Suppose a 225 kg motorcycle is heading toward a hill at a speed of 29 m/s. The two wheels weigh 12 kg each and are each annular rings with an inner radius of 0.280 m and an outer radius of 0.330 m. How high can it coast up the hill, if you neglect friction in m?
a) m = 180 kg
b) v = 29 m/s
c) h = 32 m

Complete Question

The complete question is shown on the first uploaded image  

Answer:

The  wavelength is  [tex]\lambda = 622 nm[/tex]

Explanation:

  From the question we are told that

    The distance of the slit to the screen is  [tex]D = 5 \ m[/tex]

    The order of the fringe is m  =  6

     The distance between the slit is  [tex]d = 0.9 \ mm = 0.9 *10^{-3} \ m[/tex]

    The fringe distance is  [tex]Y = 1.9 \ cm = 0.019 \ m[/tex]

Generally the for a dark fringe the fringe distance is  mathematically represented as

        [tex]Y = \frac{[2m - 1 ] * \lambda * D }{2d}[/tex]

=>     [tex]\lambda = \frac{Y * 2 * d }{[2*m - 1] * D}[/tex]

substituting values

=>      [tex]\lambda = \frac{0.019 * 2 * 0.9*10^{-3} }{[2*6 - 1] * 5}[/tex]

=>     [tex]\lambda = 6.22 *10^{-7} \ m[/tex]

       [tex]\lambda = 622 nm[/tex]

Answer:

a. 24 m

Explanation:

Destructive interference occurs when two waves arrive at a point, out of phase. In a completely destructive interference, the two waves cancel out, but in a partially destructive interference, they produce a wave with a time varying amplitude, but maintain a wavelength the wavelength of one of the original waves. Since the two waves does not undergo complete destructive interference, then the possible value of the new wave formed can only be 24 m, from the options given.

Answer:

The correct answer is A    

Explanation:

In this exercise we are given a graph of temperature versus time.

In calorimeter processes there are two types

* one that when giving thermal energy to the system its temperature increases, this fundamentally due to the greater kinetic energy of the molecular ones, this process observes in the graphs as a straight line of constant slope

* A process donates all the thermal energy that is introduced is cracked in breaking the molecular bonds, taking matter from one thermodynamic state to another, for example: liquid to gas.

This process in curves as a horizontal line, that is, there is no temperature change,

When analyzing the graph shown, parts C and D are the one that show a change in temperature with thermal energy. The correct answer is A

Answer:

C and D

Explanation:

Just took the quiz

Answer:

The magnitude of flux remains the same, and the field increases.

Explanation:

This is because the number of field lines leaving the sphere remains constant and the electric field increases because the line density increases

Answer:

The current will be 18 A

Explanation:

Given;

potential difference, V = 10 V

current between the resistor, I = 2 A

Apply ohm's law;

V = IR

R = V / I

R = 10 / 2

R = 5Ω

Resistance is given as;

[tex]R = \frac{\rho l}{A}[/tex]

where;

ρ is resistivity

l is length

A is area

[tex]R = \frac{\rho l}{A} \\\\R = \frac{\rho l}{\pi r^2} = \frac{\rho l}{\pi (\frac{d}{2}) ^2} = \frac{\rho l}{\pi (\frac{d^2}{4}) }\\\\R = \frac{4*\rho l}{\pi d^2} \\\\R = (\frac{4*\rho l}{\pi } )\frac{1}{d^2} \\\\R = (k)\frac{1}{d^2} \\\\k = Rd^2\\\\R_1d_1^2 = R_2d_2^2\\\\R_2 = \frac{R_1d_1^2}{d_2^2}[/tex]

When the diameter of the resistor is tripled

d₂ = 3d₁

[tex]R_2 = \frac{5*d_1^2}{(3d_1)^2} \\\\R_2 = \frac{5d_1^2}{9d_1^2} \\\\R_2 = 0.556 \ ohms[/tex]

The current is now calculated as;

Apply ohms law;

V = IR

I = V / R

I = 10 / 0.556

I = 17.99 A

I = 18 A

Therefore, the current will be 18 A

Answer:

The magnitude of the gravitational force is 4.53 * 10 ^-7 N

Explanation:

Given that the magnitude of the gravitational force is F = GMm/r²

mass M = 850 kg

mass m = 2.0 kg

distance d = 1.0 m , r = 0.5 m

F = GMm/r²

Gravitational Constant G = 6.67 × 10^-11 Newtons kg-2 m2.

F = (6.67 × 10^-11 * 850 * 2)/0.5²

F = 0.00000045356 N

F = 4.53 * 10 ^-7 N

Q: An appliance with a 20 Ω resistor has a power rating of 15.0 W. Find the maximum current which can flow safely through the appliance g

Answer:

0.866 A

Explanation:

From the question,

P = I²R............................. Equation 1

Where P = power, I = maximum current, R = Resistance.

Make I the subject of the equation

I = √(P/R).................... Equation 2

Given: P = 15 W, R = 20 Ω

Substitute these values into equation 2

I = √(15/20)

I = √(0.75)

I = 0.866 A

Hence the maximum current that can flow safely through the appliance = 0.866 A

Answer:

The number of turns of wire needed is 3536 turns.

Explanation:

Given;

length of the wire, L = 8 cm = 0.08 m

magnetic field on the wire, B = 0.1 T

current in the wire, I = 1.8 A

The magnetic field produced by a solenoid is calculated as;

B = μ₀ n I

where;

n is the number of turns per length = N / L

μ₀ is permeability of free space = 4π x 10⁻⁷ N/A²

[tex]B = \frac{\mu_o N I}{L} \\\\N = \frac{BL}{\mu_o I} \\\\N = \frac{0.1 *0.08}{4\pi*10^{-7} *1.8} \\\\N = 3536.32 \ turns[/tex]

Therefore, the number of turns of wire needed is 3536 turns.

A 2.0-cm length of wire centered on the origin carries a 20-A current directed in the positive y direction. Determine the magnetic field at the point x = 5.0m on the x-axis.

1.6nT [in the negative z direction]

The magnetic field, B, due to a distance of finite value b, is given by;

B = (μ₀IL) / (4πb[tex]\sqrt{b^2 + L^2}[/tex])                -----------(i)

Where;

I = current on the wire

L = length of the wire

μ₀ = magnetic constant = 4π × 10⁻⁷ H/m

From the question,

I = 20A

L = 2.0cm = 0.02m

b = 5.0m

Substitute the necessary values into equation (i)

B = (4π × 10⁻⁷ x 20 x 0.02) / (4π x 5.0 [tex]\sqrt{5.0^2 + 0.02^2}[/tex])

B = (10⁻⁷ x 20 x 0.02) / (5.0 [tex]\sqrt{5.0^2 + 0.02^2}[/tex])

B = (10⁻⁷ x 20 x 0.02) / (5.0 [tex]\sqrt{25.0004}[/tex])

B = (10⁻⁷ x 20 x 0.02) / (25.0)

B = 1.6 x 10⁻⁹T

B = 1.6nT

Therefore, the magnetic field at the point x = 5.0m  on the x-axis is 1.6nT.

PS: Since the current is directed in the positive y direction, from the right hand rule, the magnetic field is directed in the negative z-direction.

Answer:

The frequency will be reduced by a factor of √2/2

Explanation:

Pls see attached file

The new frequency of oscillation will be half the original frequency of oscillation of spring-block system.

Let the initial mass of block be m.

And new mass is, 4m.

The frequency of oscillating motion is defined as the number of complete oscillation made during the time interval of 1 second. The mathematical expression for the frequency of oscillation of block-spring system is given as,

[tex]f = \dfrac{1}{2 \pi}\sqrt{\dfrac{k}{m}}[/tex]

Here,

k is the spring constant.

If the mass of block increased to 4m, then the new frequency of oscillation of spring will be,

[tex]f' = \dfrac{1}{2 \pi} \sqrt{\dfrac{k}{4m}}\\\\\\f' =\dfrac{1}{2} \times \dfrac{1}{2 \pi} \sqrt{\dfrac{k}{m}}\\\\\\f' =\dfrac{1}{2} \times f[/tex]

Thus, we can conclude that the new frequency of oscillation will be half the original frequency of oscillation of spring-block system.

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Answer:

Explanation:

Formula of lateral displacement

[tex]S_{lateral}=\frac{t}{cosr} \times sin(i-r)[/tex]

t is thickness of slab , i  and r are angle of incidence and refraction respectively .

Given t = .45 m

sin i / sin r = 2.2

sin 46 / sin r = 2.2

sin r = .719 / 2.2 = .327

r = 19°

[tex]S_{lateral}=\frac{t}{cosr} \times sin(i-r)[/tex]

[tex]S_{lateral}=\frac{.45}{cos19} \times sin(46-19)[/tex]

= .45 x .454 / .9455

= .216 m

= 21.6 cm .

The displacement, D, of the beam when it exits the slab is; 21.65 cm.

We are given;

Refractive index of slab material; nm = 2.2

Thickness of slab; t = 0.45 m

Refractive index of air; na = 1

Angle of incidence; θa = 46°

From snell's law, we can calculate the angle of refraction from;

na × sin θa = nm × sin θm

Thus;

1 × sin 46 = 2.2 × sin θm

0.7193 = 2.2 × sin θm

sin θm = 0.7193/2.2

θm = sin^(-1) 0.32695

θm = 19.08°

Formula for the displacement of the beam is;

D = (t/cos θm) × sin (θa - θm)

Plugging in the relevant values gives;

D = (0.45/cos 19.08) × sin (46 - 19.08)

D = 0.4783 × 0.4527

D = 0.2165m = 21.65 cm

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Answer:

a. Bx is positive

Explanation:

See attached file

Answer:

The critical angle is  [tex]i = 41.84 ^o[/tex]

Explanation:

From the  question we are told that

    The index of refraction of the sugar solution is  [tex]n_s = 1.5[/tex]

   The  index of refraction of air is  [tex]n_a = 1[/tex]

Generally from Snell's  law

      [tex]\frac{sin i }{sin r } = \frac{n_a }{n_s }[/tex]

Note that the angle of incidence in this case is equal to the critical angle

Now for total internal reflection the angle of reflection is [tex]r = 90^o[/tex]

So  

      [tex]\frac{sin i }{sin (90) } = \frac{1 }{1.5 }[/tex]

      [tex]i = sin ^{-1} [\frac{ (sin (90)) * 1 }{1.5} ][/tex]

      [tex]i = 41.84 ^o[/tex]

Explanation:

It is given that, in the first trial, the initial velocity is [tex]v_o[/tex] and in the second it is [tex]4v_o[/tex].

The total energy of the system remains constant. So,

[tex]\dfrac{1}{2}mv^2+\dfrac{1}{2}kx^2=\text{constant}[/tex] ....(1)

x is amplitude

It means that the amplitude is directly proportional to velocity. If velcoity increases to four times, then the amplitude also becomes 4 times.

Differentiating equation (1) we get :

[tex]mv\dfrac{dv}{dt}+kx\dfrac{dx}{dt}=0[/tex]

Since,

[tex]\dfrac{dv}{dt}=a,\ \text{acceleration}[/tex] and [tex]\dfrac{dx}{dt}=v,\ \text{velocity}[/tex]

So,

[tex]mva+kxv=0[/tex]

It means that the acceleration is also proportional to the amplitude. So, acceleration also becomes 4 times.

Hence, the correct option is (B) "both the amplitude and the maximum acceleration are four times as great"

Answer:

F' = F

Hence, the magnitude of the attractive force remains same.

Explanation:

The force of attraction between two bodies is given by Newton's Gravitational Law:

F = Gm₁m₂/r²   --------------- equation 1

where,

F = Force of attraction between balls

G = Universal Gravitational Constant

m₁ = mass of first ball

m₂ = mass of 2nd ball

r = distance between balls

Now, we double the masses of both balls and the separation between them. So, the force of attraction becomes:

F' = Gm₁'m₂'/r'²

here,

m₁' = 2 m₁

m₂' = 2 m₂

r' = 2 r

Therefore,

F' = G(2 m₁)(2 m₂)/(2 r)²

F' = Gm₁m₂/r²

using equation 1:

F' = F

Hence, the magnitude of the attractive force remains same.

Answer:

d. four times as far

Explanation:

Initial velocity of car and truck, u = 0

let acceleration of both the truck and car = a

let the length of time for the acceleration = t

Let the time the truck accelerated = 2t

The distance traveled by the car is calculated as;

s = ut + ¹/₂at²

s₁ = 0(t) + ¹/₂at²

s₁ = ¹/₂at²

The distance traveled by the truck is calculated as;

s = ut + ¹/₂at²

s₂ = 0(2t) + ¹/₂a (2t)²

s₂ =  ¹/₂a x 4t²

s₂ = 4 (¹/₂at²)

s₂ = 4(s₁)

Truck distance = four times car distance

Therefore, Compared with the car, the truck will travel four times as far

d. four times as far

Answer:

The direction of the magnetic field causing this force is

In the plane of the screen and towards the bottom of the egde

Explanation:

This is by applying Fleming s right hand rule which explains that

When a conductor such as a wire attached to a circuit moves through a magnetic field, an electric current is induced in the wire due to Faraday's law of induction. The current in the wire can have two possible directions. Fleming's right-hand rule gives which direction the current flows.

The right hand is held with the thumb, index finger and middle finger mutually perpendicular to each other (at right angles), as shown in the diagram.[1]

The thumb is pointed in the direction of the motion of the conductor relative to the magnetic field.

The first finger is pointed in the direction of the magnetic field. (north to south)

Then the second finger represents the direction of the induced or generated current within the conductor (from the terminal with lower electric potential to the terminal with higher electric potential, as in a voltage source)

Correct answer is 2.7 x 10^-3 J/m3

I hope that helps ! <33

The maximum energy density of the capacitor is closest to: 2.7 x 10^-3 J/m3.

Energy density is defined as the total energy per unit volume of the capacitor. Since, Now, for a parallel plate capacitor, A × d = Volume of space between plates to which electric field E = V / d is confined. Therefore, Energy is stored per unit volume.

All Answers (14) Energy density is equal to 1/2*C*V2/weight, where C is the capacitance you computed and V should be your nominal voltage (i.e 2.7 V). Power Density is V2/4/ESR/weight, where ESR is the equivalent series resistance.

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Answer:

The value for  A  is A= 0.6

The angular acceleration is  [tex]\alpha (t) = 2.4 \ t \ m/s^2[/tex]

Explanation:

From the question we are told that  

    The radius of the disk is  [tex]r = 25.0 \ cm = 0.25 \ m[/tex]

     The linear acceleration is  [tex]a(t) = At[/tex]

     At time   [tex]t = 3 \ s[/tex]

     [tex]a(3) = 1.80 \ m/s^2[/tex]

Generally angular acceleration is  mathematically represented as  

         [tex]\alpha(t) = \frac{a(t)}{r}[/tex]

Now  at t = 3 seconds  

         a(3) =  A *  3

=>      1.80 =  A  *  3  

=.>       A =  0.6

So  therefore

             a(t) =  0.6 t  

Now  substituting this into formula for angular acceleration

        [tex]\alpha (t) = \frac{0.6 t }{R}[/tex]

substituting for  r  

         [tex]\alpha (t) = \frac{0.6 t }{0.25}[/tex]

         [tex]\alpha (t) = 2.4 \ t \ m/s^2[/tex]

Answer:

The  magnitude of the  electric field intensity is  [tex]E = 7.89 *10^{6} \ V/m[/tex]

Explanation:

From the question we are told that

    The  voltage is  [tex]\epsilon = 72.7 \ mV = 72.7 *10^{-3} V[/tex]

    The  thickness of the membrane is  [tex]t = 9.22 \ nm = 9.22 *10^{-9} \ m[/tex]

Generally the electric field intensity is mathematically represented as

                [tex]E = \frac{\epsilon }{t}[/tex]

 substituting values

                [tex]E = \frac{72.7 *10^{-3} }{9.22 *10^{-9}}[/tex]

                [tex]E = 7.89 *10^{6} \ V/m[/tex]

Answer:

Explanation:

Load will be moved by 4L when effort moves by distance L .

4L = 10 m ( given )

L = 2.5 m

work output = work input = 400 x 10 = 4000 J

work by friction = 100 J

net work output = 3900 J .

efficiency = net output of work / work input

= (3900 / 4000) x 100

= 97.5 %

2 )

work input = 4000 J

distance moved by effort = 2.5 m

If effort be F

F X 2.5  = 4000

F = 1600 N .

Answer:

To calculate the predicted surface elevation of a 50km thick crust above a surface of 2.5km we are given a density of 3 gram per centimeter cube.

The displacement of the material will be calculated by subtracting the surface elevation of 2.5 km from the 50 km thick crust. Therefore 50-25= 47.5 km.

Thus let the density of the material be Pm

50*3= 47.5*Pm

Therefore: Pm= (50*3)/47.5= 3.16gram per centimeter cube

Thus with an average density of 2.8gram per centimeter cube

50*2.8= (50-x)*3.16

(50-x)= (50*2.8)/3.16

50-x=44.3

x=50-44.3= 5.7

Explanation:

To calculate the predicted surface elevation of a 50km thick crust above a surface of 2.5km we are given a density of 3 gram per centimeter cube.

The displacement of the material will be calculated by subtracting the surface elevation of 2.5 km from the 50 km thick crust. Therefore 50-25= 47.5 km.

Thus let the density of the material be Pm

50*3= 47.5*Pm

Therefore: Pm= (50*3)/47.5= 3.16gram per centimeter cube

Thus with an average density of 2.8gram per centimeter cube

50*2.8= (50-x)*3.16

(50-x)= (50*2.8)/3.16

50-x=44.3

x=50-44.3= 5.7

Answer: 3217.79 hours.

Explanation:

Given, A 140 lb. climber saved her potential energy as she descended from Mt. Everest (Elev. 29,029 ft) to Kathmandu (Elev. 4,600 ft).

Power = 0.4 watt

Mass of climber = 140 lb

= 140 x 0.4535 kg  [∵ 1 lb= 0.4535 kg]

⇒ Mass of climber (m) = 63.50 kg

Let [tex]h_1=29,029\ ft= 8848.04\ m\ \ \ \ [ 1 ft=0.3048\ m ][/tex] and [tex]h_2= 4,600 ft = 1402.08\ m[/tex]

Now, Energy saved =[tex]mg(h_1-h_2)=(63.50)(9.8)(8848.04-1402.08)=4633620.91\ J[/tex]

[tex]\text{Power}=\dfrac{\text{energy}}{\text{time}}\\\\\Rightarrow 0.4=\dfrac{4633620.91}{\text{time}}\\\\\Rightarrow\ \text{time}=\dfrac{4633620.91}{0.4}\approx11584052.28\text{ seconds}\\\\=\dfrac{11584052.28}{3600}\text{ hours}\ \ \ [\text{1 hour = 3600 seconds}]\\\\=3217.79\text{ hours}[/tex]

Hence, she can power her 0.4 watt flashlight for 3217.79 hours.

Answer:

0.055 kg

Explanation:

According to the given situation the solution of the mass of the string is shown below:-

Speed of the wave is

[tex]v = \sqrt{\frac{F_T\times Length\ of\ string}{Mass\ of\ string}}[/tex]

[tex]30.0 m/s = \sqrt{\frac{10 kg m/s^2\times 5.00 m}{Mass\ of\ string}[/tex]

Mass of string is

[tex]= \sqrt{\frac{10 kg m^2/s^2\times 5.00 m}{900 m^2 s^2}[/tex]

After solving the above equation we will get the result that is

= 0.055 kg

Therefore for calculating the mass of the string we simply applied the above formula.

Answer:

Current = 132.35 A

The motor needs to draw 132.35 Amperes current from the battery.

Explanation:

The formula of electric power is given as follows:

Power = (Voltage)(Current)

Current = Power/Voltage

In this question, we have:

Power = 45 KW = 45000 W

Voltage of Battery Pack = 340 V

Current needed to be drawn = ?

Therefore,

Current = 45000 W/340 V

Current = 132.35 A

The motor needs to draw 132.35 Amperes current from the battery.

Answer:

5.1*10^3 J/m^3

Explanation:

Using E = q/A*eo

And

q =75*10^-6 C

A = 0.25

eo = 8.85*10^-12

Energy density = 1/2*eo*(E^2) = 1/2*eo*(q/A*eo)^2 = [q^2] / [2*(A^2)*eo]

= [(75*10^-6)^2] / [2*(0.25)^2*8.85*10^-12]

= 5.1*10^3 J/m^3

Answer:

Explanation:

Focal length f = - 4 cm

Object distance u = - 10 cm

v , image distance = ?

Mirror formula

[tex]\frac{1}{v} +\frac{1}{u} = \frac{1}{f}[/tex]

Putting the given values

[tex]\frac{1}{v} - \frac{1}{10} = - \frac{1}{4}[/tex]

[tex]\frac{1}{v}= - \frac{3}{20}[/tex]

v = - 6.67 cm .

magnification

m = v / u

= - 6.67 / - 10

= .667

so image will be smaller in size in comparison with size of object .

Characteristics will be that ,

1 ) it will be inverted and

2 ) it will be real image .

Answer:

A. 9.31 x10^10J

B. -8.47x10 ^ 12J

C. 8.38x 10^12J

Explanation:

See attached file pls

Answer:

48 i believe

Explanation:

Explanation:

Work done is given by the product of force and displacement.

Case 1,

1. A boy lifts a 2-newton box 0.8 meters.

W = 2 N × 0.8 m = 1.6 J

2. A boy lifts a 5-newton box 0.8 meters.

W = 5 N × 0.8 m = 4 J

3. A boy lifts a 8-newton box 0.2 meters.

W = 8 N × 0.2 m = 1.6 J

4. A boy lifts a 10-newton box 0.2 meters.

W = 10 N × 0.2 m = 2 J

Out of the four options, in option (2) ''A boy lifts a 5-newton box 0.8 meters'', the work done is 4 J. Hence, the greatest work done is 4 J.