suppose two cards, one twice as massive as the other, fly apart when compressed, spring that joins them is released. how fast does the heavier car roll compared with the lighter card

When solar energy is transmitted straight backward from a surface, reflection takes place. Albedo is the portion (or percentage) of radiation that is reflected back.

As more solar energy is received, more heat is reflected back into space, raising the temperature of the atmosphere. The Earth system does not become hotter as a result of solar radiation that Earth's surface or atmosphere reflect back into space. Heat is produced as a result of absorbed radiation. Only a small portion of the energy that reaches the Earth's surface is reflected. Around 30% of the incoming radiation is reflected back to space and does not heat the surface, leaving the remaining 70% to be absorbed by the atmosphere and the Earth's surface.

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Here we have to calculate horizontal distance and vertical displacement of a ball thrown at a particular angle and a particular speed.

How to calculate horizontal distance and vertical displacement？

The ball is thrown at an angle, θ=30o.

Initial velocity of the ball, u=15 m/s

Horizontal range of the ball, R=12.3 m

We know that, R=u cosθ t,

where t is the time of flight

⟹t=53​17.3​=2 secs

using equation of motion we get:-

−h=ut−1/2gt²

=15×2−1/2×9.8×2²=−10.4

⟹ Height at which the ball reaches, h=10.4 m

The vertical distance fallen during each consecutive second will increase. (i.e., there is a vertical acceleration).

The vertical displacement follows the equation above (y = 0.5 • g • t2).

Furthermore, since there is no horizontal acceleration, the horizontal distance traveled by the projectile each second is a constant value -

Formula for horizontal distance is

x= vix × t=20 m/s

Thus, the initial horizontal velocity of 20 m/s. Thus, the horizontal displacement is 20 m at 1 second, 40 meters at 2 seconds, 60 meters at 3 seconds, etc. We can tabulate it as shown in the attachment.

TIME HORIZONTAL DISPLACEMENT

0 s          0 m

1 s          30 m

2 s          60 m

3 s          90 m

4 s          120m

5 s           150 m

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Answer:

Heat in = 715 K

Heat out = 250 K

Heat converted to work = 715 - 250 = 465 K

Efficiency = 465 / 715 = .65

(a)    Maximum efficiency = 65%

The shortest possible distance through which the force must be applied must be 0.83 meters.

What is force?
A force is indeed an influence that can alter an object's motion according to physics. A force may cause an object to mass to accelerate when it changes its velocity, such as when it moves away from rest. An intuitive way to describe force is as a push or even a pull. A force is a vector quantity because it has both magnitude and direction. It is calculated using the newton SI unit (N). Force is denoted by the letter F. (formerly P). The net force acting on an object seems to be equal to the speed that its momentum changes over time, according to Newton's second law in its original formulation.

The shortest possible distance through which the force must be applied for each meter that the object is raised is 0.83 meters.
This is because the force needed to lift the object is 25 N,
and the mass of the object is 30 kg (30 x 9.8 = 294 N).
Therefore, the amount of work done for each meter of lifting is 25 N x 0.83 m = 20.75 Joules (J).
This means that each meter of lifting requires 20.75 J of work, and therefore the shortest possible distance through which the force must be applied must be 0.83 meters.

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The displacement and the distance traveled by the particle during the time interval  [-2, 5] are -26.83 units and 27.17 units.

Displacement is the straight path between the initial and end positions, whereas distance traveled is the actual length the body covers.

Here, the velocity is given as v(t)=(-t²)+3t-2 and the interval is [-2, 5]. By integrating the given velocity function, we will get the total distance traveled and displacement within the given interval.

The displacement is given as follows,

[tex]\begin{aligned}\int\limits^5_{-2} v(t)dt&=\int\limits^5_{-2} ((-t^2)+3t-2)dt\\&=\left[\frac{-t^3}{3}+\frac{3t^2}{2}-2t\right]^5_{-2}\\&=\left(\frac{5^3}{3}+\frac{3(5)^2}{2}-2(5)\right)-\left(-\frac{(-2)^3}{2}-2(-2)\right)\\&=-\frac{85}{6}-\left(\frac{38}{3}\right)\\&=-\frac{161}{6}\\&=-\mathrm{26.83\;units}\end{aligned}[/tex]

The total distance traveled is given by,

[tex]\begin{aligned}\int\limits^a_b|v(t)|dt&=\int\limits^5_{-2}|(-t^2)+3t-2|dt\\&=\int\limits^1_{-2}(t^2-3t+2)dt+\int\limits^2_1(-t^2-3t+2)dt+\int\limits^5_2(t^2-3t+2)dt\\&=\left[\frac{t^3}{3}-\frac{3t^2}{2}+2t\right]^1_{-2}+\left[-\frac{t^3}{3}+\frac{3t^2}{2}-2t\right]^2_{1}+\left[\frac{t^3}{3}-\frac{3t^2}{2}+2t\right]^5_2\\&=\frac{27}{2}+\frac{1}{6}+\frac{27}{2}\\&=\frac{163}{6}\\&=\mathrm{27.17\;units}\end{aligned}[/tex]

Therefore, the displacement and distance traveled are calculated using the given time interval.

The complete question is -

The velocity function is v(t)=(-t²)+3t-2  for a particle moving along a line. Find the displacement and the distance traveled by the particle during the time interval [-2, 5].

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The force exerted on the motorcycle of mass 500 kg is 2272.72 N.

Force can be calculated by multiplying the mass of a body to its acceleration. The S.I Unit of force is Newton (N).

To calculate the force exerted on the motorcycle, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the force acting on the motorcycle is 2272.72 N.

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For a long straight wire carrying conductor the magnitude of the magnetic field produced around it  is proportional to I/r, and the direction is out of the page at P.

A magnetic field is produced by moving charges. Charges are constantly moving in a conductor carrying current; as a result, magnetic fields are created all around the conductor.

The right-hand thumb rule indicates the direction of this magnetic field. The thumb of the right hand is used in this rule to indicate the current's direction. The direction of the magnetic field surrounding the wire is indicated by the curled fingers.

The magnitude of the magnetic field produced by the current carrying conductor depends on the following factors:

The magnitude of the current flowing through the conductor

The distance to the point where the field value is calculating.

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At maximal displacement, the speed is zero, the kinetic energy is zero, and the only source of energy is the potential energy held in the spring. E = 1/2 kA² is the energy at the greatest distance.

The process of any variable or measure fluctuating repeatedly about its equilibrium value in time is known as oscillation. A periodic change in a substance's quality between discrete choices or around its central value is another way to describe oscillation.

Here, A represents the oscillation's amplitude.

Dropping the sandbag won't change the system's overall energy since all of the energy is derived from the energy stored of spring.

Therefore, the amplitude won't be affected.

The square of oscillation's intensity determines the system's energy in an exact correlation. The energy in the system remains constant, hence the oscillation's amplitude does not vary.

Hint:

Utilize the energy at balance to ascertain whether the maximum speed for dropping the sandbag at the cart's maximal changes in any way.

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The maximum speed of the piston  is  8.6 m/s  and the maximum force acting on the piston when the engine is running at 3 800 rpm is   7 486 N

The given information is that the motion of a piston in an auto engine is simple harmonic. if the piston travels back and forth (side to side) over a distance of 12 cm, and the piston has a mass of 1.5 kg, The maximum speed of the piston is determined by the equation for the simple harmonic motion:

v = (2πfA)^0.5  where f is the frequency of the motion (in this case, 3 800 rpm), and A is the maximum displacement (in this case, 12 cm).  

v = (2π(3800)(0.12))^0.5   v = 8.6 m/s.

The maximum force acting on the piston is determined by the equation for the simple harmonic motion:  

F = mω^2A, where m is the mass of the piston (in this case, 1.5 kg), ω is the angular velocity (in this case, 2πf = 2π(3800) = 23 883 rad/s) and A is the maximum displacement (in this case, 12 cm).  

F = (1.5)(23 883)^2(0.12)   F = 7 486 N

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Assuming the cd is a uniform solid disk, Then the net torque acting on it is τ≈7.4×10⁻⁴ N

The product of an object's moment of inertia and angular acceleration is the torque operating on that item. We must know the CD player's moment of inertia and angular acceleration in order to calculate the torque operating on it.

Angular Acceleration:

α=ω2−ω1/t

α=22 rad/s²−0/0.91

α=24.17582rad/s²

Momemt of inertia:

I=1/2mr²

I=1/2(17×10⁻³ kg)(6.0×10⁻²m)²

I=0.0000306 kg.m²

Now, Torque:

τ=Iα

τ=(0.0000306)(24.17582)

τ=0.000739780092 kg⋅m²/s2

τ≈7.4×10⁻⁴ N

Therefore,  Torque≈7.4×10⁻⁴ N

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Loma saw greatest 24-hour temperature fluctuation on January 15, 1972. Temperature rose by an equal 103 degrees from -54 degrees to 49 degrees. This sets global standard for a 24-hour changes in temperature.

The distance here between kelvin (K), a component of kelvin scale, and then a degree on the Temperature scale depends on where zero lies. This melting point seems to be the zero point upon that Celsius scale, whereas absolute zero is really the zero point upon that Kelvin scale. Accordingly, 0oK is equal to -273.15oC and 0oC is equivalent to 273.15 kelvins.

The freezing point, boiling point, or any combo of water and a chemical were all taken into consideration when the Celsius and Fahrenheit scales were developed. Scientists adopted the Absolute temperature scale because they desired a scale where 0 depicts the total lack of thermal energy.

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The oscillating and regular motion of an object is known as the SHM. The object must move 0.532 meters from x(t) = 0.65 meters to x(t) = A = 1.182 meters.

It is a periodic and oscillating movement that moves in a rectilinear fashion.

Knowing that there will always be a restoring force (F) that tends to return the motion to its initial location when it moves an amount called an amplitude is important when thinking about simple harmonic motion.

There are some important factors to take into account with this motion,

The movement's position, X (m), in its initial, equilibrium, and other positions.

The speed is a (m/s2).

Speed, V (m/s)

The volume, A (m)

The periodicity, w (rad/s),

The distance that the object needs to move from x(t) = 0.65m to x(t) = A = 1.182m is 0.532m.

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if 4 different amplitudes are used, the numbers of bits that can be transmitted with each amplitude change is 2 bits.

Distance between the wave's resting position and its highest displacement is known as amplitude. Frequency is the quantity of waves that pass by a particular place each second.

The distance between the center line (or the still position) and the top or bottom of a wave's crest or trough is known as the amplitude (). Be cautious when using this amount because a diagram may not always show the center line. Meters are used to measure amplitude ( ).

For example:

If there is 4 amplitudes, it will be: 00,01,10,11 then  2 bits

If there is 8 frequencies it will be: 000,001,010,011 ,100,101,110, 111 and then  3 bits

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See full question below

With Amplitude Shift Keying (ASK), if 4 different amplitudes are used, how many bits can be transmitted with each amplitude change?

The resultant force will be f/2. This means that the resultant force is half of the original repulsive force between the two charged particles.

According to B, the electrical force between two charged objects is inversely proportional to the square of the separation distance between the two objects and directly proportional to the product of the charges on the objects.

Mathematical expression of Coulomb's law:

[tex]F=\frac{kQ_{1}Q_{2} }{d^{2} }[/tex]

Here,

F = Electrical force

Q1 = Charge on the first object (in Coulombs)

Q2 = Charge on the second object (in Coulombs)

d = Distance between the two objects (in meters)

k = A proportionality constant (Coulomb's law constant)

According to the problem given, the force would double if one of the charges were doubled. The force would be four times lower if the distance were doubled. These two variations working together would result in a two-fold reduction in force thus resulting into f/2.

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If the moon were five times more distant from earth than it is now, the gravitational force would decrease.

                                   [tex]F= G\frac{M_{1}M_{2}}{R^{2} }[/tex]

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The elastic potential energy in the spring at this elongation is 45J.

What is elastic potential energy?

The energy that is stored when a force is used to deform an elastic object is known as elastic potential energy. Until the force is released and the item bounces back to its original shape, doing labor in the process, the energy is retained. The item may be compressed, stretched, or twisted during the deformation.

To solve this problem we need to use the equations related to Elastic Potential Energy, which allows us to know the Energy stored in a spring based on its elastic constant and its respective compression. By definition it is described as

[tex]P E=\frac{1}{2} k x^2[/tex]

Where,

k = Spring constant

x = Displacement

Our values are given as

[tex]x_1=0.08 \mathrm{~m}[/tex]

As we do not know the spring constant but if the energy stored at the compression given then,

[tex]\begin{aligned}& P E=\frac{1}{2} k x^2 \\& 20=\frac{1}{2} k(0.08)^2 \\& k=6250 \mathrm{~N} / \mathrm{m}\end{aligned}[/tex]

In the case of the second compression and understanding that the spring constant is intrinsic to the internal force of the spring, then

[tex]x_2=0.12 m$$[/tex]

Replacing,

[tex]$$\begin{aligned}& P E=\frac{1}{2}(6250)(0.12)^2 \\& P E=45 . J\end{aligned}$$[/tex]

Therefore the elastic potential energy in the spring at this elongation is 45J.

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If a  0.6 kg squirrel falling at 14 m/s hits a pile of leaves and comes to rest in 2 s , the normal force of the leaves on the squirrel as it comes to rest would be 4.2 Newtons.

What is Newton's second law?

Newton's Second Law states that The resultant force acting on an object is proportional to the rate of change of momentum.

As given in the problem a 0.6 kg squirrel falling at 14 m/s hits in a pile of leaves and comes to rest in 2 s.

The change in the moment of the squirrel = 0.6 × 14

=8.4  Kg - m/s

The normal force = rate of the change of the momentum

                            = 8.4 / 2

                            = 4.2 Newtons

Thus,  the normal force of the leaves on the squirrel as it comes to rest would be 4.2 Newtons.

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0.84 m is the distance the painter walk before the plank starts to fall.

Torque is a measure of the force that rotates an object about an axis. A force accelerates an object with linear kinematics. Similarly, torque causes angular acceleration. Therefore, torque can be defined as the rotational equivalent of a linear force. The straight line around which an object rotates is called the axis of rotation. In physics, torque is simply the tendency of a force to twist or twist. Various terms such as moment and moment of force are used interchangeably to describe torque. The distance from the point of force application to the axis of rotation is sometimes called the moment arm or lever arm.

Mass of the painter (m₁) = 79 kg

Weight of painter (w₁) = 79 × 9.8

= 774.2 N

Mass of bucket (m₂) = 74 kg

Weight of bucket (w₂) = 23 × 9.8

= 225.4 N

Distance between them (L) = 2.9 m

Let d be the distance at which the painter can walk before the plank starts to fall.

At distance d, the torque due to painter and bucket is equal to each other:    

T₁ = T₂

w₁d = w₂L

d = (w₂L)/w₁

d = (225.4 × 2.9)/774.2

d = 0.84 m

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In an PNP transistor, the base controls the amount of current passing through it while allowing current flow from the base to the emitter.

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The galaxy with a hydrogen beta absorption of 496 nm then the galaxy's distance from us in mega-light years (mly) will be equal to 277.54 Mly.

The distance between two identical locations (adjacent crests) in successive cycles is known as the wavelength, and it is used to describe waveform signals that are transmitted over wires or into space. Typically, in wireless systems, this length is specified in meters (m), centimeters (cm), or millimeters (mm).

As per the given information in the question,

The line's hydrogen laboratory wavelength, λ = 486.1 nm

The galaxy's spectrum's wavelength, λ' = 496.0 nm

Then, the change in wavelength,

Δλ = λ' - λ

Δλ = 9.9 nm

The speed of light, c = 2.998 × 10⁵ km/s

Use the equation of Doppler's effect,

v = c × Δλ/λ

v = 6,105.75 km/s

So, the radial velocity will be 6105.78 km/s.

v = H₀d

Here, v is the velocity of the galaxy, d is the distance between galaxies and H₀ is Hubble's constant.

d = v/H₀

d = 6105.75/22

d = 277.54 Mly

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The energy (in Joules) of a single photon of blue light =  [tex]4.83 * 10^-^1^9 J[/tex]

What is the energy of photon?

The energy that a single photon carries is known as photon energy. Energy is inversely correlated with electromagnetic frequency of the photon.

The energy of a photon is given by the formula

E = h*v

where,

h = planks constant

v = frequency

Given,

h =  [tex]6.626 * 10^-^3^4 J s[/tex]

v = 7.30 × [tex]10^1^4[/tex] Hz

1 Hz = 1 [tex]s^-1[/tex]

v = 7.30 × [tex]10^1^4 s^-1[/tex]

E = [tex]6.626 * 10^-34 * 7.30 * 10^1^4[/tex]

E = [tex]48.36 *10^-^2^0 J[/tex]

E = [tex]4.83 * 10-19 J[/tex]

The energy (in Joules) of a single photon of blue light = [tex]4.83 * 10^-^1^9 J[/tex]

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Maximum normal stress and the maximum shearing stress in the tank are 60MPa and 18.277 MPa respectively.

Define hoop stress

A "hoop stress" is a stress distribution that maintains its original shape while the stressed item is rotated around a fixed axis. Any force exerted on the cylindrical pipe wall by a pressure differential in a straight, closed pipe will eventually result in hoop stresses.

According to the definition, shearing stress is "a kind of stress that acts parallel to the cross section of the material." Shear forces result in shear stress. They are a pair of forces that have the same magnitude and are directed in the opposite direction and operate on opposite sides of a body. A vector quantity is shear stress.

Given Data

Diameter: d = 180mm

Wall Thickness: t = 12mm

Torque: T = 12kN.m

Pressure in cylinder: p = 8MPa

Inner Radius ,c1  = d/2

                      c1  = 180/2

                      c1 = 90*10^-3 m

Outer radius, c2  = c1+ t

                      c2 = 90+12

                       c2 = 102*10^-3m

Polar moment of inertia ,J is 3.14/2*(c2^4- c1^4)

                        J ≈66.968×10^-6 m^4

The maximum torsional shear stress,  τ= Tc/J

                       τ=18.277MPa

​The normal stress due to pressure, σ1 = pr/t

                        σ1 = 60MPa

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The first quarter moon rises in the East. Option (c) is the right answer.

The first quarter moon occurs halfway between the new moon and the full moon. One-quarter of the moon is visible from Earth, meaning that you see half the daylit side of the moon.

Just like the Sun and the nighttime stars, the Moon's apparent rising in the east and set in the west each day is not from the Moon's orbit around the Earth, it's from the Earth spinning. The lunar orbit is slower and harder to see but you can still spot it.

The moon rises in the east and sets in the west, every day. It has to. The rising and setting of all celestial objects are due to Earth's continuous daily spin beneath the sky.

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The fraction of the person submerged when floating gently on the freshwater is 0.973.

The average density of the human body = 973 kg/m³.

According to the Archimedes' principle, when a body floats in a fluid it experience is an upward force on it which is called buoyancy the buoyancy on an object is equal to the weight of the fluid that is displaced by the body.

If a body floats than the buoyancy must be equal to the weight of the body.

therefore buoyancy B can be given as

B = Vρg

V is the volume of the body,

ρ is the density of the body.

Also

B = V'xg

V' is the portion of the body submerged in fresh water,

x is the density of the fresh water.

Density of fresh water is 1000kg/m³.

Equating both the equations of 'B'

Vρ = V'x

ρ/x = V'/V

V'/V = 973/1000

So, the fraction of the human body submerged in freshwater is 0.973.

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Additional Saving in power is 1.48mw.

As a result of primary action, power dissipation is the process by which power is lost as heat. The process of power dissipation happens naturally. The power will be dissipated by each resistor in the circuit that has a voltage drop across it.

Since Pdyn = fc v²oo is proportional to v²oo reducing power supply

from 5v to 3v reduces the power dissipation by a factor of

(3.3)²/5² = 0.436

The power dissipation now become 0.436×10×10⁻³ = 436×10⁻³ = 4.36mw.

Since Pdyn is proportional to reducing f by the some factor as the supply voltage 3.3/5 = 0.66results in reducing the power dissipation

further by factor of 0.66

Additional Saving in power = (1.0.66) X(4.36 × 10⁻³ )

Additional Saving in power = 1.48mw.

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Answer:

C. Artificial Resevoirs

Explanation:

For two main reasons; the first is the capacity of water of water they contain, and the second one is for mainteinance purpouse.

The eye piece focal length is    fe = -0.19 m   where,   fe= focal length of eye ,

What Is Focal Length? Focal length is the distance (measured in millimeters) between the point of convergence of your lens and the sensor or film recording the image. The focal length of your film or digital camera lens dictates how much of the scene your camera will be able to capture.

Briefing :  According to the question we assume ,

let  The focal length is  F(o) =5.5 mm = -.00055m and distance between objective and eyepiece = 19 cm

This negative sign shows the the microscope is diverging light

 The  angular magnification is m=250

  The  distance between the objective and the eyepieces lenses is  z=19cm=0.19m

Generally the magnification is mathematically represented as

m={z-fe/fe}{0.25/f(o)}

Where fe is the eyepiece focal length of the microscope

 Now  making fe the subject  of the formula,

fe=z/{(1-1{M-fo)/0.25}

then : fe=0.19/([tex]1-(\frac{250+ - 0.0055}{.25} )[/tex])}

=   fe = -0.19 m

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Complete Question : The distance between the objective and eyepiece lenses in a microscope is 19 cm . The objective lens has a focal length of 5.5 mm .What eyepiece focal length will give the microscope an overall angular magnification of 250?

(a) The work done is 1.50 x 10^-6 J

(b) The potential of the starting point with respect to the endpoint is 357.14 V.

(c) The magnitude of E is 5952.38 N/C.

Given that,

Charge = 4.20 nC

Distance = 6.00 cm

Kinetic energy K.E = 1.50 x 10^-6 J

The particle start from rest. So, the initial kinetic energy i zero.

(A) We need to calculate the work by the electric force

Using formula of work done

W = ∆K.E

W = K.Ef - K.Ei

Put the value into the formula

W = 1.50 × 10^-6 - 0

W = 1.50 x 10^-6 J

The work done is 1.50 x 10^-6 J

(B). We need to calculate the potential of the starting point with respect to the endpoint

We know that.

Change in potential energy = change in kinetic energy

∆P.E = ∆K.E

So, U = 1.50 x 10^-6

Using formula of potential

V = U/q

Put the value into the formula

V = 1.50 × 10^-6/4.20 x 10^-9

V = 357.14 V

The potential of the starting point with respect to the endpoint is 357.14 V

(C) We need to calculate the magnitude of E

Using formula of work done

W = F x r (1)

Using formula of force

F = qE

Put the value in the equation (1)

W = qE x r

E = W/q x r

Put the value into the formula

E = 1.50 x 10^-6/4.20 x 10^-9 x 6.00 x10^-2

E = 5952.38 N/C

Hence, The magnitude of E is

5952.38 N/C

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After collision velocity of yellow ball become 3 m/s.

What is collision velocity?

Collision is short-duration interaction between two bodies or more than two bodies simultaneously causing change in motion of bodies involved due to internal forces acted between them during this. Collisions involve forces (there is a change in velocity).

Velocity of red ball = 3 m/s

Velocity of yellow ball = -2m/s

Red ball and yellow ball both have same mass

So, after head on collision their velocity will be exchanged.

So after collision velocity of yellow ball become 3 m/s.

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