A stone is dropped from the upper observation deck (the Space Deck) of the CN Tower, 450m above the ground.
a) Find position function s(t) of the stone above the ground level at time t. Assume g=9.8 m/s2.
b) How long does it take the stone to reach the ground?
c) What is the impact velocity of the stone when it hits the ground? d) If the stone is thrown downward with a speed of 5m/s. How long does it take to reach the g

The reaction is the force applied by the player's glove on the ball.

Newton's third law of motion states that when one body exerts a force on the other body, the first body experiences a force which is equal in magnitude in the opposite direction of the force which is exerted”.

The statement means that in every interaction, there is a pair of forces acting on the two interacting objects. The size of the forces on the first object equals the size of the force on the second object.

The direction of the force on the first object is opposite to the direction of the force on the second object.

According to this question, a player catches a ball. The action is the force to the ball against the player's glove while the reaction or opposite force will be the player's glove against the ball.

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The value of speed will be 21.67 m/s

It is given that,

Mass of the car = m=1200 kg

Radius of the round road = r=87.0 m,

Coefficient of static friction= 0.55

As we know,

The value of friction can be determined by using the relationship:

Friction = mCfg

Where, Cf = centripetal force, which can be calculated by relationship:

centripetal force = mv^2/r

As we know,

The point at which the speed is maximum

Then,

Ff = Fc

So, we can write it as:

[tex]mC_fg = \frac{mv^2}{r}\\v^2=\frac{rmC_fg}{m}\\v={\sqrt{C_fgr}[/tex]

So, the value of speed will be:

[tex]v = \sqrt{0.55 \times 9.81 \times 87)}\\v = 21.6658 \approx 21.67\: m/s[/tex]

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Answer:

An object must be in motion

Explanation:

In order for an object to have kinetic energey it must be moving. However, if it has potential energy, it hasn't started moving yet, but it has the potential to move.

If the two objects are brought into thermal contact, object B gives up more heat and changes its temperature more than object A. The heat released by one object is absorbed by the other, and the temperature change of each is the same because the specific heats are the same.

When two objects with different temperatures come into contact with one another, energy moves from the hotter (higher temperature) object to the cooler (lower temperature) object until both objects reach the same temperature.

The thermal energy of the object increases as the average kinetic energy of its constituent particles rises. Therefore, as an object's temperature rises, so does its thermal energy.

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a weight of mass 1.09 kg is suspended by a string wrapped around a pulley wheel, which consists of a solid disk of mass 4.22 kg and radius 1.04 m. the system is released from rest. vertical distance does the hanging mass move in 3.0 seconds is 18.27 m

distance can be calculate as follows:

Suspended mass, m = 1.09 kg

Pulley mass, M=4.22 kg

pulley radius, r = 1.04 m

now,

Let's put some tension on the "T" string

For this,

vertical net force

mg - T = ma …………(1)

Where,

g is the gravitational acceleration

a is the acceleration of the suspended mass.

Pulley torque = Iα

I is the moment of inertia of the pulley

α is the angular acceleration

Pulley torque is due to string movement

therefore,

Torque = T x r

Also

α = a/r

and I = (Mr²/2) (for circular discs)

Substituting the values ​​of the above relationship for torque, we get

T × r = (Mr²/2) × (a/r)

T = (Ma)/2 …………(2)

from 1 and 2

mg - [(Ma)/2] = ra

mg= a(M + r)

          2

(1.09x9.8) =  a( 4.22 + 1.04)

                         2

a= 4.06

now we know that

s= ut+1/2 at²

where s is the distance traveled

u is the initial velocity = 0 (in this case)

t is time = 3 seconds

So if you replace the value

s= (0x3)+ 1/2 4.06 (3)²

s = 18.27 m

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Because Einstein could neither see or accept the cosmos expanding or contracting, he added a component to his equations that prevented the universe from changing.

Even the existence of matter in the cosmos is unknown to us. The early cosmos should have created an equal amount of mass and positron, which would subsequently destroy one another, according to modern physics theories.

Yet modern physicists will be the first to recognize they are not in possession of all the solutions. Dr. Daniel Whiteson, a physicist at the University of California and a co-author of the new book, claims that "there are fundamental facts about the world that we're ignorant of."

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Because Einstein could neither see or accept the cosmos expanding or contracting, he added a component to his equations that prevented the universe from changing.

Even the existence of matter in the cosmos is unknown to us. The early cosmos should have created an equal amount of mass and positron, which would subsequently destroy one another, according to modern physics theories.

Yet modern physicists will be the first to recognize they are not in possession of all the solutions. Dr. Daniel Whiteson, a physicist at the University of California and a co-author of the new book, claims that "there are fundamental facts about the world that we're ignorant of."

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The average emf induced in his wedding ring, given its diameter is 2.20 cm and assuming it takes 0.250 s to move it into the field is 3mV.

What is magnetic field?

The magnetic impact on moving electric charges, electric currents, and magnetic materials is described by a magnetic field, which is a vector field. A force perpendicular to the charge's own velocity and the magnetic field acts on it while the charge is travelling through a magnetic field.

Given:

[tex]- $B=2 T$[/tex] is the magnetic field strength

[tex]- $d=2.2 \mathrm{~cm}=0.022 \mathrm{~m}$[/tex] is the ring diameter

[tex]- $t=0.25 \mathrm{~s}$[/tex] is the time needed to move the ring

(a) The electromotive force (emf) can be calculated using Faraday's law as:

[tex]$$\epsilon=-\frac{d \phi}{d t}$$[/tex]

We can expand the magnetic flux term here:

[tex]$$\epsilon=-\frac{d}{d t}[B A]$$[/tex]

The magnetic field here is constant so it is the area that is changing:

[tex]$$\epsilon=-B\left(\frac{d A}{d t}\right)$$[/tex]

Since we have no actual functions and just the initial area exposed to the magnetic field (zero) and the final area (entire ring area), we can re-write this as:

[tex]$$\epsilon=-B\left(\frac{0-\pi r^2}{t}\right)$$[/tex]

We substitute and recall that the radius is half the diameter:

[tex]$$\epsilon=-(2 T)\left(\frac{0-\pi\left(\frac{0.022 \mathrm{~m}}{2}\right)^2}{0.25 \mathrm{~s}}\right)$$[/tex]

We thus get:

[tex]$$\epsilon=0.003 \mathrm{~V} \approx 3 \mathrm{mV}$$[/tex]

(b) Wedding rings are usually made of metals like gold or silver, which means they are conducting. This means that the resistance of a wedding ring should be low. So here if we use Ohm's law:

[tex]$\epsilon=I R$[/tex]

We can assume that the current is also small here since the emf is fairly small and the resistance is expected to be small. With a small current, the temperature of the wedding ring shouldn't change much.

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Complete Question:

Two slits spaced 0.260 mm apart are placed 0.700 m from a screen and illuminated by coherent light with a wavelength of 660 nm. The intensity at the center of the central maximum ( = 0°) is [tex]I_{0}[/tex].

What is the distance on the screen from the center of the central maximum to the point where the intensity has fallen to [tex]I_{0}/2[/tex]

The distance on the screen from the center of the central maximum 0.44 mm where the intensity has fallen to [tex]I_{0}/2[/tex]

The two slits are separated by 0.260 mm.

The screen's distance from the slits is 0.700 meters.

The coherent light has a wavelength of 660 nm.

The value of the path difference will equal to [tex]\pi /2[/tex]  because the intensity has decreased to [tex]I_{0}/2[/tex].

This path difference's above formula can be expressed as,

[tex]y_{n} = \frac{(2n-1)D\alpha }{2d}[/tex]

D is the distance of the screen to the slits.

[tex]\alpha[/tex] is the wavelength of the light

d is the distance between slits.

The intensity at the center of the central maximum is [tex]I_{0}[/tex]

Now,

[tex]y = \frac{(2*1)D}{d} *\frac{\alpha }{2\pi } *\frac{\pi }{2}[/tex]

Putting all the values in the formula, we get:

y = 0.44 m

Thus, the distance on the screen from the center of the central maximum 0.44 mm.

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If the sun mysteriously gets twice as massive as it is right now, it's gravitational pull on Mars will be twice as much.

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The torque of rope F = 500 N * 3 m * sin(30 degrees) = 800 Nm.

What is torque?
Torque seems to be the rotational equivalent of force in physics and mechanics. Depending on the area of study, it is also known as that of the moment, instant of force, rotational force, or turning effect. It illustrates how a force can cause a change in the body's rotational motion. In his famous adage, "Give me a lever as well as a place to stand, and I'll move the Earth," Archimedes, who studied the use of levers, is credited with developing the idea. A torque could be thought as a twist to the an object around a particular axis, similar to how a linear force is indeed a push or a pull.

The torque of rope F is equal to the product of the force (F) and the lever arm (r). The lever arm is equal to the length of the rope multiplied by the sine of the angle between the rope and the axis of rotation.

Therefore, the torque of rope F = F * r = F * (length of rope) * sin(angle between rope and axis of rotation).

For example, if F = 500 N, the length of the rope = 3 m, and the angle between the rope and the axis of rotation is 30 degrees, then the torque of rope F = 500 N * 3 m * sin(30 degrees) = 800 Nm.

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The percentage by mass of the salt, given it was dissolved in 500 g of water is 9.09%

we'll begin by obtaining the mass of the solution. This is shown below:

Mass of solution = Mass of salt + Mass of water

Mass of solution = 50 + 500

Mass of solution = 550 grams

Finally, we shall determine the percentage of the salt. Details below:

Percentage = (mass of solute / mass of solution) × 100

Percentage of salt = (50 / 550) × 100

Percentage of salt = 9.09%

Thus, the percentage of the salt is 9.09%

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The gravitational acceleration symbol is G. The standard value of the g is 9.8 m/s2 at sea level.

The magnitude of g, or Earth's gravitational acceleration, is 9.8 m/s2. The acceleration of a free falling object on Earth would be 9.8 meters per second, according to this. This acceleration is due to the Earth's gravitational pull.

The acceleration that every thing experiences as it moves toward or away from the earth is due to gravity, and the average acceleration is the same for all objects. The object's mass has no bearing on i.

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-37.03 dB is the intensity level of the sound for the more distant listener relative to that for the nearer listener.

What is intensity level?

The intensity level of a sound, in decibels, is described as 10 times the logarithm to the base 10 of the ratio of the intensity of this sound to a reference intensity.

By using the inverse square law,

As one listener is 71.1 times farther away from the source of the sound than the other.

Then Increasing the distance by 71.1 times reduces the intensity by

(71.1)^2 = 5055.21

The intensity level of the sound (in decibels) for the more distant listener relative to that for the nearer listener is:

= 10log(ratio of intensities)

= 10log(1/5055.21)

= 10log(0.00019782)

=10 × -3.7028

= -37.03 dB (The negative sign represents the sound is less intense for the farther listener)

So, the intensity level of the sound (in decibels) for the more distant listener relative to that for the nearer listener is -37.03 dB.

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R=60cm We determine that Dina's upright picture is produced as she steps back from the mirror, which is spherical with a concave f=30 cm. Thus, the mirror is spherical but concave and the image of the object is

A form with an inward curvature is said to be concave. Concave shapes include those like the sideview window of a car, which curls inward. When a shape curves outward, it is said to be convex. One excellent example of a convex form is the outward-curving (American) football.

One that veers inward at a single point is said to have a concave shape. A polygon with a sharp inside angle or a curved form with an inwardly curving part can both fit the bill. When a line connects two points inside a shape and leaves the shape at an angle, the shape is said to be concave.

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If the distance between two charged particles is doubled, the force between them changes by a factor of 1/4.

What is force?

A force is an effect that can alter an object's motion according to physics. An object with mass can change its velocity, or accelerate, as a result of a force. An obvious way to describe force is as a push or a pull. A force is a vector quantity since it has both magnitude and direction.

Force between two charge particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

Therefore, if the distance between two charged particles is doubled, the force between them changes by a factor of 1/4.

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Answer:

a. radiation

b. convention

c. conduction

Explanation:

The correct diagram is option F where GRAVITY arrow pointed to the right.

A planet's gravitational influence on a moon is felt. The moon is dragged into a slightly extended shape because the near side of the moon experiences a stronger pull than the far side. We have ocean tides because the moon has a similar differential attraction on the Earth.

This specific instance of tidal locking was brought on by the gravitational pull of the Moon and Earth (called synchronous rotation).

The Earth takes 365 1/4 days, or one year, to complete one orbit of the Sun. The Moon revolves around the Earth as it revolves around the Sun. The orbit of the Moon lasts 27 1/2 days.

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The vertical speed is 29.4 m/s.

What is vertical speed?

In aeronautics, the rate of climb is an aircraft's vertical speed, that is the positive or negative rate of altitude change with respect to time. In most ICAO member countries, even in otherwise metric countries, this is usually expressed in feet per minute; elsewhere, it is commonly expressed in meters per second.

The acceleration of gravity is 9.8 m/s².  This simply means that when anything falls, its downward speed keeps increasing, and it falls 9.8 m/s faster every second than it fell 1 second earlier.

After 3 seconds of falling, the object is falling at (3 x 9.8 m/s) = 29.4 m/s faster than at the beginning of the 3 seconds.  If it had no vertical speed at the beginning of the 3 seconds, then THAT's its speed after 3 seconds . . . . . 29.4 m/s downward.

As far as being thrown horizontally off the cliff . . . that has no effect on its vertical speed. Horizontally, it doesn't matter whether it rolls gently over the edge, or somebody throws it horizontally, or it gets shot horizontally out of a high power rifle.  It hits the ground at the same time and at the same speed in every case.

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The speed of the three couple car after the collision is 1.8 m/s and the total loss in kinetic energy of the system during the collision is 2.16 x 10⁴ J.

The mass M of the each railroad car is given to be 2 x 10³ kg and the speed U of the each railroad car is 3m/s. The speed V of the coupled car is given to be 1.20 m/s.

(a) According to the law Conservation of Linear Momentum, the linear momentum before and after the collision is always conserved.

So, we can write here,

MU + 2MV = (M+2M)V'

Where,

V' is the speed after collision.

U + 2V = 3V'

V' = (U+2V)/3

V' = (3+2.4)/3

V' = 1.8m/s.

(b) The loss in kinetic energy of the system can be calculated as,

∆K = final kinetic energy - initial kinetic energy

∆K = (1/2MU²+1/2×2MV²) - 1/2 × 3MV'²

Putting values,

∆K = (0.5×2.00×10⁴×(3.00)2+0.5×2(2.00×10⁴)(1.20)2)−0.5×3(2.00×10⁴)(1.8)2

∆K = 2.16 x 10⁴ J.

So, the loss in kinetic energy of the system after the collision is 2.16x10⁴ J.

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The frequency of wave generated is [tex]6.9 * 10^{14} Hz[/tex].

The electromagnetic wave travels at the speed of light.

Speed of light (c) = [tex]3 * 10^{8} m/s[/tex]

Given wavelength is 435nm = [tex]435 * 10^{-9} m[/tex]

We can find the frequency(f) of the wave by using the relationship between f and c:

Frequency = speed of light/ wavelength

                  = [tex]3 * 10^{8} / 435 * 10^{-9}[/tex]

                  = [tex]6.9 * 10^{14} Hz[/tex]

So the frequency of wave generated is [tex]6.9 * 10^{14} Hz[/tex].

Complete question:

An electromagnetic wave of wavelength 435nm is traveling in vacuum in the − z-direction. The electric field has amplitude 2. 70×10−3v/m and is parallel to the x-axis. Find frequency of wave generated.

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Highest to Lowest temperature:

Mercury

Earth

Mars

Jupiter

Neptune

What is average surface temperature?

Planetary surface temperatures range from over 400°C on Mercury and Venus to below -200°C on distant planets. The factors that determine temperature are the complex balance of heat received and lost.

For these five planets, temperature correlates with distance from the Sun. The closer to the sun, the hotter the earth. Note, however, that this is not always the case, as the planet's temperature also depends on its reflectance and the strength of the greenhouse effect (if present). For example, although Venus is almost twice as far from the Sun, the average temperature on Venus is higher than on Mercury due to the greenhouse effect.

Therefore, the temperature on each planet is according to the composition of that planet and the surrounding atmospheric gases.

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In the case of the gearbox as the system, the outer surface temperature is 297 K, and the rate of entropy formation is 2.3*10-3kW.A surface's temperature is its ambient temperature.

More specifically, it can be talking about: Surface temperature, the temperature of the air at the earth's Surface temperature. A state of disorder, randomness, or uncertainty are frequently associated with the scientific notion of entropy, which is also a quantifiable physical attribute. Since work is produced by ordered molecular motion, entropy also serves as a proxy for a system's molecular disorder or unpredictability.

Q = ha(Ta-Tb) (Ta-Tb)

Q = (0.171)((1.0)(347k) (347k)

Q = 2.3*10^-3kW

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The earth’s oceans is not fusing hydrogen into helium, transforming our planet into a star because Protons (hydrogen nuclei) carry positive electric charge and thus repel each other.

The third planet from the sun, Earth is the only place in the known universe confirmed to host life and has a radius of 3,959 miles, Earth is the fifth largest planet in our solar system, and it is the only one known for sure to have liquid water on its surface.

In order for two protons to come close enough to each other that the nuclear force that has short range can bind them, they must be moving at very high speeds.

This is only possible at temperatures in the solar core, but it is very hard to achieve these temperatures on Earth, thus the reason why fusion power has been so difficult to develop.

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Nyquist rate = 2*(maximum signal frequency)

Sampling rate must exceed Nyquist rate in order to be able to fully reconstruct the signal.

a) x(t) = 1 + cos (2000πt) + sin(4000πt)

Frequency for each term:-

Term 1 is DC -> w₁ = 0

Term 2 -> w₂ = 2000π

Term 3 -> w₃ = 4000π

Maximum signal frequency (wm) =  4000π

Another way of saying this is that X(jw) = 0 for |w| > 4000π

Acc to Sampling theorem ws > 2wm, ws>8000π

So, the Nyquist rate is 8000π

b) x(t) = sin(4000πt) / πt

Using Fourier Transport table, we have X(jw) = 1 for |w| < 4000π

.0 for |w| > 4000π

Therefore, maximum signal frequency (wm) = 4000π

Acc to the sampling theorem ws > 2wm, ws > 8000π

c) x(t) = {sin(4000πt) / πt}²

We can rewrite the above function as x(t) = x₁(t) x₁(t), where,

x₁(t) = sin(4000πt) / πt

Using the convolution property X(jw) = (1/2π)X₁(jw) * X₁(jw)

We know that convolving a signal with itself will double the maximum frequency therefore:

Therefore, maximum signal frequency (wm) = 8000π

Acc to the sampling theorem ws > 2wm, ws > 16000π

Therefore, the frequency to determine the Nyquist rate is 16000π.

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The object can move as farther as 0.2m.

Using the Sine Equation,

= x(t) = Asin(ωt)

=Here, t=0, x=0,

Given that,

Distance = x(t) = 0.60 = A sin(ωt)

Velocity = v(t) = 2.20 m/s = Aωcos(ωt)

Acceleration = a(t) = 8.40 m/s² = -Aω²sin(ωt)

Using wave equation,

= x(t) / a(t) = A sin(ωt) / -Aω²sin(ωt)

= ω² = 14 rad²/s²

= ω = 3.74 rad/s

The amplitude of the motion =

=  x(t) / v(t) = A sin(ωt) / Aωcos(ωt)

= A = 0.2 m

Therefore, the amplitude of the motion is 0.2 m

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The magnitude of the force of friction between the crate and the floor is calculated to be  5 N.

Force generated by two surfaces that contact and slide against each other is referred to as frictional force.

Given: A force of 10 N towards right is exerted on a wooden crate initially moving to the right on horizontal wooden floor and weight of crate is 25 N

The magnitude of the force of friction between the crate and the floor is given as ;

F= μ* m * g

=  0.2 * 25

= 5N

The magnitude of the force of friction between the crate and the floor is 5 N.

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The heat exchangers, evaporator and condenser, which are where the most irreversibilities are seen, are the most important parts of the VCR system.

The evaporator operates in opposition to the condenser; here, refrigerant liquid is transformed into gas while absorbing heat from compartment's air. The pressure of the liquid refrigerant has decreased by the time it reaches the evaporator, losing its heat content thus causing it to become significantly colder than the fan air circulating around it.

Condenser coils discharge heat into outdoor air while evaporator coils absorb heat from indoor air. When heated refrigerant vapor cycles into the coil and condenses to liquid, it quickly releases the load of heat energy that has been collected from your home and compacted in it.

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The rate that the water level would first decrease if it is not refilled is 1.06 mm/min.

water volume (plural water levels) the height at which a water body is measured, particularly when done beyond a datum line. the height of the underground water table. the ship's waterline. a device that uses the water's surface on a trough or in vertical tubes connected by the a pipe to indicate level.

The accuracy of water levels is theoretically limited only by human vision. The length of the tube and the thickness of the liquid are two significant problems that can impair accuracy.

h = height of the water level above the hole = 1 m

dh = diameter of hole = 4 mm = 0.004 m

Ah = Area of cross-section of hole = (0.25)\pi d^{2}  (for hole)

dt = diameter of tank = 2 m

At = Area of cross-section of tank =  (0.25)\pi d^{2}  (for tank)

R = rate at which the water level drop

Rate at which the water level drop is given as

R=[Ah(\sqrt{2gh)]/At

R= [ (0.25)\pi d^{2}(\sqrt{2gh) ] /2^{2}

R=17.7*(10)^-6 m/s

R=0.0177mm/s

R=(0.0177)(60) mm/min.

R=1.06 mm/min.

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The initial speed of the cart is  1.3m/s.

The velocity of an object is the rate of change of its position with respect to a given time interval.

Given

Mass m of the cart  = 12kg

Spring constant =290 N/m.

The compressed length of the spring  = 10 cm.

The initial kinetic energy of the cart is given below.

    K.E. = 1/2 m v2

    v =  initial velocity of the cart.

When the cart hits the spring, it is compressed by the cart. When the cart stops, due to the maximum compression, the kinetic energy of the cart will be zero. Hence its kinetic energy will be converted into elastic potential energy of the spring. This is given as,

U = 1/2 kx²

k = spring constant

x = compressed length of the spring.

This elastic potential energy of the spring will be equal to the initial kinetic energy of the cart.

U = 1/2 * 290*(0.80)² = 0.64.

U = 64J.

Elastic potential energy of the spring will be equal to the initial kinetic energy of the cart.

64 = (1/2) * 80 * v²

128 = 80 * v²

v² = 128/ 80

v² = 1.6

v = 1.26 ≅ 1.3

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The buoyant force that supports him in the sea water of density is 3931.613N.

On the water's surface, a swimmer is lying on his back. if his volume is 0.060 m, and his density is 980 kg/m³.

When an object floats, a force called buoyancy is responsible for this. It is specifically the external force that an object that is partially or completely submerged in water or any other fluid experiences. A body or object is said to be buoyant when it is placed in or submerged in a fluid.

We can also define buoyancy as the upward force applied by the fluid on a body or object in this way. The pressure on two sides of a body submerged in a static fluid causes the buoyancy phenomenon.

The Buoyant Force is measured in Newtons (N), which is also the unit of Force (F).

F=hpg

h=∛0.060

=0.3914m

F=0.3914 x 1025 x 9.8

F=3931.613N

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