A scientist is testing the seismometer in his lab and has created an apparatus that mimics the motion of the earthquake felt in part (a) by attaching the test mass to a spring. If the test mass weighs 13 N, what should be the spring constant of the spring the scientist use to simulate the relative motion of the test mass and the ground from part (a)?

Explanation:

Newton's third law of motion states that every action has an equal and opposite reaction. This means that forces always act in pairs. Action and reaction forces are equal and opposite, but they are not balanced forces because they act on different objects so they don't cancel out.

Answer:

The vertical velocity of the skater upon landing is 10.788 meters per second.

Explanation:

Skateboarder experiments a parabolic movement. As skateboarder jumps horizontally off the top of the staircase, it means that vertical component of initial velocity is zero and accelerates by gravity, the final vertical speed is calculated by the following expression:

[tex]v = v_{o} + g\cdot t[/tex]

Where:

[tex]v_{o}[/tex] - Initial vertical speed, measured in meters per second.

[tex]v[/tex] - Final vertical speed, measured in meters per second.

[tex]g[/tex] - Gravitational acceleration, measured in meters per square second.

[tex]t[/tex] - Time, measured in seconds.

Given that [tex]v_{o} = 0\,\frac{m}{s}[/tex], [tex]g = -9.807\,\frac{m}{s^{2}}[/tex] and [tex]t = 1.10\,s[/tex], the final velocity of the skater upon landing is:

[tex]v = 0\,\frac{m}{s} + \left(-9.807\,\frac{m}{s^{2}} \right)\cdot (1.10\,s)[/tex]

[tex]v = -10.788\,\frac{m}{s}[/tex]

The vertical velocity of the skater upon landing is 10.788 meters per second.

Answer:

-10.8

Explanation:

Answer on Khan Academy

Answer:

5.33333... seconds

Explanation:

800 divided by 150 is equal to 5.33333... because it is per second that the cheetah moves at 150miles, the answer is 5.3333.....

Answer:

The inventors  claim is not real

a)  No the the freezer cannot operate in such conditions

Explanation:

From the question we are told that

     The  power input is  [tex]P_i = 0.25 kW = 0.25 *10^{3} \ W[/tex]

      The  rate of heat transfer [tex]J = 3050 J/s[/tex]

       The temperature of the freezer content is [tex]T = 270 \ K[/tex]

       The  ambient temperature is  [tex]T_a = 293 \ K[/tex]

Generally the coefficient of performance of a refrigerator at idea conditions is mathematically represented as

      [tex]COP = \frac{T }{Ta - T}[/tex]

substituting values

     [tex]COP = \frac{270 }{293 - 270}[/tex]

     [tex]COP =11.7[/tex]

Generally the coefficient of performance of a refrigerator at real conditions is mathematically represented as

       [tex]COP = \frac{J}{P_i}[/tex]

substituting values

       [tex]COP = \frac{3050}{0.25 *10^{3}}[/tex]

       [tex]COP = 12.2[/tex]

Now given that the COP  of an ideal refrigerator is  less that that of a real refrigerator then the claims of the inventor is rejected

This is because the there are loss in the real refrigerator cycle that are suppose to reduce the COP compared to an ideal refrigerator cycle where there no loss that will reduce the COP

Answer:

The  potential energy is [tex]PE = 2.031 *10^{-7} \ J[/tex]

Explanation:

From the question we are told that

    The inner radius is  [tex]r_i = 5 \ mm = 0.005 \ m[/tex]

      The outer radius is  [tex]r_o = 11 \ mm = 0.011 \ m[/tex]

     The  common length is  [tex]l = 160 \ m[/tex]

      The  potential  difference is   [tex]V = 6 \ V[/tex]

Generally the capacitance of the cylindrical capacitor is mathematically represented as

       [tex]C = \frac{2 \pi * k * \epsilon_o }{ ln \frac{ r_o }{r_i} } * l[/tex]

Where  [tex]\epsilon _o[/tex] is the permitivity of free space with the values [tex]\epsilon _o = 8.85*10^{-12} \ m^{-3} \cdot kg^{-1}\cdot s^4 \cdot A^2[/tex]

and  k  is the dielectric constant  of the dielectric material here the  dielectric material is free space so  k  =   1

     Substituting values

             [tex]C = \frac{2* 3.142 * 1 * 8.85*10^{-12} }{ ln \frac{ 0.011}{0.005} } * 160[/tex]

             [tex]C = 1.129 *10^{-8} \ F[/tex]

The potential energy stored is mathematically represented as

       [tex]PE = \frac{1}{2} * C * V ^2[/tex]

substituting values

      [tex]PE = 0.5 * 1.129 *10^{-8} * (6)^2[/tex]

      [tex]PE = 2.031 *10^{-7} \ J[/tex]

Answer:

c. 66 V

Explanation:

p =IV

I =P/V

P1/V1=P2/V2

60/110=36/V2

0.55 = 36/V2

V2 =36/0.55 = 65.5V

V2 = 66V

Note: if the professor wants the distance between the m = 0 and m = 1 maxima to be 25 cm

Answer:

d = 1.0128×10⁻⁵m

Explanation:

given:

length L = 4.0m

maximum distance between m = 0 and m = 1 , y = 25cm = 0.25m

wavelength λ = 633nm = 633×10⁻⁹m

note:

dsinθ = mλ (constructive interference)

where d is slit seperation, θ is angle of seperation , m is order of interference , and λ is wavelength

for small angle

sinθ ≈ tanθ

[tex]d (\frac{y}{L}) =[/tex] mλ

[tex]d (\frac{y}{L}) = (1)(633nm)[/tex]

[tex]d(\frac{0.25}{4} ) = (1)(633nm)[/tex]

d = 1.0128×10⁻⁵m

Explanation:

1.  Impulse = change in momentum

J = Δp

J = mΔv

In the x direction:

Jₓ = mΔvₓ

Jₓ = (0.40 kg) (30 m/s cos 45° − (-20 m/s))

Jₓ = 16.5 kg m/s

In the y direction:

Jᵧ = mΔvᵧ

Jᵧ = (0.40 kg) (30 m/s sin 45° − 0 m/s)

Jᵧ = 8.49 kg m/s

The magnitude of the impulse is:

J = √(Jₓ² + Jᵧ²)

J = 18.5 kg m/s

The average force is:

FΔt = J

F = J/Δt

F = 1850 N

2. Momentum is conserved.

m₁u₁ + m₂u₂ = (m₁ + m₂) v

In the x direction:

(1000 kg) (0 m/s) + (1500 kg) (-12 m/s) = (1000 kg + 1500 kg) vₓ

vₓ = -7.2 m/s

In the y direction:

(1000 kg) (20 m/s) + (1500 kg) (0 m/s) = (1000 kg + 1500 kg) vᵧ

vᵧ = 8 m/s

The magnitude of the final speed is:

v = √(vₓ² + vᵧ²)

v = 10.8 m/s

3. Momentum is conserved.

m₁u₁ + m₂u₂ = (m₁ + m₂) v

In the x direction:

(0.8 kg) (18 m/s cos 45°) + (0.36 kg) (9.0 m/s) = (0.8 kg + 0.36 kg) vₓ

vₓ = 11.6 m/s

In the y direction:

(0.8 kg) (-18 m/s sin 45°) + (0.36 kg) (0 m/s) = (0.8 kg + 0.36 kg) vᵧ

vᵧ = -8.78 m/s

The magnitude of the final speed is:

v = √(vₓ² + vᵧ²)

v = 14.5 m/s

Answer:

Longest wavelength, lowest intensity

Explanation:

Answer:

It has a long wavelength

Explanation:

GRADPOINT

Answer:

a) The potential difference should be applied to the d dimension face.

b) The maximum current density j = V/3ρd

c) 3. to the faces that are a distance 3d apart

Explanation:

a) Current density is the ratio of current flowing through a conductor, and cross-sectional area of the conductor. mathematically, it is written as

j = I/A

where I is the electric current, and

A is the area of the conductor.

From the equation, we can see that reducing the area of the conductor will increase the current density for a given amount of current passing through the conductor. The face d wide will give the least cross-sectional area of current flow.

b) current density can be gotten from

j = σE    ....equ 1

where σ is the conductivity of the conductor which is the inverse of resistivity ρ. this means that

σ = 1/ρ    ....equ 2

where ρ is the resistivity of the conductor

E is the electric field and is the volt through the conductor per unit length of the conductor

in this case, the maximum current density will be when the length is length 3d, and the volt is the potential difference V

therefore,

E = V/3d    ....equ 3

substituting equ 2 and equ 3 in equ1, we'll have

the maximum current density j = V/3ρd

c) To get the maximum current, the potential difference should be applied to the faces that are 3d wide apart because the resistance of a conductor varies inversely as the cross-sectional area. The maximum current will be gotten when the resistance is at its minimum, and the minimum resistance will be gotten with the most cross-sectional area. The 3d wide face will give the maximum cross-sectional area.

Answer:

31.55° and 148.45°

Explanation:

Formula for calculating the force experiences by the proton placed in a magnetic field is as expressed below;

F = qvBsinθ where;

F is the magnetic force experienced by the proton

q is the charge on the proton

v is the velocity of the proton

B is the magnetic field

θ is the angle between the proton's velocity and the field (Required)

Given parameters

F =  7.00 * 10⁻¹³N

q = 1.602*10⁻¹⁹C

v = 4.80 * 10⁶ m/s

B = 1.74 T

θ  =?

From the formula F = qvBsinθ;

sinθ = F/qvB

sinθ = 7.00 * 10⁻¹³/1.602*10⁻¹⁹* 4.80 * 10⁶*1.74

sinθ =  7.00 * 10⁻¹³/13.38*10⁻¹³

sinθ = 0.5231689 * 10⁰

sinθ = 0.5231689

θ = sin⁻¹0.5231689

θ = 31.55°

The following are the positive values of the angle between 0° and 360°

Sin is positive in the first and second quadrant. In the second quadrant the angle is equal to 180°-31.55° = 148.45°.

Hence the possible values of the angle from smallest to largest are 31.55° and 148.45°

Answer:

b. Rodger work = 1300 J

Explanation:

Work done: This can be defined as the product of force and distance along the direction of the force.

From the question,

Work is done by Rodger using a force of 100 N  in pushing the skateboard through a distance of 13.0 m.

W = F×d............. Equation 1

Where W = work done, F = force, d = distance.

Given: F = 100 N, d = 13 m

Substitute these values into equation 1

W = 100(13)

W = 1300 J.

Hence the right option is b. Rodger work = 1300 J

Answer:

Current that flows through any one of the resistors has a value of 12 amperes.

Explanation:

When a group of resistors are connected in series, the same current flows through each resistor. According to the Ohm's Law, the circuit can be represented as follows:

[tex]V_{batt} = i\cdot (R_{1}+R_{2}+R_{3})[/tex]

[tex]i = \frac{V_{batt}}{R_{1}+R_{2}+R_{3}}[/tex]

Where:

[tex]V_{batt}[/tex] - Voltage of the battery, measured in volts.

[tex]R_{1}[/tex], [tex]R_{2}[/tex], [tex]R_{3}[/tex] - Electric resistance of the first, second and third resistors, measured in ohms.

[tex]i[/tex] - Current, measured in amperes.

If [tex]R_{1} = R_{2} = R_{3} = R[/tex], then:

[tex]i = \frac{V_{batt}}{3\cdot R}[/tex]

Current that flows through any one of the resistors has a value of 12 amperes.

The current flows via any of the resistors should have a value of 12 amperes.

At the time When a group of resistors are linked in series, so there is a similar current flow via each resistor.

Here the circuit should be

vbatt = i.(R1 + R2+ R3)

i = Vbatt/R1 + R2 + R3

here

Vbatt means the voltage of the battery

R1,R2, and R3 means the resistance of the first, second and third resistors

I means the current

So, in the case when

R1 = R2 = R3 = R

So,

i = Vbatt/3.R

Learn more about current here: https://brainly.com/question/14956680

Answer:

0.3nanocouloumb

Explanation:

Pls see attached file

Answer:

The double slit experiment showed for the first time that light can be interfered, producing bands of light and dark fringes on a screen. This phenomenon was a unique and typical characteristic of waves.

Explanation:

Th double slit experiment by Thomas Young proved, and sealed for the first time the wave nature of light; showing that light just as any other wave can produce interference which was a unique, typical phenomenon of waves. The Interference of light was shown by allowing light to pass through narrow slits and superimpose on a wall or screen, at a distance away from the slit, producing a clear pattern of light and dark fringes. This was the first experiment to proof that darkness can be produced by the addition of light on light. Interference is accompanied by a spatial redistribution of the optical intensity without violation of power conservation. The phenomenon of interference proved the intuitive ideas of Huygens regarding the wave nature of light against Newton's particle nature of light theory.

Answer:

Different surfaces have different impact force during collision which depends on the time it takes the person to come to rest after collision.

Explanation:

Given;

speed on concrete = 12 m/s (27 mi/h)

speed on soil = 15 m/s (34 mi/h)

speed on water = 34 m/s (76 mi/h)

The impact force on this person during collision is rate of change of momentum;

[tex]F = \frac{\delta P}{\delta t}[/tex]

During collision, the force exerted on this person depends on how long the collision lasts; that is, how long it takes for this person to come to rest after collision with each of the surfaces.

The longer the time of collision, the smaller the force exerted by each.

It takes shorter time for the person to come to rest on concrete surface than on soil surface, also it takes shorter time for the person to come to rest on soil surface than on water surface.

As a result of the reason above, the force exerted on the person during collision by the concrete surface is greater than that of soil surface which is  greater than that of water surface.

A wedge of glass of refractive index 1.64 has a silver coating on the bottom, as shown in the image attached below.

Determine the smallest distance x to a position where 450-nm light reflected from the top surface of the glass interferes constructively with light reflected from the silver coating on the bottom. The light changes phase when reflected at the silver coating.

Answer:

the smallest distance x  = 2.74 × 10⁻³ m or 2.74 mm

Explanation:

From the given information:

The net phase change is zero because both the light ray reflecting from the air-glass surface and silver plate undergo a phase change of [tex]\dfrac{\lambda}{2}[/tex] , as such the condition for the  constructive interference is:

nΔy = mλ

where;

n = refractive index

Δy = path length (inside the glass)

So, from the diagram;

[tex]\dfrac{y}{x}=\dfrac{10^{-5} \ m}{0.2 \ m}[/tex]

[tex]\dfrac{y}{x} = 5 \times 10^{-5}[/tex]

[tex]y = 5 \times 10^{-5} x[/tex]

Now;

Δy can now be = 2 ( 5 × 10⁻⁵ [tex]x[/tex])

Δy =1 ×  10⁻⁴[tex]x[/tex]

From nΔy = mλ

n( 1 ×  10⁻⁴[tex]x[/tex] ) = mλ

[tex]x = \dfrac{m \lambda}{n \times 1 \times 10^{-4} }[/tex]

when the thickness is minimum then m = 1

Thus;

[tex]x = \dfrac{1 \times 450 \times 10^{-9} \ m}{1.64 \times 1 \times 10^{-4} }[/tex]

x =  0.00274 m

x = 2.74 × 10⁻³ m or 2.74 mm

Answer: B. The surface of the coating is rough, so light that shines on it gets scattered in many directions.

Explanation: On Edge!!!!!!!!!!!!!!!!!!!!

Answer:

Explanation:

area of the coil  A = .08 x .08 = 64 x 10⁻⁴ m ²

flux through the coil Φ = area of coil x no of turns x magnetic field

= 64 x 10⁻⁴ x 50 x B where B is magnetic field

emf induced = dΦ / dt = ( 64 x 10⁻⁴ x 50 x B - 0 ) / .2

= 1.6 B

current induced = emf induced / resistance

12 x 10⁻³ = 1.6 B / 15

B = 112.5 x 10⁻³ T .

Answer:

Δx = 9 x 10⁻³ m = 9 mm

Explanation:

The formula for fringe spacing in Young's Double Slit Experiment is given as follows:

Δx = λL/d

where,

Δx = fringe spacing = ?

λ = wavelength of light = 450 nm = 450 x 10⁻⁹ m

L = Distance between slits and screen = 2 m

d = distance between slits = 0.1 mm = 0.1 x 10⁻³ m

Therefore,

Δx = (450 x 10⁻⁹ m)(2 m)/(0.1 x 10⁻³ m)

Δx = 9 x 10⁻³ m = 9 mm

Answer:

Explanation:

length of pipe A is L

frequency of fundamental note of pipe A which is closed organ pipe

= velocity of sound / 4 x length of pipe

=  V / 4 x L where V is velocity of sound .

Similarly frequency of fundamental note of pipe B which is open organ pipe

= velocity of sound / 2 x length of pipe

= V / (2 x 2L) =  V / 4L , This is also called first harmonic

so fundamental frequency of pipe A will be equal to first harmonic of pipe B .

Answer:

V = 451.47 volts

Explanation:

Given that,

Distance, d = 0.21 m

Initial speed, u = 0

Time, t = 33.3 ns

Let v is the final velocity. Using second equation of motion as :

[tex]d=ut+\dfrac{1}{2}at^2[/tex]

a is acceleration, [tex]a=\dfrac{v-u}{t}[/tex] and u = 0

So,

[tex]d=\dfrac{1}{2}(v-u)t[/tex]

[tex]v=\dfrac{2d}{t}\\\\v=\dfrac{2\times 0.21}{33.3\times 10^{-9}}\\\\v=1.26\times 10^7\ m/s[/tex]

Now applying the conservation of energy i.e.

[tex]\dfrac{1}{2}mv^2=qV[/tex]

V is voltage

[tex]V=\dfrac{mv^2}{2q}\\\\V=\dfrac{9.1\times 10^{-31}\times (1.26\times 10^7)^2}{2\times 1.6\times 10^{-19}}\\\\V=451.47\ V[/tex]

So, the voltage is 451.47 V.

Answer:

The force is  [tex]F = 172 \ N[/tex]

Explanation:

From the question we are told that

    The  mass of the block is  [tex]m_b = 27.0 \ kg[/tex]

     The  coefficient of  static friction is  [tex]\mu_s = 0.65[/tex]

     The coefficient of kinetic friction is  [tex]\mu_k = 0.50[/tex]

The  normal force acting on the block is  

      [tex]N = m * g[/tex]

substituting values

     [tex]N = 27 * 9.8[/tex]

     [tex]N = 294.6 \ N[/tex]

Given that the force we are to find is the force required to get the block to start moving then the force acting against this force is the static frictional force which is mathematically evaluated as

        [tex]F_f = \mu_s * N[/tex]

substituting values

        [tex]F_f = 0.65 * 264.6[/tex]

        [tex]F_f = 172 \ N[/tex]

Now for this  block to move the force require is  equal to [tex]F_f[/tex] i.e

       [tex]F= F_f[/tex]

=>    [tex]F = 172 \ N[/tex]

Answer:

A) 1.76U×10⁻³N

B) 2.716×10⁻³N

C) 264.5⁰

Explanation:

See detailed workings for (a), (b), (c) attached.

Answer:

Power = Force × Distance/time

Power = Force × Velocity

Power = 2,300.0 N × 28.0 m/s²

Power = 64400 Nm/s

Explanation:

First show the formula of Power

Re-arrange formula and used to work out Power

Pretty simple stuff!

Hope this Helps!!

Answer:

If the magnitude of the field is decreasing with time the direction of the induced magnetic field is CLOCKWISE

Explanation

This is because If the magnetic field decreases with time, the electric field will be produced in order to oppose the change in line with lenz law. Thus The right hand rule can be applied to find that the direction of electric field is in the clockwise direction.

Answer:

Explanation:

The greatest speed is attained at middle point or equilibrium point or where displacement from equilibrium point is zero .

When the object remains at one of the extreme point it experiences greatest acceleration but at that point velocity is zero . Due to acceleration , its velocity goes on increasing till it come to equilibrium point . At this point acceleration becomes zero . After that its velocity starts decreasing because of negative acceleration . Hence at middle point velocity is maximum .

The greatest acceleration is attained at maximum displacement or at one of the two extreme end .

Greatest restoring force too will be at position where acceleration is maximum because acceleration is produced by restoring force .

Restoring force is proportional to displacement or extension against restoring force . So it will be maximum when displacement is maximum .

Zero restoring force exists at equilibrium position or middle point or at point where displacement is zero . It is so because acceleration at that point is zero .

Answer:

A) 1.4167 × 10^(-11) F

B) r_a = 0.031 m

C) E = 3.181 × 10⁴ N/C

Explanation:

We are given;

Charge;Q = 3.40 nC = 3.4 × 10^(-9) C

Potential difference;V = 240 V

Inner radius of outer sphere;r_b = 4.1 cm = 0.041 m

A) The formula for capacitance is given by;

C = Q/V

C = (3.4 × 10^(-9))/240

C = 1.4167 × 10^(-11) F

B) To find the radius of the inner sphere,we will make use of the formula for capacitance of spherical coordinates.

C = (4πε_o)/(1/r_a - 1/r_b)

Rearranging, we have;

(1/r_a - 1/r_b) = (4πε_o)/C

ε_o is a constant with a value of 8.85 × 10^(−12) C²/N.m

Plugging in the relevant values, we have;

(1/r_a - 1/0.041) = (4π × 8.85 × 10^(−12) )/(1.4167 × 10^(-11))

(1/r_a) - 24.3902 = 7.8501

1/r_a = 7.8501 + 24.3902

1/r_a = 32.2403

r_a = 1/32.2403

r_a = 0.031 m

C) Formula for Electric field just outside the surface of the inner sphere is given by;

E = kQ/r_a²

Where k is a constant value of 8.99 × 10^(9) Nm²/C²

Thus;

E = (8.99 × 10^(9) × 3.4 × 10^(-9))/0.031²

E = 3.181 × 10⁴ N/C

Answer:

constant horizontal force developed in the coupling C = 11.25KN

the friction force developed between the tires of the truck and the road during this time is 33.75KN

Explanation:

See attached file

The friction force between the tires of the truck and the road is 22500 N.

It is given that a 2 Mg truck ( m = 2000 Kg) is initially moving with a speed of u = 15 m/s.

Distance traveled before coming to rest, s = 10m

The final velocity of the truck will be zero, v = 0

When the breaks are applied, only the frictional force is acting on the truck and it is opposite to the motion of the truck.

The frictional force is given by:

f = -ma

the acceleration of the truck = -a

The negative sign indicates that the acceleration is opposite to the motion.

Applying the third equation of motion we get:

v² = u² -2as

0 = 15² - 2×a×10

225 = 20a

a = 11.25 m/s²

So the magnitude of frictional force is:

f = ma = 2000 × 11.25 N

f = 22500 N

Learn more about friction force:

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Answer:

Body inertia I = 4.5 kg/m^2

Explanation:

Here, we want to calculate the body inertia when the arms are stretched outwards.

We know from the question that angular momentum is conserved

Thus;

I * 3 = 4.5 * 3

I = 4.5 kg/m^2

Answer:

n = 223 revolutions

Explanation:

It is given that,

The angular acceleration of a helicopter blade, [tex]\alpha =0.98\ rad/s^2[/tex]

Initial speed of the helicopter blade, [tex]\omega_i=0[/tex]

The final speed of the blade, [tex]\omega_f=500\ rpm=500\times \dfrac{2\pi}{60}\ rad/s=52.35\ rad/s[/tex]

We need to find the number of revolutions. Firstly we will find the angle turned by the blade. Let the angle is [tex]\theta[/tex]. So,

[tex]\omega_f^2-\omega_i^2=2\alpha \theta[/tex]

[tex]\theta=\dfrac{\omega_f^2}{2\alpha}[/tex]

[tex]\theta=1398.22\ rad [/tex]

Let there are n number of revolutions made by the blade. So,

[tex]n=\dfrac{\theta}{2\pi}\\\\n=\dfrac{1398.22}{2\pi}\\\\n=222.53\ rev[/tex]

or

n = 223 rev

So, there are 223 revolutions.