude is V0 = 41.0V .
A. What is the root-mean-square potential difference Vrms?
B. What is the average potential difference Vav between the two terminals of the power supply?

Answer:

2.55m

Explanation:

Using 1/do+1/di= 1/f

di= (1/f-1/do)^-1

( 1/0.0500-1/0.0510)^-1

= 2.55m

Answer:

The speed will be "16.67 m/s".

Explanation:

The given values are:

Distance

= 72 m

Angle

= 30°

Acceleration

= [tex]g(sin \theta-ucos \theta)[/tex]

                    = [tex](9.8\times sin30^{\circ}) - (0.53\times cos30^{\circ})[/tex]

                    = [tex]1.929 \ m/s^2[/tex]

Let the speed be "v".

⇒  [tex]v^2=u^2+2as[/tex]

⇒  [tex]v^2=0(2\times 1.929\times 72)[/tex]

⇒  [tex]v^2=277.226[/tex]

⇒  [tex]v=\sqrt{277.776}[/tex]

⇒  [tex]v=16.67 \ m/s[/tex]

Answer:

Explanation:

We know that the equivalent resistance of resistors connected in parallel is expressed as

[tex]\frac{1}{Re} =\frac{1}{R1} +\frac{1}{R2}+\frac{1}{R3}\\\\\frac{1}{Re} =\frac{1}{R} +\frac{1}{2R}+\frac{1}{3R}\\[/tex]

the L.C.M is 6R

[tex]\frac{1}{Re} =\frac{6+3+2}{6R} = \frac{11}{6R} \\\\Re= \frac{6R}{11}[/tex]

Answer:

gₓ = 6.52 m/s²

Explanation:

The value of acceleration due to gravity on the surface of earth is given as:

g = GM/R²   -------------------- equation 1

where,

g = acceleration due to gravity on surface of earth

G = Universal Gravitational Constant

M = Mass of Earth

R = Radius of Earth

Now, for the alien planet:

gₓ = GMₓ/Rₓ²

where,

gₓ = acceleration due to gravity at the surface of alien planet

Mₓ = Mass of Alien Planet = 2.4 M

Rₓ = Radius of Alien Planet = 1.9 R

Therefore,

gₓ = G(2.4 M)/(1.9 R)²

gₓ = 0.66 GM/R²

using equation 1

gₓ = 0.66 g

gₓ = (0.66)(9.81 m/s²)

gₓ = 6.52 m/s²

Answer:

The correct answer would be - dependent independent variable experiment.

Explanation:

Dr. Stein hypothesized that excess sugar causes hyperactivity, so sugar treatment /no sugar treatment would be independent variable. By giving some children sugar and others a sugar cookies he can manipulate the independent variable.

Similarly , the dependent variable is the result or outcome of independent variable, or what Dr. Stein hypothesize to be the result of excess sugar . In this sugar experiment, then, the dependent variable is the children's hyper activity level.

Thus, the correct answer would be - dependent independent variable experiment.

The best research method to use for the research of hyperactivity,  would be dependent-independent variable experiment.

The given problem is based on the effect of sugar on hyperactivity. Hyper activity refers to the increased movement, impulse actions and a shorter attention span.

Thus, we can conclude that the best research method to use,  would be - dependent-independent variable experiment.

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Answer:

Final energy = Uf = initial energy × d₂/d₁

Explanation:

Energy is the ability to do work.

capacitor is an electronic device that store charges

where

V is the potential difference

d is the distance of seperation between the two plates

ε₀ is the dielectric constant of the material used in seperating the two plates, e.g., paper, mica, glass etc.

A = cross sectional area

U =¹/₂CV²

C =ε₀A/d

C × d=ε₀A=constant

C₂d₂=C₁d₁

C₂=C₁d₁/d₂

charge will  'q' remains same in the capacitor, if the capacitor was disconnected from the electric potential source (v) before the separation of the plates was replaced

Energy=U =(1/2)q²/C

U₂C₂ = U₁C₁

U₂ =U₁C₁ /C₂

U₂ =U₁d₂/d₁

Final energy = Uf = initial energy × d₂/d₁

Answer:

The ball traveled 0.827 m

Explanation:

Given;

distance between the metal plates of the room, d = 3.1 m

mass of the glass, m = 1.1g

charge on the glass, q = 4.7 nC

speed of the glass ball, v = 4.8 m/s

voltage of the ceiling, V = +3.0 x 10⁶ V

The repulsive force experienced by the ball when shot to the ceiling with positive voltage, can be calculated using Coulomb's law;

F = qV/d

|F| = (4.7 x 10⁻⁹ x 3 x  10⁶) / (3.1)

|F| = 4.548 x 10⁻³ N

F = - 4.548 x 10⁻³ N

The net horizontal force experienced by this ball is;

[tex]F_{net} = F_c - mg\\\\F_{net} = -4.548 *10^{-3} - (1.1*10^{-3} * 9.8)\\\\F_{net} = -15.328*10^{-3} \ N[/tex]

The work done between the ends of the plate is equal to product of the  magnitude of net force on the ball and the distance traveled by the ball.

[tex]W = F_{net} *h\\\\W = 15.328 *10^{-3} * h[/tex]

W = K.E

[tex]15.328*10^{-3} *h = \frac{1}{2}mv^2\\\\ 15.328*10^{-3} *h = \frac{1}{2}(1.1*10^{-3})(4.8)^2\\\\ 15.328*10^{-3} *h =0.0127\\\\h = \frac{0.0127}{15.328*10^{-3}}\\\\ h = 0.827 \ m[/tex]

Therefore, the ball traveled 0.827 m

The height at which the ball goes for the given parameters is; 0.827 m

We are given;

distance between the metal plates; d = 3.1 m

mass of glass; m = 1.1g = 0.0011 kg

charge on the glass; q = 4.7 nC = 4.7 × 10⁻⁹ C

speed of the glass ball; v = 4.8 m/s

voltage of the ceiling; V = +3.0 × 10⁶ V

The repulsive force experienced by the ball is gotten from the formula;

F = qV/d

|F| = (4.7 × 10⁻⁹ × 3 ×  10⁶)/3.1

|F| = 4.548 × 10⁻³ N

F = -4.548 × 10⁻³ N (negative because it is repulsive force)

The net horizontal force experienced by the ball is;

F_net = F - mg

F_net = (-4.548 × 10⁻³) - (0.0011 × 9.8)

F_net = -15.328 × 10⁻³ N

To get the height of the ball, we will use the formula;

F_net * h = ¹/₂mv²

h = (¹/₂ * 0.0011 * 4.8²)/(15.328 × 10⁻³)

We took the absolute value of F_net, hence it is not negative

h = 0.827 m

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Answer:

(a) f

(b) r

(c) s

Explanation:

There are two forces on the sphere: weight and buoyancy.

Sum of forces in the y direction:

∑F = ma

B − mg = 0

B = mg

Buoyancy is equal to the weight of the displaced fluid, or ρVg, where ρ is the density of the fluid and V is the displaced volume.

ρVg = mg

ρV = m

V = m/ρ

(a) The mass decreases, so the displaced volume decreases.

(b) The sphere's density is constant and its radius increases, which means its mass increases, so the displaced volume increases.

(c) The mass stays the same, so the displaced volume is the same.

Answer:

2.5×10¹⁹

Explanation:

4 C/s × (1 electron / 1.60×10⁻¹⁹ C) = 2.5×10¹⁹ electrons/second

Answer:

Motor unit is made up of motor neurons. Group of Motor Units work together to coordinate contraction of single muscle. When an individual needs to carry several boxes down stairs then his brain gives signal to neurons who innervates a group of skeletal muscle. When neurons receive signal they stimulate all muscle fibers in that particular motor unit.

Explanation:

Motor unit is made up of motor neurons. Group of Motor Units work together to coordinate contraction of single muscle. When an individual needs to carry several boxes down stairs then his brain gives signal to neurons who innervates a group of skeletal muscle. When neurons receive signal they stimulate all muscle fibers in that particular motor unit.

Answer:

acting force is the answer

The direction of the magnetic force on the moving electron is upward.

The direction of the magnetic force on the electron can be determined by applying right hand rule.

This rule states that when the thumb is held perpendicular to the fingers, the thumb will point in the direction of the speed while the fingers will point in the direction of the field and the magnetic force will be perpendicular to the field.

Thus, we can conclude that, the direction of the magnetic force on the moving electron is upward.

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Answer:

5.95 A

Explanation:

From the question

R = ρL/A..................... Equation 1

Where R = resistance of the tungsten wire, ρ = Resistivity of the tungsten wire, L = length, A = cross sectional area.

Given: L = 1.5 m, A = 0.8 mm² = 0.8×10⁻⁶ m, ρ = 5.60×10⁻⁸ Ω.m

Substitute these values into equation 1

R = 1.5(5.60×10⁻⁸)/0.8×10⁻⁶

R = 0.084 Ω.

Finally, using Ohm law,

V = IR

Where V = Voltage, I = current

Make I the subject of the equation

I = V/R............... Equation 2

I = 0.5/0.084

I = 5.95 A

Answer:

I would say its a deep ocean trench

Explanation:

This is because deep ocean trenches are found at the deepest part of the ocean and also at Pacific ocean margins or Rim where subduction usually occurs and Aleutian islands are part of the Pacific Rim

Answer:

Explanation:

For series connected elements (an inductor, a capacitor, and a resistor) in a simple AC circuit, the same current will flows through the elements since are are no presence of nodes between the elements. The total current from the source is what will flow through all of them.

For example, let assume the total current flowing in the circuit is 3A, the amount of current that will flow through the inductor, capacitor and resistor will be the same 3A because of the nature of their connection (series). It is the voltage across each of them that differs.

Answer:

 F = 2,8289 i ^ + 1,0909 j ^) 10⁻² N

F = 3.0226 10⁻² N ,  θ  = 21.16º

Explanation:

For this exercise we use Coulomb's law

         F = k q₁q₂ / r₁₂²

We also use that the force is a vector magnitude, so we must calculate each component of the force , see the adjoint for the direction of the vectors

X axis

          Fₓ = -F₁₄ + F₁₃ₓ

Y axis

        [tex]F_{y}[/tex] = F₁₂ -F_{13y}

let's look for the expression for each force

where the side of the square is a = 1.25 m

  F₁₂ = k Q₁Q₂ / a²

  F₁₄ = k Q₁Q₄ / a²

the distance between 1 and 3 is

         d = √(a² + a²) = a √2

   F₁₃ = k Q₁Q₃ / d²

let's use trigonometry to find the components

              cos 45 = F₁₃ₓ / F₁₃

              F₁₃ₓ = F₁₃ cos 45

              F₁₃ₓ = k Q₁Q₃ / 2a²

              sin 45 = F_{13y} / F₁₃

              F_{13y} = F₁₃ sin 45

              F_{13y} = k Q₁Q₃ / 2a²  sin 45

Taking all terms, we substitute in the force for each axis

X axis

          Fₓ = - k Q₁Q₄ / a² + k Q₁Q₃ / 2a₂ cos 45

          Fₓ = k Q₁ / a² ( -Q₄ + Q₃ /2   cos 45)

          Fₓ = 9 10⁹ 1.5 10⁻⁶ / 1.25²   (- 4.5 10⁻⁶ + 3.5/2  cos 45  10⁻⁶)

          Fₓ = 8.64 10³ (3.2626 10⁻⁶)

          Fₓ = 2.8189 10⁻² N

Y axis

          F_{y} = k Q₁Q₂ / a² - k Q₁Q₃ /2a²   sin 45

          F_{y} = k Q₁ / a² (Q₂ - Q₃ /2 sin45)      

          F_{y} = 9 10⁹ 1.5 10⁻⁶/ 1.25²    (2.5 10⁻⁶ - 3.5/2   sin 45  10⁻⁶)

          F_{y} = 8.64 10³ (1.26256 10⁻⁶)

          F_{y} = 1.0909 10⁻² N

The result can be given in two ways

1) F = Fₓ i ^ + F_{y} j ^

     F = 2,8289 i ^ + 1,0909 j ^) 10⁻² N

2) in the form of a module and an angle, for which we use the Pythagorean theorem and trigonometry

       F = √ (Fₓ² + F_{y}²)

       F = 10⁻² √ (2,8189² + 1,0909²)

       F = 3.0226 10⁻² N

       tan θ = F_{y} / Fx

       θ = tan⁻¹ (F_{y} / Fₓ)

       θ = tan⁻¹ (1.0909 / 2.8189)

        θ  = 21.16º

Answer:

a) Em= K +U,  b) Em= K

Explanation:

The system in this case is formed by the mobilizes and the hill.

Let's write the expressions correctly and completely.

a) When the car moves in the path, the mechanical energy is the siua of the kinetic energy of the car and the potential energy of the car when going up the hill.

              Em = K + U

be) when the car moves in the flat part all the mechanical energy is formed by its kinetic energy that is calculated with the mass and speed of the car

             Em = K

c) When the car goes up the hill the energy the mechanical energy is conserved, but part of the kinetic energy is transformed into potential energy.

Answer:

leaves

kinetic energy

mass

potential energy

mass

Explanation:

Answer:

C. The magnitude of the electron's acceleration inside the field

D. The radius of the circular path the electron travels

Explanation:

The radius of the electron's motion in a uniform magnetic field is given by

[tex]R = \frac{MV}{qB}[/tex]

where;

m is the mass of the electron

q is the charge of the electron

B is the magnitude of the magnetic field

V is speed of the electron

R is the radius of the electron's

Thus, the radius of the of the electron's motion will change since it depends on speed of the electron.

The magnitude of the electron's acceleration inside the field  is given by;

[tex]a_c = \frac{V^2}{R}[/tex]

where;

[tex]a_c[/tex] is centripetal acceleration of electron

Thus, the magnitude of the electron's acceleration inside the field will change since it depends on the electron speed.

The time the electron is in the magnetic field is given by;

[tex]T = \frac{2\pi M}{qB}[/tex]

The time of electron motion will not change

The magnitude of the net force acting on the electron inside the field will not change;

[tex]qVB = \frac{MV^2}{R} \\\\qVB - \frac{MV^2}{R} = 0[/tex]

Therefore, the correct options are "C" and "D"

Answer: D) 1 and 2 tie, then 3, then 4.

Explanation: Gravitational Force is one of the 4 fundamental forces of nature (the others being eletromagnetic, weak force and strong force) and is explained by Newton's Law of Universal Gravitation, in which, every massive particle attracts every other massive particle.

The way to calculate gravitational force is:

[tex]F_{G} = \frac{GMm}{r^{2}}[/tex]

G is Universal Gravitational Constant and it is constant anywhere in the universe.

M and m are mass of each object;

r is distance between the objects;

The formula shows that gravitational force acts at an inverse square law, i.e., if objects are 2 distances apart, Force between them will decrease to one quarter of it was.

So, analysing the question, a particle inside an uniform spherical shell not at the center and at the center will have equal forces.

Outside at a distance 2r, force will be less than at a distance r.

Then the order is 1=2 > 3 > 4

Answer:

The speed of light will be c=3x10^8m/s

Explanation:

This is the same as the speed of light because your speed does not affecttje speed of light so you will see the light approaching you at the same speed of light c

Answer:

(a) D.  Zero.

(b) C.  Equal to the battery's terminal voltage.

Explanation:

The question is incomplete, see the complete question for your reference and information.

A resistor and a capacitor are connected in series across an ideal battery having a constant voltage

across its terminals. At the moment contact is made with the battery

(a) the voltage across the capacitor is

A) equal to the battery's terminal voltage.

B) less than the battery's terminal voltage, but greater than zero.

C) equal to the battery's terminal voltage.

D) zero.

(b) the voltage across the resistor is

A) equal to the battery's terminal voltage.

B) less than the battery's terminal voltage, but greater than zero.

C) equal to the battery's terminal voltage.

D) zero

A RC circuit is a circuit that is composed of both resistors and capacitors connect to a source of current or voltage.

basically when a voltage source is applied to an RC circuit, the capacitor, C charges up through the resistance, R

Explanation:

It is given that,

Speed of bus 1 is 36 km/h and speed of bus 2 is 108 km/h. We need to find the distance between bus 1 and 2 after 20 minutes.

Time = 20 minutes = [tex]\dfrac{20}{60}\ h=\dfrac{1}{3}\ h[/tex]

As the buses are moving in opposite direction, then the concept of relative velocity is used. So,

Distance, [tex]d=v\times t[/tex]

v is relative velocity, v = 108 + 36 = 144 km/h

So,

[tex]d=144\ km/h \times \dfrac{1}{3}\ h\\\\d=48\ km[/tex]

So, the distance between them is 48 km after 20 minutes.

Answer:

Its approx location is (5.18,1.9)

Explanation:

Using F( 5,2) = ( xy-1, y²-11)

= ( 5*2-¹, 2²-11)

= (9,-5)

= so at point t=1.02

(5,2)+(1.02-1)*(9,-5)

(5,2)+( 0.02)*(9,-5)

(5+0.18, 2-0.1)

= ( 5.18, 1.9)

The image is missing, so i have attached it.

Answer:

The force exerted on the large block by the small block = 8.4 N

Explanation:

From the image attached, the mass of the small block = 2M while the mass of the large block = 3M

Also,Force on small block = F and force on large block = 2F

Equilibrium of forces on the left gives;

2F - N = 3Ma

Thus,

Ma = (2F - N)/3 - - - - eq1

Also, on right hand side, Equilibrium of forces gives;

N - F = 2Ma

Ma = (N - F)/2 - - - - eq2

Equating eq(1) and eq(2) gives us;

(2F - N)/3 = (N - F)/2

Where N is the force exerted on the large block by the small block.

Making N the subject gives;

4F - 2N = 3N - 3F

5N = 7F

N = 7F/5

We are given F = 6N

Thus;

N = 7(6)/5

N = 8.4 N

Answer:

The  contribution of people to the cooling load of the store is 19722.5 W

Explanation:

Total amount of customers = 225

Total amount of employees = 20

Total amount of people in the store at that instant n = 245 people

Average rate of heat generation Q = 115 W

percentage of these heat generated that is sensible heat = 70%

Sensible heat raises the surrounding temperature. Latent heat only causes a change of state.

The total heat generated by all the people in the store = n x Q

==> 245 x 115 = 28175 W

but only 70% of this heat is sensible heat that raises the temperature of the store, therefore, the contribution of people to the cooling load of the store = 70% of 28175 W

==> 0.7 x 28175 = 19722.5 W

Answer:

a) v    r = 0.7318 cm , b)  r = 7.23 cm

Explanation:

The magnetic field generated by a wire carrying a current can be found with Ampere's law

       ∫ B. ds = μ₀ I

the length of a surface circulates around the wire is

    s = 2π r

where r is the point of interest of the calculation of the magnetic field

         B = μ₀ I / 2π r

In this exercise we have two wires, write the equation of the magnetic field of each one

wire 1     I = 5.8 A

         B₁ = μ₀ 5,8 / 2π r₁

wire 2    I = 3.0 A

         B₂ = μ₀ 3/2π r₂

the direction of the field is given by the rule of the right hand, the thumb indicates the direction of the current and the other fingers the direction of the magnetic field

Let's apply these expressions to our case

a) the two streams go in the same direction

     using the right hand rule for each wire we see that between the two wires the magnetic fields have opposite directions so there is some point where the total value is zero

          B₁ - B₂ = 0

           B₁ = B₂

         μ₀ 5,8 / 2π r₁ = μ₀ 3 / 2π r₂

          5.8 / r₁ = 3 / r₂

          5.8 r₂ = 3r₁

the value of r is measured from each wire, therefore

        r₁ = 2.3 + r

        r₂ = 2.3 -r

we substitute

          5.8 (2.3 - r) = 3 (2.3 + r)

           r (3 + 5.8) = 2.3 (5.8 - 3)

           r = 2.3 2.8 / 8.8

           r = 0.7318 cm

b) the two currents have directional opposite

with the right hand rule in the field you have opposite directions outside the wires

suppose it is zero on the right side where the wire with the lowest current is

         B₁ = B₂

        5.8 / r₁ = 3 / r₂

        5.8 r₂ = 3 r₁

         r₁ = 2.3 + r

         r₂ = r - 2.3

        5.8 (r - 2.3) = 3 (2.3 + r)

        r (5.8 -3) = 2.3 (3 + 5.8)

        r = 2.3 8.8 / 2.8

        r = 7.23 cm

Answer:

velocity = 2.62m/s

Explanation:

950= (4 x A)/0.12

950 x 0.12 = 4 x A

114 = 4 x A

A = 114/4

A = 28.5m/s²

The maximum velocity of the mass is equal to 1.85,/s when the amplitude of oscillation is 0.12m.

The spring force will be acting on the spring when the spring is stretched or compressed, which opposes the load force. These springs are divided into many types based on how this load force is applied to them.

F = -kx

where k is the spring constant and x is the displacement of the spring attached with mass.

Given, the mass attached to the spring, m = 4.0 Kg

The value of spring constant, k = 950 N/m

The amplitude of oscillation, A = 0.12m

The maximum velocity can be calculated as:

[tex]\frac{mv_{max}^2}{2} =\frac{kA^2}{2}[/tex]

[tex]v_{max} =\sqrt{\frac{kA^2}{m} }[/tex]

Substitute the values of the m, k, and A in the above equation:

Vmax = [tex]=\frac{950N/m(0.12m)^2}{4Kg}[/tex]

Vmax = √3.42 m/s

Vmax = 1.85m/s

Therefore, the maximum velocity of the mass is equal to 1/85 m/s.

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Answer: C

Frictional force

Explanation:

The description of the question above is an example of a circular motion.

For a car travelling in a curved path, the frictional force between the tyres and the road surface will provide the centripetal force.

Since the road is banked, and the cross section of the banked road is constructed like a ramp. The car drives transversely to the slope of the ramp, so that the wheels of one side of the car are lower than the wheels on the other side of the car, for cornering the banked road, the car will not rely only on the frictional force.

Therefore, the correct answer is option C - the frictional force.

Answer:

Q = 832 kJ

Explanation:

It is given that,

Mass of the water, m = 2.5 kg

The latent heat of fusion, L = 333 kJ/kg

We need to find the heat needed to melt water at its melting point. The formula of heat needed to melt is given by :

Q = mL

[tex]Q=2.5\ kg\times 333\ kJ/kg\\\\Q=832.5\ kJ[/tex]

or

Q = 832 kJ

So, the heat needed to melt the water is 832 kJ.

Answer:

480 Ohms

Explanation:

Resistance: This can be defined as a opposition to current flow in an electric circuit. The S.I unit of resistance is  ohms(Ω).

From the question,

V = IR................... Equation 1

Make R the subject of the equation

R = V/I............... Equation 2

V = The House voltage, I = Current, R = Resistance of the bulb.

Given: V = 240 Volts, I = 0.5 Amps.

Substitute into equation 2

R = 240/0.5

R = 480 Ohms

Hence the resistance of the bulb is 480 Ohms

Answer:

fem = 0

Explanation:

The electromotive force is given by Faraday's law

         fem = - d [tex]\phi _{B}[/tex] / dt

where \phi _{B} is the flux of the magnetic field

The low magnetic flux is

         \phi _{B} = B. A = B A cos θ

substituting

      fem - d (B A cos θ) / dt

therefore for an electromotive force to exist there must be a change with respect to the time of

* The magnetic field

* The area waxed by the loop

* the angle between the magnetic field and the normal loop

* Any combination of the above

In this case, as the generator is stopped (inactive), there is no change in the parameters, therefore the electromotive force is zero (fem = 0).