11. A circular racetrack has a radius of 500 m. What is the displacement of a bicyclist when she travels around the track from the north side to the south side

Answer:

a

     [tex]l_o  =52 \  m[/tex]

b

      [tex]l = 37.13 \ LY[/tex]

Explanation:

From the question we are told that

    The  speed of the spaceship is  [tex]v  =  0.800c[/tex]

    Here  c is the speed of light with value  [tex]c =  3.0*10^{8} \ m/s[/tex]

    The  length is  [tex]l = 31.2 \  m[/tex]

     The  distance of the star for earth is [tex]d = 145 \  light \  years[/tex]

     The  speed is [tex]v_s = 2.90 *10^{8}[/tex]

Generally the from the length contraction equation we have that

       [tex]l  =  l_o  \sqrt{1 -[\frac{v}{c } ]}[/tex]

Now the when at rest the length is  [tex]l_o[/tex]

So  

      [tex]l_o =\frac{l}{\sqrt{ 1 - \frac{v^2}{c^2 } } }[/tex]

      [tex]l_o =\frac{ 31.2 }{ \sqrt{1 - \frac{(0.800c ) ^2}{c^2} } }[/tex]

      [tex]l_o=52 \  m[/tex]

Considering b  

  Applying above equation

            [tex]l  =l_o \sqrt{1 -  [\frac{v}{c } ]}[/tex]

Here [tex]l_o  =145 \  LY(light \ years )[/tex]

So

           [tex]l=145 *  \sqrt{1 -  \frac{v_s^2}{c^2 } }[/tex]

            [tex]l =145 *  \sqrt{ 1 - \frac{2.9 *10^{8}}{3.0*10^{8}} }[/tex]

            [tex]l = 37.13 \ LY[/tex]

Answer:

t = 0.25 seconds

Explanation:

Given that,

Initial speed of a bullet, v = 800 m/s

Distance from the target is 200 m

We need to find the time required for the bullet to reach the target. Time is simply calculated by the definition of velocity i.e.

[tex]t=\dfrac{d}{v}\\\\t=\dfrac{200\ m}{800\ m/s}\\\\t=0.25\ s[/tex]

So, it will take 0.25 seconds to reach the target.

Answer:

The force is  [tex]F = 423.04 \ N[/tex]

Explanation:

From the question we are told that

   The weight is  [tex]W = 35 .0 \ N[/tex]

    The  force constant is  [tex]k = 220 \ N/m[/tex]

    The frequency is  [tex]f = 10.5 \ Hz[/tex]

     The amplitude is  [tex]A = 3.00 \ cm = 0.03 \ m[/tex]

Generally the maximum driving force is mathematically represented as

     [tex]F = m * w^2 A[/tex]

Here  m is the mass of the weight which is  mathematically represented as  

       [tex]m = \frac{ W }{g}[/tex]

=>     [tex]m = \frac{ 35 }{9.8 }[/tex]

=>     [tex]m = 3.571 \ kg[/tex]

  Also   [tex]w[/tex] is the angular frequency of the weight which is mathematically represented as

         [tex]w = 2 \pi * f[/tex]

         [tex]w = 2* 3.142 * 10[/tex]

=>      [tex]w = 62.84 \ rad/s[/tex]

So

    [tex]F = 3.571 * 62.84^2 * 0.03[/tex]

    [tex]F = 423.04 \ N[/tex]

Complete Question

The human eye can readily detect wavelengths from about 400 nm to 700 nm. If white light illuminates a diffraction grating having 710 lines/mm, over what range of angles does the visible m = 1 spectrum extend

Answer:

The  value  [tex]\theta = 16.5 ^ o[/tex]

Explanation:

From the question we are told that

   The  diffraction grating haves [tex]a =  710 \  lines /mm[/tex]

Generally the separation of the slit is mathematically represented  as

      [tex]d = \frac{1}{710} \ mm =0.001408 \ mm =   1.408 *10^{-6} \  m[/tex]

 Generally the condition for constructive interference is mathematically represented as  

           [tex]dsin(\theta ) = n \lambda[/tex]

So

          [tex]\theta =  sin ^{-1} [\frac{n * \lambda }{d} ][/tex]

=>       [tex]\theta  =  sin^{-1}[\frac{1 *  400 *10^{-9}}{ 1.408*10^{-6}} ][/tex]

=>         [tex]\theta = 16.5 ^ o[/tex]

Answer:

The Sun is known to emit almost all wavelengths of electromagnetic radiation but 99% of the radiation emitted by the sun lie in the ultraviolet, visible, and infrared regions.

Ultraviolet (UV) is a form of electromagnetic radiation with wavelength from 10 nm to 400 nm (750 THz). The wavelength is shorter than that of visible light but longer than X-rays. UV rays make up about 10% of the e-m waves from the sun. UV radiation is carcinogenic to the skin, and is absorbed by the melanin pigment in the skin.

Visible light is the only e-m wave that our eyes can pick up, i.e the only e-m wave we can see. The frequency of this spectrum corresponds to a band in the vicinity of 405–790 THz. It can further be separated into different colors. It makes up a large portion of the e-m waves coming from the sun.

Infrared wave is an e-m radiation whose wavelengths longer than those of visible light. It is is generally invisible to the human eye. The wavelength of an infrared wave extend from the red edge of the visible spectrum at 700 nanometers (frequency 430 THz), to 1 millimeter (300 GHz). Most of the thermal radiation emitted by objects near room temperature is infrared. Most of the heat from the sun reach us as infrared radiation. As with all e-m radiation, infrared radiation carries radiant energy and behaves both like a wave and like a photon.

Answer:

2.1 minutes/ 126 seconds

Explanation:

Distance = speed x time

We can rearrange this equation for time:

Time = Distance/Speed

For you (89km/h):

Distance = 58km, Speed = 89km/h

Therefore time = 58/89 = 0.652 (3dp) hours

For friend:

Distance = 58km, Speed = 94km/h

Therefore time = 58/94 = 0.617 (3dp) hours

Difference in time = 0.652 - 0.617 = 0.035 hours.

Convert to minutes: 0.035 x 60 (because 60 min in hour) = 2.1

Your friend will be waiting for 2.1 minutes, or 126 seconds (2.1 x 60).

Hope this helped!

Answer:

Zero

Explanation:

Because using

Deta X= dsinစ x n(lambda)

But we know that for central maxima

n is zero

So after substituting

Deta x = 0

Complete Question

A wave is described by y(x,t) = 0.1 sin(3x + 10t), where x is in meters, y is in centimetres and t is in seconds. The angular wave  frequency is

Answer:

The  value is [tex]w =  10 \ rad /s[/tex]

Explanation:

From the question we are told that  

    The equation describing the wave is y(x,t) = 0.1 sin(3x + 10t)

Generally the sinusoidal equation representing the motion of a wave is mathematically represented as

         [tex]y(x,t) =  Asin(kx + wt )[/tex]

Where  w  is the  angular frequency

Now comparing this equation  with that given we see that

       [tex]w =  10 \ rad /s[/tex]

Answer:

the width of the slit is dividing therefore the distance to the minimums increases as the width of the slit decreases

Explanation:

In the diffraction phenomenon the intensity minima are described by

         a sin θ = (m + ½) λ

without using trigonometry we can find an expression for the sine

        tan θ = y / L

        for small angles

        Tan θ = sin θ/ cos θ = sin θ = y / L

        a y / L = (m + ½) lam

        y = (m + ½) λ L / a

we see that the width of the slit is dividing therefore the distance to the minimums increases as the width of the slit decreases

In the observation of the experiment the length of the pattern increases with the decrease in the width of the slit

Answer:

The electric field due to charge at distance r is [tex](-0.8169\times10^{6},0.8169\times10^{6}, 2.800\times10^{6})\ N/C[/tex]

Explanation:

Given that,

Initial position of particle [tex]r_{1}=4.00\times10^{-9}i-5.00\times10^{-9}j-2.00\times10^{-9}k\ m[/tex]

Final position of particle [tex]r_{2}=-2.00\times10^{-9}i+4.00\times10^{-9}j+ 3.00\times10^{-9}k\ m[/tex]

We need to calculate the magnitude of the position vector

Using formula of position vector

[tex]\vec{r}=\vec{r_{2}}-\vec{r_{1}}[/tex]

Put the value into the formula

[tex]\vec{r}=-2.00\times10^{-9}i+4.00\times10^{-9}j+ 3.00\times10^{-9}k-(4.00\times10^{-9}i-5.00\times10^{-9}j-2.00\times10^{-9}k)[/tex]

[tex]\vec{r}=-9\times10^{-9}i+9\times10^{-9}j+5\times10^{-9}k[/tex]

[tex]\vec{|r|}=\sqrt{(9^2+9^2+5^2)\times10^{-18}}[/tex]

[tex]\vec{|r|}=13.6\times10^{-9}\ m[/tex]

We need to calculate the unit vector along electric field direction

Using formula of unit vector

[tex]\hat{r}=\dfrac{\vec{r}}{|\vec{r}|}[/tex]

Put the value into the formula

[tex]\hat{r}=\dfrac{-9\times10^{-9}i+9\times10^{-9}j+5\times10^{-9}k}{13.6\times10^{-9}}[/tex]

[tex]\hat{r}=-0.66i+0.66j+0.36k[/tex]

We need to calculate the electric field due to charge at distance r

Using formula of electric field

[tex]E=\dfrac{kq}{r^2}\hat{r}[/tex]

Put the value into the formula

[tex]E=\dfrac{9\times10^{9}\times1.6\times10^{-19}}{(13.6\times10^{-9})^2}\times(-0.66i+0.66j+0.36k)[/tex]

[tex]E=7.78\times10^{6}\times(-0.66i+0.66j+0.36k)[/tex]

[tex]E=-0.8169\times10^{6}i+0.8169\times10^{6}j+2.800\times10^{6}k\ N/C[/tex]

[tex]E=(-0.8169\times10^{6},0.8169\times10^{6}, 2.800\times10^{6})\ N/C[/tex]

Hence, The electric field due to charge at distance r is [tex](-0.8169\times10^{6},0.8169\times10^{6}, 2.800\times10^{6})\ N/C[/tex]

Answer:

Statics and dynamics

Explanation:

Rigid-body mechanics is divided into two areas: statics deals with the equilibrium of bodies, that is, those that are either at rest or move with a constant velocity; whereas dynamic is concerned with the accelerated motion of bodies.

In rigid-body mechanics, there are two various branches: statics and dynamics. Statics studies the stability of bodies, i.e., those that are at rest or move at a constant speed, whereas dynamics studies the accelerated movement of bodies.

Even if neither a system's energy state nor its phase of motion tends to change over time, the system is said to be in equilibrium.

A simple mechanical body is considered to have been in equilibrium if it neither suffers accelerometers nor angular acceleration. Unless an external force disrupts this state, it will remain in equilibrium indefinitely.

When all forces acting on a single particle are added together and equal to zero, equilibrium results. In addition to the conditions outlined in the article above, a rigid body is said to be in equilibrium if the vector sum of any torques operating on it equals zero, maintaining the body's steady state of rotational motion.

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Answer:

soccer ball

Explanation:

Because it's round in shape and therefore cannot be stopped as both moves at same speed. There's no edges or corners to bounce up and slow the ball.

Answer:

They will both be since they are going the same speed

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Answer:

1670 kg

Explanation:

Convert the dimensions to cm.

12 ft × (12 in/ft) × (2.54 cm/in) = 365.76 cm

32 in × (2.54 cm/in) = 81.28 cm

Calculate the volume.

V = πr²h

V = π (81.28 cm / 2)² (365.76 cm)

V = 1,897,813.27 cm³

V = 1,897,813.27 mL

V = 1,897.81 L

Density of benzene is 0.88 kg/L.

m = (0.88 kg/L) (1,897.81 L)

m = 1670 kg

Answer:

True

Explanation:

In the foundational topics of physics mechanics consists of motion, energy and forces, theses areas are core concerns in the study of physics hence they are the foundational topics and are often times treated first in all matters.

What is motion?

Simply put, it is alternating from points to points.

the areas of study that involves motion and force together is call dynamics.

while the area of study of motion without any applied force is call statics.

Answer:

energy is stored is 2.2 × 10⁻¹³ J

Explanation:

The capacitance  of the cell is given with the expression

C = (KE₀A) / d

k is the dielectric constant, A is the area of the cell, d is the thickness of the cell.

Now given that; the diameter is 50,

Area A = 4πR²

A = 4π × ( 25 × 10⁻⁶ m)²

A = 7850×10⁻¹² m²

our capacitance C = (KE₀A) / d

C = [9 ( 8.85 × 10⁻¹² C²/N.m²  × 7850×10⁻¹² m² )] / 7×10⁻⁹ m

C = 8.93 × 10⁻¹¹ F

Now Energy stored

E = 1/2 × CV²

E = 1/2 × (8.93 × 10⁻¹¹ F) × ( 70 × 10⁻³ V)²

E = 2.2 × 10⁻¹³ J

Therefore energy is stored is 2.2 × 10⁻¹³ J

The energy that should be stored in the electric field should be 2.2 × 10⁻¹³ J.

Since

The capacitance  of the cell should be

C = (KE₀A) / d

Here,

k is the dielectric constant,

A is the area of the cell,

d is the thickness of the cell.

Now the diameter is 50,

So,

Area A = 4πR²

A = 4π × ( 25 × 10⁻⁶ m)²

A = 7850×10⁻¹² m²

Now

our capacitance C = (KE₀A) / d

C = [9 ( 8.85 × 10⁻¹² C²/N.m²  × 7850×10⁻¹² m² )] / 7×10⁻⁹ m

C = 8.93 × 10⁻¹¹ F

Now Energy stored should be

E = 1/2 × CV²

E = 1/2 × (8.93 × 10⁻¹¹ F) × ( 70 × 10⁻³ V)²

E = 2.2 × 10⁻¹³ J

Therefore energy is stored is 2.2 × 10⁻¹³ J.

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Answer:

1) 5.52 cm , C) 5.5 cm

Explanation:

When a measurement is carried out, in addition to the value of the magnitude, the error or uncertainty of the measurement must occur, in a direct measurement with an instrument the uncertainty is equal to the appreciation of the instrument.

Uniform see the errors by the number of significant figures days, in this cases they are two decimals for which the appreciation of the instrument ± - 0.01

now we can analyze the measurements made

1) 5.52 cm. Validate. It is a valid measurement is within the uncertainty range

2) 6.63 cm. It does not validate. It is out of the error range

3) 5.5 cm Valid. It is within the given error range,

4) 5.93 cm Not Valid. It is out of the error range.

Answer:

6.63 and 5.93

Explanation:

Complete question:

The length of nylon rope from which a mountain climber is suspended has an effective force constant of 1.40 ×10⁴ N/m.

What is the frequency (in Hz) at which he bounces, given that his mass plus the mass of his equipment is 84.0 kg?

Answer:

The frequency (in Hz) at which he bounce is 2.054 Hz

Explanation:

Given;

effective force constant, K = 1.40 ×10⁴ N/m.

The total mass = his mass plus the mass of his equipment, m = 84 kg

The frequency (in Hz) at which he bounce is given by;

[tex]f = \frac{1}{2\pi} \sqrt{\frac{k}{m}}\\\\f = \frac{1}{2\pi} \sqrt{\frac{1.4*10^4}{84}}\\\\f = 2.054 \ Hz[/tex]

Therefore, the frequency (in Hz) at which he bounce is 2.054 Hz

Explanation:

Assuming the circular path is horizontal, the sum of forces in the centripetal direction is:

∑F = ma

T = mv²/r

T = (1.0000 kg) (5.00 m/s)² / (0.500 m)

T = 50.0 N

Answer:

The antenna which is a transmitting and receiving device emits energy from current as radio waves, it does this by attracting the radio waves which are a form of EMWs and converts it to small voltages which are amplified to the final voltage signal which hear

Answer:

We know that the relation between period and frequency is:

T = period.

f = frequency.

T = 1/f.

Then, if the period is 35 μs = 35x10^-9 seconds.

The frequency will be:

f = (1/ 35x10^-9 s) = (1/35s)*10^9

now, 1Hz = 1/s

1KHz = 1/1000s = 10^-3 s

f = (10^9/35)*10^-3 KHz = 10^6/35 KHz = 28,571.429 KHz.

Now we must divide this by 2.5:

28,571.429 KHz/2.5 = 11,428.572 KHz

Now we can use the relation:

T = 1/f

T = 1/11,428.572 KHz = (1/11,428.572 Hz)*10^-3

T = 8.750x10^-8 seconds.

And we want this expressed in  μs = 10`-9 seconds, we have:

T = 8.750x10^-8 s = (10/10)8.750x10^-8 s = 87.50x10`-9s = 87.50 μs

So as expected, if the frequency is reduced by a factor of 2.5, the  period will increase by a factor of 2.5

As the initial period was 35 μs, and:

2.5*35 μs = 87.5 μs

Answer:

option D

Explanation:

also to add.... there exists a solubility equilibrium between solid solute and the solution.

The newly added solute begins to sit on the bottom of the container without dissolving this represents that the solution has become saturated, Therefore the correct answer is D.

It is a type of solution in which no more amount of solute can be dissolved any further, The saturated solution already contains the maximum amount of solute that can be dissolved within it.

The solution reached a point where the newly added solute starts to sit on the bottom this means the solution has become saturated.

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Answer:

372.94 km

d= st

= (64.3 km/h)(5.8h)

=372.94 km

Answer:

The angular acceleration of the top is 0.18 rad/s²

Explanation:

Given;

angular velocity of the top, ω = 16 rad/s

time it takes to come to a complete stop, t = 88.9s

The angular acceleration of the top, is calculated as;

[tex]\alpha = \frac{\omega}{t}[/tex]

α is the angular acceleration

ω is angular acceleration

t is the time

[tex]\alpha = \frac{\omega}{t}\\\\\alpha = \frac{16}{88.9}\\\\\alpha =0.18 \ rad/s^2[/tex]

Therefore, the angular acceleration of the top is 0.18 rad/s²

Answer:

2260000 J

Explanation:

From the question,

Q = ml.................... Equation 1.

Where Q = Heat, m = mass of water, l = specific latent heat of vaporization.

But we can get the mass o water using the formula of density.

D = m/v........... Equation 2

Where D = density of water, v = volume of water.

make m the subject of the formula in equation 2

m = D×v............ Equation 3

Substitute equation 3 into equation 1

Q = D×v×l................. Equation 4

Given: v = 1.00 L = 0.001 m³.

Constant: l = 226000 J/kg, D = 1000 kg/m³

Substitute these values into equation 4

Q = 0.001(2260000)(1000)

Q = 2260000 J

Answer:

[tex] \boxed{\sf Acceleration \ (a) = 5.7 \ m/s^2} [/tex]

Given:

Initial velocity (u) = 10 m/s

Final velocity (v) = 30 m/s

Time taken (t) = 3.5 seconds

To Find:

Acceleration (a) of the car

Explanation:

From equation of motion:

[tex] \boxed{ \bold{ v = u + at}}[/tex]

Substituting value of v, u & t in the equation:

[tex] \sf \implies 30 = 10 + a(3.5) \\ \\ \sf \implies 30 - 10 = 3.5a \\ \\ \sf \implies 20 = 3.5a \\ \\ \sf \implies 3.5a = 20 \\ \\ \sf \implies a = \frac{20}{3.5} \\ \\ \sf \implies a = 5.7 \: m/s^2[/tex]

[tex] \therefore[/tex]

Acceleration (a) of the car = 5.7 m/s²

A cyclist must lean into a turn to prevent tipping over in the other direction.The frictional force provides the centripetal force necessary to turn the cyclist to the left.But the frictional force also produces a clockwise torque that will cause the rider and the bicycle to tip clockwise to the right.The force is provided by the friction of the tires.

Answer:

to become stable

Explanation:

when it bends it body, it moves closer to the center of gravity which makes the bicycle stable and hence the turn can be taken easily

In each case, the larger unit is the one that represents a greater quantity or magnitude compared to the other unit. For example, a centimeter is larger than a millimeter because one centimeter is equal to 10 millimeters. Similarly, a megagram is larger than a kilogram as one megagram is equivalent to 1,000 kilograms. The pattern continues for each pair, where the larger unit represents a higher order of magnitude or a greater number of the smaller units.

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Answer:

Radio waves have longer wavelength

Explanation:

Radio wave is an electromagnetic frequency that has the ability to travel through long distance. They have frequencies shuttling been the range of 10^4 hz and a frequency of 10^12 hz

Light wave is also called visible light. This is because it is visible to the naked eye, despite it being in the electromagnetic spectrum. It's frequency is usually between 4*10^-7 hz and a frequency of 7*10^-7 hz.

As can be seen from both, the radio waves length are quite far stronger than that of the light waves.

Answer:

Explanation:

1) Any motion in which the acceleration is orthogonal to the direction of travel will have this characteristic:

  circular motion in a plane

  motion of a charged particle in a magnetic field perpendicular to the direction of travel

__

2) Motion in which the speed is constant, regardless:

  motion of a photon through a varying gravitational field

Answer:

Direction is downwards

Explanation:

This is by employing Flemings Right hand rule which says If you point your pointer finger in the direction the positive charge is moving, and then your middle finger in the direction of the magnetic field, your thumb points in the direction of the magnetic force pushing on the moving charge.