. a 750 kg automobile is moving at 20.0 m/s at a height of 5.0 m above the bottom of a hill when it runs out of gasoline. the car coasts down the hill and then continues coasting up the other side until it comes to rest. ignoring frictional forces and air resistance, what is the value of h, the highest position the car reaches above the bottom of the hill?

ΔU = q+w The system does work, which gives a negative value: -77kJ

The heat absorbed is q, which is 115J = 0.115kJ

Change of internal energy= 0.115kJ + (-77kJ) = -76.885kJ

Taking two sig figs: -77kJ

What is internal energy and an illustration?

The term "internal energy" describes the power contained in all of the chemical bonds that hold a system's molecules together as well as the kinetic energy of the molecules themselves. Every time heat, work, and internal energy interact, there is a transfer of energy and a conversion.

What makes it internal energy?

W. Thomson first used the word in thermodynamics in 1852. (the later Lord Kelvin). Because certain energy contributions are ignored, the adverb "internal" is used. For instance, the entire system possesses kinetic energy when it is moving uniformly.

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The average speed is 228.75 km/h.

Speed is the time rate at which an object is travelling along a route. To put it another way, velocity is a vector, whereas speed is a scalar value.

What is the speed-distance formula?

Speed is equal to distance traveled and time spent.

Distance is determined by multiplying the time and the speed.

Time is determined by speed and distance.

Given:

Distance = 30.5 kilometers

Time= 8 minutes

= 8/60 hour = 2/15 hour

Now, average speed equals distance / time.

= 30.5 x 15/2

= 228.75 Km/ h

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(a) Potential energy can be calculated using the formulae

[tex]P= mgh[/tex]

where,

[tex]m[/tex] is the mass of block

[tex]g[/tex] is acceleration due to gravity

[tex]h[/tex] is height

Therefore,

[tex]P= (100)(9.8)(5)[/tex]

[tex]P=4900[/tex]

(b) Kinetic Energy can be calculated using the formulae

[tex]\frac{1}{2} mv^{2}[/tex]

for this velocity ([tex]v[/tex]) can be calculated using

[tex]v=\sqrt{2gh}[/tex]

[tex]v=\sqrt{(2)(9.8)(5)}[/tex]

[tex]v=9.899[/tex]

now,

[tex]k=\frac{1}{2}mv^{2}[/tex]

[tex]k=-\frac{1}{2}(100)(9.8)^{2}[/tex]

[tex]k=-5000J[/tex]

(c) Velocity ([tex]v[/tex]) can be calculated using

[tex]v=\sqrt{2gh}[/tex]

[tex]v=\sqrt{(2)(9.8)(5)}[/tex]

[tex]v=9.899[/tex]

What is Potential energy?

Potential energy is a type of energy that results from a change in position or state.

What is kinetic energy?

The kinetic energy of something is the amount of work it can do due to its motion.

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The turntable's angular velocity, in rpm, just after this event is 39,72 rad/m

We can use the law of conservation of angular momentum.

Its a law that states the amount of momentum before and after producing is equal or constant collision.

The equation:

L₁ = L₂

I₁ x ω₁ = I₂ x ω₂

We have,

Mass of the table = 2.0 kg ⇒ m₁

Diameter of the table = 20 cm = 0.2 m ⇒ d, so R = 0.1

Angular speed = 140 rpm = 14.65 rad/s ⇒ ω₁

Mass of the blocks = 520 g = 0.52 kg ⇒ m₂

So,

I₁ x ω₁ = I₂ x ω₂

(½ mR²) ω₁ = (½ mR² + m₁R² + m₂R²)  ω₂

(½ (2.0) (0.1)² (14.65) = (½ (2.0) (0.1)² + (2.0) (0.1)² + (0.52) (0.1)²  ω₂

0.1465 = (0.01 + 0.02 + 0.02 + 0.0052) ω₂

ω₂ = 4.16 rad/s ⇒ 39,72 rad/m

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The number of independent directions in which movement is possible  dimension in the context of relative motion.

To discuss relative motion in one or more dimensions, the idea of reference frames was initially developed. When we refer to an object's velocity, we are referring to it in relation to the so-called reference frame. When measuring an object's velocity in daily life, the ground or the earth is assumed to be the reference frame.

As an illustration, if you are travelling in a train that is moving at 100 km/h, then from the perspective of another passenger in the train, you are moving at a speed of zero. He says you're standing still. However, if a bystander sees you standing on the ground outside the train, he claims that you are going with the train.

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250N is the friction force that keep body from sliding down the plane of inclination of 60 degrees.

Friction force is the force which resists the relative motion of the body or object in motion.

Solution:

Given :

Mass = 50kg

inclination = 60 degree

normal force acting on body =

F=mg

F=50*10

F=500N

Now the friction force which stops it from sliding is ;

Friction= FcosФ

Friction=500*cos 60

Friction=500*0.5

Friction=250N

Hence, 250N is the friction force that keep body from sliding down the plane of inclination of 60 degrees.

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According to the special theory of relativity, all laws of nature are the same in all uniformly moving reference frames. Option B.

Einstein's Special Theory of Relativity states that the same laws of physics apply to all inertial frames of reference and that the speed of light is the same for all observers. The basic laws of physics are the same for all inertial frames of reference.

Because otherwise, we wouldn't call it a fundamental law. Call them contingency laws and look for deeper fundamental laws that are invariant under a larger set of symmetries. Describes the propagation of matter and light at high speed. It is based on the constancy of the speed of light and the relativity principle in all inertial frames of reference.

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The potential energy of the spring when it is stretched 0.900 mm is 228 J. The potential energy when it is compressed is 2.88J.

Hooke's law states that the elongation of a material is proportional to the applied stress within the elastic limits of the material.

Using Hooke's law

F = kx

570 = k * 0.9

k = 712.5 N/m

(a) energy at x = 0.8 m

U = 0.5 k x^2 = 0.5* 712.8* 0.8^2

U = 228 J

(b) U = 0.5 * 712.8* 0.09^2

U = 2.887 J

Elastic potential energy is the potential energy released as a result of the deformation of an elastic body. B. Spring extension is stored. This is equal to the work done to stretch the spring, which depends on the spring constant k and the stretched distance. The force exerted by the spring is the restoring force that helps return the spring to its equilibrium length.

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The frequency of simple pendulum will become 1/√2 times of original frequency  if length of simple pendulum is doubled.

We know that frequency of simple pendulum is given by the formula

=>f=(1/2π)×√g/√l

where f is the frequency of simple pendulum,

l is the length of simple pendulum

and g is the acceleration due to gravity

We can see that frequency is directly proportional to length of pendulum and inversely proportional of acceleration due to gravity. Since value of  acceleration due to gravity  remains same on observations, therefore only factor where frequency gets changed when length of simple pendulum gets changed. 1/2π is constant value, it does not affected on changing the length of simple pendulum.

So, if we double the length of simple pendulum, new frequency will become

New Frequency=(1/2π) × (√g / √2l)

=>New Frequency=(1/√2)×[(1/2π×√g/√l)]

=>New Frequency=(1/√2)f.

Hence, new frequency will become 1/√2 times of original frequency.

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13.7 × [tex]10^{8}[/tex], the approximate number of capillaries in the human body, that are carrying blood from the aorta.

What is Aorta?

A huge, cane-shaped blood channel called the aorta carries oxygen-rich blood to your body. It travels across the chest and belly after beginning in the lower left corner of the heart. Blood arteries leave the aorta along the way and extend to the organs and supporting tissue.

What are the Calculations?

The speed of the blood in the aorta is  v = 35cm/s

the radius of the aorta is r = 1.1 cm

the area of the cross-section of the aorta is A =π[tex](1.1cm^{2} )[/tex]

the speed of the blood in  the capillary v ' = 0.078 cm/s

radius of the capillary is r = 6.3 × [tex]10^{-4}[/tex]cm

Now area of cross-section of capillary is A' = Π[tex](6.3 * 10^{-4}) ^{2}[/tex]

Let  there be N number of capillaries

The volume rate of flow in the aorta is the total sum of the volume rate of flows in the capillaries.

Then  Av  = N*A' *v'

    Π(1.1cm)² (35 cm/s)   = N * (Π[tex](6.3 * 10^{-4}) ^{2}[/tex])* 0.078 cm/s

N = 13.7 × [tex]10^{8}[/tex]

Hence, 13.7 × [tex]10^{8}[/tex], the approximate number of capillaries in the human body, that are carrying blood from the aorta.

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The net work required is equal to (1/2)mr^2 x 1/8 x 360 = 90mr^2.

What is work?
Work in physics is the energy that is transmitted to or from a object when a force is applied along a displacement. In its simplest form, it equals this same product of a force's magnitude and the distance travelled for a constant force directed in the same direction as the motion. When a force is applied, it is said to have a component that moves the point of application, or it is said to have positive work. If the component of a force at the point of application is in the opposite direction of the displacement, the force is said to do negative work.

The net work required to accelerate a solid cylinder from rest to a rotation rate of 1 revolution per 8.00 s is equal to the torque multiplied by the angle of rotation. Since the angle of rotation is 360 degrees, the net work required is equal to the torque multiplied by 360 degrees.

The torque is equal to the moment of inertia of the cylinder multiplied by its angular acceleration. The moment of inertia of a solid cylinder is equal to (1/2)mr^2, where m is the mass of the cylinder and r is its radius. The angular acceleration is equal to the change in angular velocity divided by the time interval. In this case, the angular velocity is 1 revolution per 8.00 seconds, so the angular acceleration is 1/8 rad/s^2.

Therefore, the net work required is equal to (1/2)mr^2 x 1/8 x 360 = 90mr^2.

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Position of the mass as a function of time is:

x(t) = 0.3829cos(12.247×t +58.511∘) m

When a mass m is connected to a spring of spring constant k the system executes a simple harmonic motion with angular frequency ω =

[tex]\sqrt{k/m[/tex]

The location of the mass at any given time t is given by

x(t) = A cos (ωt+Ф)

Where Ф = Initial phase

A = amplitude

solving our question:

mass of block m = 2 kg

spring constant k = 300 n/m

At t = 0, the velocity of the block v(0) = -4.00m/s

displacement x(0) = -0.200 m

angular frequency w = [tex]\sqrt{k/m[/tex] = 300/2 = 12.247 [tex]radian^{-1[/tex]

So, position of the mass at time t is written as

x(t) = A cos ( 12.247×t+Ф)

     0.2 = A cosФ

and v(t) = -12.247×A×sin(12.247 t +Ф)

-4 = -12.247 A sinФ

A sinФ = 0.3266

squaring and adding the two equations

[tex]A^{2}[/tex] = [tex]0.3266^{2}[/tex] + [tex]0.2^{2}[/tex]

and cosФ = 0.2/0.3829

Ф = 58.511

Therefor position of the mass is

x(t) = 0.3829cos(12.247×t +58.511∘) m

The given question is incomplete, the complete question is

A 2.00-kg, frictionless block is attached to an ideal spring with force constant 300 N/m. At t = 0, the block has velocity -4.00 m/s and displacement +0.200 m. Write an equation for the position as a function of time.

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The approximate distance to this new cluster is 1 billion light-years.

What is a Galaxy Cluster?

A galaxy cluster, also known as a cluster of galaxies, is a formation made up of a large number of gravitationally connected galaxies, typically with masses between 1014 and 1015 solar masses. Before superclusters were found in the 1980s, they were thought to be the largest known structures in the universe and are now the second-largest known gravitationally bound structures in the cosmos after galaxy filaments.

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The approximate distance to this new cluster is 1 billion light-years.

What is a Galaxy Cluster?

A galaxy cluster, also known as a cluster of galaxies, is a formation made up of a large number of gravitationally connected galaxies, typically with masses between 1014 and 1015 solar masses. Before superclusters were found in the 1980s, they were thought to be the largest known structures in the universe and are now the second-largest known gravitationally bound structures in the cosmos after galaxy filaments.

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3.3×10⁻²⁰ electrons must be added to the nail to make it electrically neutral.

Although heavier atoms typically have more neutrons than protons, there are always the same number of electrons in an atom as there are protons. As a result, an atom is electrically neutral overall. An atom becomes positively charged when one or more of its electrons are taken away.

An atom has no overall charge when it is electrically neutral, which is defined as this. Positively charged particles called protons, negatively charged particles called electrons, and non-charged particles called neutrons make up atoms.

q = ne

q = 1.6×10⁻¹⁹

e = 4.8μc

n = ?

1.6×10⁻¹⁹ = ne

n = 1.6×10⁻¹⁹ /4.8

n = 3.3×10⁻²⁰.

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(D) Since both conservative and non-conservative forces are involved, so the sum of all of them will be conserved. The kinetic energy, potential energy and thermal energy all together is conserved in the system.

What is Kinetic energy?

A moving object or particle has kinetic energy, which depends on both its mass and its rate of motion. The type of motion can be vibration, rotation on an axis, translation (or travel along a path from one place to another), or any combination of these.

What is Thermal energy?

Heat is the transfer of thermal energy, whereas thermal energy is the entire internal energy of a system's temperature.

Hence, the kinetic energy, potential energy and thermal energy all together is conserved in the system.

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If the pebble on the board do not want to lose contact with one another, so the maximum acceleration would be equal, rather would be equal to four pies square times the frequency squared times the amplitude and this has to be less than G.

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Answer:

Explanation:

A. The bird flew real far and fast.

"far" and "fast" describe the type of motion.

Nearsightedness affects Berenice, Chadwick, and Edouard.The near point, or minimum distance at which an object can be seen clearly with the unaided eye, is 25 cm.The greatest distance at which an object can be seen clearly with the unaided eye is called the far point. Diverging lenses, which create virtual images at the user's far point when presented with things at infinity, can be used to treat nearsightedness.

The sort order for words and letters is A through Z.Most frequently, an alphanumeric sort is used for data including both numbers and letters and words, such as address lines. This means that Z to A is sorted first, then 9-0, before any further operations.

The distance is explained.The distance between any two points along a line or line segment.

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The force exerted by the rockets is 62,325 N.

The force exerted by the rockets is determined by applying Newton's second law of motion.

According to Newton's second law of motion, the force exerted by an ob ject is directly proportional to the product of mass and acceleration of the object.

F(net) = ma

where;

F - Ff = ma

where;

F - 450 = (1375 x 45)

F = 61,875 + 450

F = 62,325 N

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Answer:

Energy of nth orbit of H-atom, E

n

=−

n

2

13.6

eV

∴ ΔE=E

5

−E

1

=−13.6(

5

2

1

−

1

2

1

) eV

∴ ΔE=13.6×

25

24

=13.056 eV

Answer:

Explanation:

Given:

Q = 2277 J

A = 508 J

__________

ΔU - ?

ΔU = Q - A

ΔU = 2277 - 208 = 2069 J

The period of the vibration is 3.9ms

The period (T) of a vibration is the time to complete one oscillation or revolution and is measured in seconds. The period of vibration is given as

T= 1/F

For example, if the period of a vibration is 0.1 second (one vibration takes 0.1 second), then the frequency of the vibration is 1/0.1=10 vibrations per second or 10 hertz.

Similarly if the frequency of a vibration is 256hz, the period T= 1/F= 1/256=0.0039s

1second= 1×10³ms

therefore 0.0039s = 0.0039×10³= 3.9ms

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Since. The frictionless incline and uniform height "h" at which all the blocks are released. Therefore, the total energy at the bottom of the incline will be equal to the initial potential energy (PEi = mgh). - In line with energy conservation.

Kinetic energy is the power that an object has as a result of motion. If we want to accelerate an object, we have to exert force. Applying force requires effort on our part. When the project is complete, the item will be moving at a new, constant speed because energy has been transferred to it.

In other words, the amount of work done is equal to how much the object's K.E. has changed! This is the relationship between Kinetic energy and Work Done, or the Work-Energy Theorem. In other words, the change in an object's kinetic energy represents the work done on it. W = Δ(K.E.).

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The total internal reflection is the complete reflection of a ray of light within a medium such as water or glass from the surrounding surfaces back into the medium. The phenomenon occurs if the angle of incidence is greater than a certain limiting angle, called the critical angle.

This is an internal total reflection exercise, the equation that describes this process is

        sin θ = n₂ / n₁

where n₂ is the index of the incident medium and n₁ the other medium must be met n₁> n₂

       θ = sin⁻¹ n₂ / n₁

let's calculate

      30⁰ = sin⁻¹ (n₂ / n₁)

Therefore, if the angle is greater then the totally internal reflection also increases.

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The new mAs should be a half of 20mAs, which is 10mAs.

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The mass-to-light ratio will be [tex]\frac{M_{\omega D}}{L_{\omega D}}=4.6 \times 10^6 \mathrm{~kg}/ watt[/tex]

As per the data given in the question,

We have,

Mass of white dwarf [tex]$M_{\omega_D}=0.8 M_{\text {sun }}$[/tex] where [tex]$M_{\text {sun }}$[/tex] is the mass of the Sun

We have, Luminosity of the white dwarf [tex]$$L_{\omega_D}=0.001 L_{\text {sun }} .$$[/tex] ,where [tex]$L_{\text {sun }}$[/tex] is the Luminosity of the Sun.

Calculating Mass to light Ratio =M/L

Mass to light Ratio for Sun, [tex]\frac{M_{\text {sun }}}{L_{\text {sun }}}=\frac{1.989 \times 10^{30} \mathrm{~kg}}{3.867 \times 10^{26} \text { watts. }}[/tex]

[tex]\frac{M_{\text {sun }}}{L_{\text {sun }}}=Y_0 \approx 5133 \mathrm{~kg} / \text { watt }[/tex]

Hence,

[tex]\frac{M_{w D}}{L_{w D}}=\frac{0.9 M_{\text {sim }}}{0.001 L_{\text {sun }}}=900 \frac{M_{\text {sun }}}{L_{\text {sun }}}\\\\\therefore \frac{M_{\omega D}}{L_{\omega D}}=900 Y_{\odot}[/tex]

[tex]\frac{M_{\text {wD }}}{L_{\text {sun }}} & =900 \times(5133) \mathrm{kg} / \text { watt } \\\\=4.6 \times 10^6 \mathrm{~kg} / \text { watt. }[/tex]

Therefore, [tex]\frac{M_{\omega D}}{L_{\omega D}}=900 Y_0=4.6 \times 10^6 \mathrm{~kg}/ watt[/tex]

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38 Bright fringes will be seen in the central diffraction maximum when a two-slit Fraunhofer interference-diffraction pattern is observed.

Diffraction is when waves such as light or sound spread as they travel around an object or through a slit.

In case of diffraction , angular width of central maxima = 2 λ/d

λ is wave length of light  = 660 nm

d is slit width = 0.01 mm

In case of interference , angular width of each fringe = λ /D

D is distance between two slits = 0.19 mm

Number of interference fringe in central diffraction fringe can be calculated by the formula

=2 λ/d x D/λ

= 2 x D /d = 2 x .19/0.01

= 38

38 bright fringes will be seen in the central diffraction maximum.

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Since the distance from the source point is always finite, light beams are never precisely parallel in reality. So, theoretically, we may refer to two rays as being parallel if their spacing is near to zero and their distance traveled is about infinite.

What is a light beam and give an example?

Three types of light beams are possible. Both convergent and divergent, they are parallel. A parallel Light Beam is created when the rays from a distant point source move in the same direction alongside one another. An illustration of a parallel beam of light is the sun Ray.

What materials make up light beams?

Many photons in the same condition make up coherent beams, including laser and radar beams. A light beam's photon count is more of a measurement of its brightness than of its breadth.

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Counterclockwise, Because north pole of magnet is moving towards loop and emf is induced in counterclockwise. b) Clockwise; Because north pole of magnet is moving away from the loop and flux is decreasing through loop so clockwise emf is induced.

Anything that creates a magnetic field is considered to be a magnet. The most noteworthy characteristic of a magnet—a force that pulls on other ferromagnetic elements like iron, steel, nickel, cobalt, etc.—is caused by this invisible magnetic field, which also attracts or repels other magnets.

A piece of equipment built from a substance that has been magnetized and produces a consistent magnetic field is called a permanent magnet. A typical illustration is a fridge magnet used to keep notes on the door of the refrigerator. Ferromagnetic materials are those that are both capable of magnetization and are attracted to magnets strongly (or ferrimagnetic).

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The wavelength of light will be  5.17 x10⁻⁷ m

Since we are given the angle of  15.0, and transmission grating having 5000 slits/cm, for a normal incidence

since we know the diffraction of first-order formula is :

d sineθ =nλ ,and the separation os the slits are : d= 1/N

=>d=1/ 5000  = 2x 10^-6 m

Now subsituing the value of d in the main formula of diffraction, where we get the wavelength of :

λ = dsine θ/ n

since here n is 1

λ=  2x 10 *sine 15.0/ 1

λ = 2x 10^-6 *0.2588   = 5.17 x10⁻⁷ m

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