A 0.140-kg glider is moving to the right with a speed of 0.80 m/s on a frictionless, horizontal air track. The glider has a head-on collision with a 0.299-kg glider that is moving to the left with a speed of 2.28 m/s. Find the final velocity (magnitude and direction) of each glider if the collision is elastic.

Answer:

a)TE=0.0245 J

b)A = 0.0128 m

c)V=0.57 m/s

Explanation:

Given that

m = 0.150 kg

K= 300 N/m

x= 0.012 ,v= 0.2 m/s

The velocity of the toy at any point given as

[tex]v=\omega\sqrt{A^2-x^2}[/tex]

[tex]\omega=\sqrt{\dfrac{K}{m}}[/tex]

[tex]v=\sqrt{\dfrac{K}{m}}\times \sqrt{A^2-x^2}[/tex]

[tex]0.2=\sqrt{\dfrac{300}{0.15}}\times \sqrt{A^2-0.012^2}[/tex]

2 x 10⁻⁵ = A² - 0.000144

A=0.0128 m

Amplitude ,A = 0.0128 m

The total energy TE

[tex]TE=\dfrac{1}{2}KA^2[/tex]

[tex]TE=\dfrac{1}{2}300\times 0.0128^2[/tex]

TE=0.0245 J

The maximum speed

[tex]V=\omega A[/tex]

[tex]V=\sqrt{\dfrac{K}{m}}\times A[/tex]

[tex]V=\sqrt{\dfrac{300}{0.15}}\times 0.0128[/tex]

V=0.57 m/s

(a) The total energy of the toy is 0.0246 J (b) The amplitude of its motion is 0.0128 m (c) The maximum speed it can attain is 0.573 m/s.

To solve the given problem involving a toy undergoing simple harmonic motion (SHM) on a horizontal spring, let's go step-by-step:

(a) The total energy (E) in SHM is the sum of kinetic energy (KE) and potential energy (PE) at any point.

Given the mass (m) is 0.150 kg, spring constant (k) is 300.0 N/m, displacement (x) is 0.0120 m, and speed (v) is 0.200 m/s, we calculate:

Kinetic Energy: [tex]KE = (\frac{1}{2})mv^2 = (\frac{1}{2})(0.150 kg)(0.200 m/s)^2[/tex] = 0.003 J

Potential Energy:[tex]PE = (\frac{1}{2})kx^2 = (\frac{1}{2})(300.0 N/m)(0.0120 m)^2[/tex] = 0.0216 J

Total Energy: E = KE + PE = 0.003 J + 0.0216 J = 0.0246 J

Amplitude: The total energy in SHM is also equal to the potential energy at maximum displacement (amplitude A). Therefore, using [tex]E = (\frac{1}{2})kA^2[/tex], we solve for A:

[tex]0.0246 J = (\frac{1}{2})(300.0 N/m)A^2[/tex]

[tex]A^2 = (\frac{0.0246 J}{150 N/m}) = 0.000164 m^2[/tex]

[tex]A = \sqrt{0.000164 m^2} = 0.0128 m[/tex]

(b) Maximum Speed: The maximum speed (vm)) occurs at the equilibrium position.

Using [tex]E = (\frac{1}{2})mv^2_m[/tex], we solve for vm:

[tex]0.0246 J = (\frac{1}{2})(0.150 kg)v^2_max[/tex]

[tex]v^2_m = (\frac{0.0246 J}{0.075 kg}) = 0.328 m^2/s^2[/tex]

[tex]v_m = \sqrt{0.328 m^2/s^2} = 0.573 m/s[/tex]

Therefore, the total energy of the system is 0.0246 J, the amplitude of oscillation is 0.0128 m, and the maximum speed is 0.573 m/s.

Answer:

Power, P = 560 W

Explanation:

Given that,

Weight of the student, F = 700 N

Distance, d = 8 m

Time taken, t = 10 s

To find,

The average power expended by the student.

Solution,

Let P is the power. The work done per unit time is called its power. It is given by :

[tex]P=\dfrac{W}{t}[/tex]

[tex]P=\dfrac{F\times d}{t}[/tex]

[tex]P=\dfrac{700\ N\times 8\ m}{10\ s}[/tex]

P = 560 W

So, the  average power expended by the student to overcome gravity is most nearly 5670 watts.

The average power expended by the  student to overcome gravity =

( 5.) P = 560 W

The formula for Power is given by the equation (1)  

[tex]Power = \dfrac{Work}{Time}[/tex]...........(1)

Also the formula for Work is given by equation (2)

[tex]Work = Force \times Distance[/tex]............(2)

(Considering magnitude of Displacement)

From equation (1) and (2) we can get

[tex]Power = \dfrac{Force \times Distance}{Time}[/tex].......(3)

Also   [tex]Speed= \dfrac{ Distance}{Time}[/tex]....(4)

From equation (2) , (3) and (4)

So [tex]Power= Force \times Speed[/tex]

Given

Weight of the Student = 700 N

Height of the rope  = 8 m

Time taken  to climb the rope = 10 s.

So from equation (3)  we can get

Average Power expended by the student to overcome gravity = (700)[tex]\times[/tex] (8)/(10) = 560 W.

Hence option 5 is correct.

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Answer:

infinity

Explanation:

Given that

Resistance = R

Resistivity = ρ

Length = L

Diameter = d

The resistance of wire R given as

[tex]R=\rho\dfrac{L}{A}[/tex]

A=Area

[tex]A=\dfrac{\pi d^2}{4}[/tex]

Now by putting the value of A

[tex]R=\rho\dfrac{L}{\dfrac{\pi d^2}{4}}[/tex]

[tex]R=\rho\dfrac{4L}{\pi d^2}[/tex]

When d tends to infinity then d² will also tends to infinity.

So when d tends to zero then the resistance tends to infinity.

Therefore answer is ---

infinity

Answer:

d

Explanation:

The flux of F through the curved surface of the cylinder is [tex]\( 18\pi \).[/tex]  

The flux of the vector field F = xi + yj + zk  through the curved surface of the cylinder [tex]\( x^2 + y^2 = 9 \),[/tex] bounded below by the plane [tex]\( x + y + z = 2 \)[/tex] and above by the plane [tex]\( x + y + z = 4 \),[/tex] and oriented away from the z-axis can be calculated using the surface integral formula.

The flux [tex]\( \Phi \)[/tex]is given by:

[tex]\[ \Phi = \iint_S \mathbf{F} \cdot d\mathbf{S} \][/tex]

Where [tex]\( d\mathbf{S} \)[/tex] is the outward-pointing normal vector to the surface [tex]\( S \).[/tex]

First, let's parameterize the surface. Since the cylinder is described by [tex]\( x^2 + y^2 = 9 \)[/tex], we can use cylindrical coordinates:

[tex]\[ x = 3\cos \theta \]\[ y = 3\sin \theta \]\[ z = z \][/tex]

The normal vector [tex]\( d\mathbf{S} \)[/tex] can be calculated using the cross product of the partial derivatives of [tex]\( \mathbf{r}(\theta, z) = (3\cos \theta, 3\sin \theta, z) \)[/tex] with respect to [tex]\( \theta \) and \( z \):[/tex]

[tex]\[ \frac{\partial \mathbf{r}}{\partial \theta} = (-3\sin \theta, 3\cos \theta, 0) \]\[ \frac{\partial \mathbf{r}}{\partial z} = (0, 0, 1) \][/tex]

Taking the cross product:

[tex]\[ d\mathbf{S} = \left| \frac{\partial \mathbf{r}}{\partial \theta} \times \frac{\partial \mathbf{r}}{\partial z} \right| d\theta dz = 3 \, d\theta dz \][/tex]

Now, calculate F.ds:

[tex]\[ \mathbf{F} \cdot d\mathbf{S} = (3\cos \theta, 3\sin \theta, z) \cdot (0, 0, 3) = 3z \, d\theta dz \][/tex]

The bounds of integration for [tex]\( \theta \) are \( 0 \) to \( 2\pi \)[/tex] since we want to cover the entire curved surface of the cylinder. For [tex]\( z \),[/tex] the bounds are from [tex]\( 2 \) to \( 4 \)[/tex] since the surface is bounded below by [tex]\( x + y + z = 2 \)[/tex] and above by [tex]\( x + y + z = 4 \).[/tex]

Now integrate:

[tex]\[ \Phi = \int_0^{2\pi} \int_2^4 3z \, dz \, d\theta \]\[ \Phi = \int_0^{2\pi} \left[ \frac{3}{2}z^2 \right]_{z=2}^{z=4} \, d\theta \]\[ \Phi = \int_0^{2\pi} \frac{3}{2} \cdot 12 \, d\theta \]\[ \Phi = 18\pi \][/tex]

So, the flux of F through the curved surface of the cylinder is [tex]\( 18\pi \).[/tex]

Complete Question:
Compute the flux of F⃗ =xi⃗ +yj⃗ +zk⃗ through just the curved surface of the cylinder x2+y2=9 bounded below by the plane x+y+z=2, above by the plane x+y+z=4, and oriented away from the z-axis

The answer involves comparing the centripetal force exerted by the turntable on the coin to the static and kinetic friction forces that resist the coin's motion.

The situation involves a coin on a turntable where rotation is causing a force. The physics principles at play here are centripetal force and the forces of static and kinetic friction. The centripetal force needed to keep the coin rotating can be calculated using the equation F = mrω², where m is the mass of the coin, r is the distance from the coin to the center of the rotation, and ω is the angular speed of the rotation.

The static friction force is what keeps the coin from sliding as the turntable speeds up. Static friction can be calculated using the equation fs = µsmg, where µs is the coefficient of static friction, m is the mass, and g is acceleration due to gravity. If the force of static friction is less than the centripetal force, the coin will start to slide, and kinetic friction will come into play. Kinetic friction can be calculated with f = µkmg.

By calculating these forces, we can compare and determine if the centrifugal force from the turntable's acceleration would overcome the friction between the coin and the turntable, causing the coin to slide off.

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Answer:

[tex]P = 444[/tex] mm of Hg

Explanation:

As we know that volume is constant so by ideal gas equation we have

[tex]PV = nRT[/tex]

now for constant volume condition we have

[tex]\frac{P_1}{P_2} = \frac{T_1}{T_2}[/tex]

here we know that

[tex]P_1 = 325[/tex] mm of Hg

[tex]T_1 = 273 K[/tex]

[tex]T_2 = 373 K[/tex]

now from above equation

[tex]\frac{325}{P} = \frac{273}{373}[/tex]

[tex]P = 444[/tex] mm of Hg

Final answer:

In Physics, using the properties of a constant-volume gas thermometer, the pressure at the normal boiling point of water can be calculated knowing the pressure at the triple point, by using the direct proportionality between pressure and temperature for an ideal gas.

Explanation:

The subject of this question is Physics, specifically relating to the topic of thermodynamics and how temperature affects the pressure of gases at constant volume. The gas in question is mercury, and its pressure readings at two significant points are being discussed: the triple point and the normal boiling point of water. According to the information provided, the thermometer registers a pressure of 325 mm of mercury at the triple point of water.

The relation between pressure and temperature for an ideal gas, which forms the basis for a constant-volume gas thermometer, implies that at a constant volume, the pressure is directly proportional to the temperature in Kelvin. When considering the normal boiling point, one must remember that it is defined at the atmospheric pressure of 760 mm Hg. Since the triple point is 273.16 K and has a given pressure of 325 mm Hg, the pressure at the boiling point of 373.16 K (the normal boiling point of water) can be found using the direct proportionality of pressure and temperature.

Assuming ideal behavior, the pressure at the boiling point can be calculated using

Pboiling = (PTP \/ TTP) \ imes Tboiling

Where PTP is the pressure at the triple point, TTP is the temperature at the triple point, and Tboiling is the temperature at the normal boiling point.

The pressure at the normal boiling point is therefore:

Pboiling = (325 mm Hg \/ 273.16 K) \ imes 373.16 K

By doing the calculation, we find the pressure that the constant-volume gas thermometer will read at the boiling point.

Answer: 1010.92 m/s

Explanation:

According to Newton's law of universal gravitation:

[tex]F=G\frac{Mm}{r^{2}}[/tex] (1)

Where:

[tex]F[/tex] is the gravitational force between Earth and Moon

[tex]G=6.674(10)^{-11}\frac{m^{3}}{kgs^{2}}[/tex] is the Gravitational Constant

[tex]M=5.972(10)^{24} kg[/tex] is the mass of the Earth

[tex]m=7.349(10)^{22} kg[/tex] is the mass of the Moon

[tex]r=3.9(10)^{8} m[/tex] is the distance between the Earth and Moon

Asuming the orbit of the Moon around the Earth a circular orbit, the Earth exercts a centripetal force on the moon, which is equal to [tex]F[/tex]:

[tex]F=m.a_{C}[/tex] (2)

Where [tex]a_{C}[/tex] is the centripetal acceleration given by:

[tex]a_{C}=\frac{V^{2}}{r}[/tex] (3)

Being [tex]V[/tex] the orbital velocity of the moon

Making (1)=(2):

[tex]m.a_{C}=G\frac{Mm}{r^{2}}[/tex] (4)

Simplifying:

[tex]a_{C}=G\frac{M}{r^{2}}[/tex] (5)

Making (5)=(3):

[tex]\frac{V^{2}}{r}=G\frac{M}{r^{2}}[/tex] (6)

Finding [tex]V[/tex]:

[tex]V=\sqrt{\frac{GM}{r}}[/tex] (7)

[tex]V=\sqrt{\frac{(6.674(10)^{-11}\frac{m^{3}}{kgs^{2}})(5.972(10)^{24} kg)}{3.9(10)^{8} m}}[/tex] (8)

Finally:

[tex]V=1010.92 m/s[/tex]

To find the moon's speed, we use Newton's law of universal gravitation and the formula for centripetal acceleration, substituting the Earth's mass and Earth-Moon distance to solve for the moon's orbital speed.

Calculating the Speed of the Moon from Earth-Moon Distance

To find the speed of the moon in its orbit using Newton's law of universal gravitation, we apply the formula for gravitational force, F, which is given by F = (G * m1 * m2) / r^2, where G is the gravitational constant, m1 and m2 are the masses of two objects, and r is the distance between their centers. For the Earth and Moon, we use Earth's mass (m2) and the Earth-Moon distance (r).

The moon's orbital speed (v) can be related to the gravitational force (F) since the force providing the moon's centripetal acceleration (a_c) required for circular motion is the same as the gravitational force exerted by Earth. That is, a_c = (v^2)/r. Setting the expression for gravitational force equal to mass times centripetal acceleration (F = m * a_c), and solving for v, we find v = sqrt(G * m2 / r).

We are given the distance between the Earth and Moon (r = 3.9 × 10^8 m) and the Earth's mass. Substituting these values into the equation, we can solve for the orbital speed of the Moon.

Answer:

Frequency will be 485 Hz

So option (c) will be the correct option

Explanation:

We have given frequency f = 500 Hz

Velocity of observer [tex]v_o=20m/sec[/tex]

Velocity of source [tex]v_s=10m/sec[/tex]

When both observer and source are moving then frequency is given by

[tex]f'=\frac{v-v_o}{v-v_s}\times f[/tex] , here v is the velocity of sound

So [tex]f'=\frac{340-20}{340-10}\times 500=485Hz[/tex]

So option (c) will be the correct option

Answer:

Height reached by the ball, h = 3.57 meters

Explanation:

It is given that,

Mass of the disk, m = 42 kg

Diameter of the disk, d = 3.2 m

Radius, r = 1.6 m

Angular speed of the disk, [tex]\omega=4.27\ rad/s[/tex]

The kinetic energy of the disk is equal to its potential energy. Using the conservation of energy as :

[tex]\dfrac{1}{2}mv^2+\dfrac{1}{2}I\omega^2=mgh[/tex]

[tex]\dfrac{1}{2}mv^2+\dfrac{1}{2}(mr^2/2)\omega^2=mgh[/tex]

[tex]\dfrac{1}{2}v^2+\dfrac{1}{2}(r^2/2)\omega^2=gh[/tex]

[tex]\dfrac{1}{2}(r\omega)^2+\dfrac{1}{2}(r^2/2)\omega^2=gh[/tex]

[tex]\dfrac{1}{2}(1.6\times 4.27)^2+\dfrac{1}{2}(1.6^2/2)\times 4.27^2=gh[/tex]

[tex]h=\dfrac{35.0071}{9.8}[/tex]

h = 3.57 meters

So, the solid disk will reach to a height of 3.57 meters.

The height attained by the disk on the hill is 3.57 m.

The given parameters;

The height attained by the disk is calculated by applying the law of conservation of energy as follows;

[tex]\frac{1}{2}mv^2 + \frac{1}{2}I \omega ^2 = mgh\\\\mv^2 + I \omega ^2 = 2mgh\\\\mv^2 + (\frac{mr^2}{2} ) \omega ^2 = 2mgh\\\\v^2 + \frac{1}{2} r^2 \omega ^2 = 2gh\\\\(\omega r)^2 + 0.5(\omega r )^2 = 2gh\\\\1.5 (\omega r)^2 = 2gh\\\\h = \frac{1.5 (\omega r)^2}{2g} \\\\h = \frac{1.5 \times (4.27 \times 1.6)^2 }{2\times 9.8} \\\\h = 3.57 \ m[/tex]

Thus, the height attained by the disk on the hill is 3.57 m.

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Answer:

6.46*10^-11m

Explanation:

We can use the equation of the center of the mass of two atoms

[tex]Xcm=\frac{mcxc+moxo}{mc+mo}[/tex]

If we take the origin at the center of the molecule carbon monoxice, xc will be 0, so

[tex]Xcm=\frac{moxo}{mc+mo}[/tex]=[tex]\frac{xo}{mc/mo+1}[/tex]

[tex]Xcm=\frac{1.13.10^-3}{0.750mo/mo+1}[/tex]=6.46*10^-11m

The spring constant is 181.0 N/m

Explanation:

We can solve the problem by applying the law of conservation of energy. In fact, the elastic potential energy initially stored in the compressed spring is completely converted into gravitational potential energy of the dart when the dart is at its maximum height. Therefore, we can write:

[tex]\frac{1}{2}kx^2 = mgh[/tex]

where the term on the left represents the elastic potential energy of the spring while the term on the right is the gravitational potential energy of the dart at maximum height, and where

k is the spring constant of the spring

x = 2.08 cm = 0.0208 m is the compression of the spring

m = 12.3 g = 0.00123 kg is the mass of the dart

[tex]g=9.8 m/s^2[/tex] is the acceleration due to gravity

h = 3.25 m is the maximum height of the dart

Solving for k, we find:

[tex]k=\frac{2mgh}{x^2}=\frac{2(0.00123)(9.8)(3.25)}{(0.0208)^2}=181.0 N/m[/tex]

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Answer:

Technical director.

Explanation:

The answer is the Technical director.

This is very important for every company or organization to manage the activity in a technical way. Because if we did not follow the good technique and did not use a proper technical method then definitely the task will not be completed in the specified time limit.

Answer: 150.427 K

Explanation:

The complete question is as follows:

The robot HooRU is lost in space, floating around aimlessly, and radiates heat into the depths of the cosmos at the rate of [tex]14.5 W[/tex] . HooRU's surface area is [tex]1.79 m^{2}[/tex] and the emissivity of its surface is [tex]0.279[/tex]. Ignore the radiation HooRU absorbs from the cold universe. What is HooRU's temperature?

This problem can be solved by the Stefan-Boltzmann law for real radiator bodies:  

[tex]P=\sigma A \epsilon T^{4}[/tex] (1)

Where:

[tex]P=14.5 W[/tex] is the energy radiated by HooRU

[tex]\sigma=5.6703(10)^{-8}\frac{W}{m^{2} K^{4}}[/tex] is the Stefan-Boltzmann's constant.  

[tex]A=1.79 m^{2}[/tex] is the Surface of the robot

[tex]\epsilon=0.279[/tex] is the robot's emissivity

[tex]T[/tex] is the effective temperature of the robot (its surface absolute temperature) in Kelvin

So, we have to find [tex]T[/tex] from (1):

[tex]T=(\frac{P}{\sigma A \epsilon})^{\frac{1}{4}}[/tex] (2)

[tex]T=(\frac{14.5 W}{(5.6703(10)^{-8}\frac{W}{m^{2} K^{4}}) (1.79 m^{2}) (0.279)})^{\frac{1}{4}}[/tex]

Finally:

[tex]T=150.427 K[/tex]

Answer:

new moon

Explanation:

A solar eclipse take place at new moon phase, when the moon passes between the earth and the sun and its shadows fall on the Earth's surface which by definition a solar eclipse.

The moon must be in the new moon phase for a solar eclipse to occur.

The moon must be in the new moon phase for a solar eclipse to occur. During the new moon phase, the moon is located between the Earth and the Sun, causing the moon to cast a shadow on Earth and block the Sun's light.

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Answer:

mass of the baryon = [tex]\frac{(qRB)^{2} }{2K}[/tex]

speed of the baryon = [tex]\frac{2K}{qRB}[/tex]

Explanation:

For any body to move in a circular path, there must be a centripetal force which is directed towards the center of the circle. Here, the centripetal force is provided by the magnetic Lorentz force that acts on the baryon. Therefore we can equate the magnitudes of centripetal force and magnetic Lorentz force.

Magnitude of Centripetal force = [tex]\frac{mv^{2} }{R}[/tex]

Magnitude of Magnetic Lorentz force =  qvB

where,

m = mass of the baryon

v = velocity of the baryon

Thus,

[tex]\frac{mv^{2} }{R}[/tex] = qvB

[tex]\frac{mv}{R}[/tex] = [tex]qB[/tex] (cancelling v on both sides)

v = [tex]\frac{qRB}{m}[/tex]

We know, Kinetic energy, K = [tex]\frac{1}{2} mv^{2}[/tex]

Substituting v in the above equation we get,

K = [tex]\frac{1}{2} m(\frac{qRB}{m} )^{2}[/tex]

K = [tex]\frac{(qBR)^{2} }{2m}[/tex] (simplifying)

Thus,

m = [tex]\frac{(qRB)^{2} }{2K}[/tex]

We already got that

v = [tex]\frac{qRB}{m}[/tex]

substituting the value of m in this equation gives,

[tex]v = \frac{qRB}{\frac{(qRB)^{2} }{2K}}[/tex]

v = [tex]\frac{2K}{qRB}[/tex] (simplifying)

Thus,

mass of the baryon = [tex]\frac{(qRB)^{2} }{2K}[/tex]

velocity of the baryon = [tex]\frac{2K}{qRB}[/tex]

The magnitude of the frictional force on the crate is 20 N.

The magnitude of the frictional force on the crate can be determined using the equation fs = μsN, where fs is the frictional force, μs is the coefficient of static friction, and N is the normal force. In this case, the normal force is equal to the weight of the crate, which is 40 N. Therefore, the frictional force is fs = (0.5)(40 N) = 20 N.

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Answer:

60 ft

Explanation:

The tree man and their shadow system forms two similar right angle triangles.

the figure is in the attachment.

let ∠BAC= θ

Therefore, in triangle ABC

tanθ = BC/AC= 35/75= 7/15

now in ΔAEF also

tanθ = EF/AE = 7/75-x= 7/15

solving we get x=60 ft

Now AC and FA are the shadows of the tree and the man respectively.

now FA =75-x=75-60= 15 ft

Therefore, the man must stand at a distance of 60 ft from the tree can you stand and still be completely in the shadow of the tree

A person 7 feet tall can stand 60 feet away from a 35-foot tree casting a 75-foot shadow to be completely in the shadow of the tree.

To solve for how far away from the tree a person can stand and still be completely in the shadow of the tree, we can use similar triangles. Since the tree is 35 feet tall and casts a 75-foot shadow, and a person is 7 feet tall, the height ratio between the tree and the person is 5:1 (35 feet : 7 feet). Therefore, the length of the shadow that the person will cast will also be 5 times shorter than the length of the tree's shadow.

We calculate the length of the person's shadow as follows:

Length of person's shadow = Length of tree's shadow / Height ratio

Length of person's shadow = 75 feet / 5

Length of person's shadow = 15 feet

The total distance from the tree at which the person can stand and still be completely in the shadow is the length of the tree's shadow minus the length of the person's shadow.

Total distance from the tree = Length of tree's shadow - Length of person's shadow

Total distance from the tree = 75 feet - 15 feet

Total distance from the tree = 60 feet

Answer:

V = 9.33 m/s

Explanation:

Given that,

Mass of the batsman, [tex]m_1=91\ kg[/tex]

Mass of the boat, [tex]m_2=510\ kg[/tex]                            

Initial speed of the boat, v = 11 m/s

Let V is the velocity of the boat after Batman lands in it. The net momentum of the system remains constant. Using the conservation of linear momentum to find it as :

[tex]510\times 11=(91+510)V[/tex]

[tex]V=\dfrac{510\times11}{(91+510)}[/tex]

V = 9.33 m/s

So, the velocity of the boat after Batman lands in it 9.33 m/s. Hence, this is the required solution.                                                          

When Batman lands in the boat, it causes a change in the boat's velocity due to the force exerted by Batman. Using the principle of conservation of momentum, we can find the final velocity of the boat. The final velocity of the boat is 10.0 m/s, moving in the opposite direction at an angle of 26.6° to a line drawn across the river.

When Batman jumps into the boat, he exerts a force on the boat due to his mass and acceleration. According to Newton's third law of motion, the boat exerts an equal and opposite force on Batman. This force causes a change in the velocity of the boat.

To find the final velocity of the boat, we can use the principle of conservation of momentum. The initial momentum of the boat-criminal system is equal to the final momentum of the system after Batman lands in the boat. Using the equation for momentum, we can find the final velocity of the boat.

After plugging in the given values, we find that the velocity of the boat after Batman lands in it is 10.0 m/s. The boat moves in the opposite direction, at an angle of 26.6° to a line drawn across the river.

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Answer:

d = 25.51 m

Explanation:

the law of the conservation of energy says that:

[tex]E_i - E_f = W_f[/tex]

where [tex]E_i[/tex] is the inicial energy, [tex]E_f[/tex] is the final energy and [tex]W_f[/tex] is the work of the friction.

so:

[tex]E_i[/tex] = [tex]\frac{1}{2} MV^2[/tex]

[tex]E_f = 0[/tex]

where M is the mass and V the velocity.

also,

[tex]W_f = U_kNd[/tex]

where [tex]U_k[/tex] is the coefficient of kinetic frictio, N is the normal force and d is the distance.

therefore:

[tex]\frac{1}{2}MV^2=U_kNd[/tex]

also, N is equal to the mass of the hockey puck multiplicated by the gravity.

replacing:

[tex]\frac{1}{2}m(5)^2=(0.05)(m(9.8))(d)[/tex]

canceling the m:

[tex]\frac{1}{2}5^2=0.05(9.8)(d)[/tex]

solving for d:

[tex]d = \frac{\frac{1}{2}5^2 }{0.05(9.8)}[/tex]

d = 25.51 m

The distance which the hockey puck slide before coming to rest is equal to  25.51 meters.

Given the following data:

We know that the acceleration due to gravity (g) of an object on planet Earth is equal to 9.8 [tex]m/s^2[/tex].

To find how far (distance) the hockey puck slide before coming to rest, we would use the law of conservation of energy:

According to the law of conservation of energy:

[tex]K.E_i - K.E_f = W_f[/tex]

The final kinetic energy of the hockey puck is zero (0) because it came to rest or stop.

[tex]K.E_i - 0 = W_f\\\\K.E_i = W_f\\\\\frac{1}{2}mv_i^2 = umgd\\\\\frac{1}{2}v_i^2 = ugd\\\\v_i^2 = 2ugd\\\\d = \frac{v_i^2}{2ug}[/tex]

Substituting the given parameters into the formula, we have;

Distance, d = 25.51 meters

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The main important characteristic that distinguishes meteorites and terrestrial rocks is the presence of fusion crust and the presence of iron metal alloys.

Meteorites are usually covered with dark, pitted crust resulting from their fiery passage through the atmosphere. Terrestrial rock usually has a metal content and can able to attract the magnet.

Meteorite has rare earth element such as iridium, and terrestrial rocks do not have rare earth elements. Meteorite has a dark crust from burning Earth's atmosphere. A fusion crust is present only in meteorites whereas terrestrial rock doesn't.

Meteorites have high metal content and it has different isotope ratios of the particular elements. The terrestrial rocks do not have isotope and metal content.

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Final answer:

A meteorite is distinguished from a terrestrial rock primarily by its composition and origin, with meteorites often containing metallic elements and coming from asteroids. Primitive and differentiated are two main categories of meteorites, providing insight into the early solar system and respective parent bodies’ structures.

Explanation:

The characteristic that distinguishes a meteorite from a terrestrial rock is mainly its origin and composition. Meteorites are typically fragments from asteroids and are often rich in metallic elements, unlike many terrestrial rocks. A key distinction between meteoritic and terrestrial rocks can be made on the basis of whether they are primitive or differentiated. Primitive meteorites are composed of materials that have not been altered by heat or pressure since their formation and provide insights into the early solar system. On the other hand, differentiated meteorites are remnants of larger parent bodies that experienced molten states, allowing materials to separate by density, similar to the process on Earth but with different conditions. Examples of differentiated meteorites include irons and stony-irons, which come from the metal cores or mantle-core boundaries of their parent bodies.

Typical stony meteorites closely represent the terrestrial crust or mantle, while typical iron meteorites have compositions akin to the Earth's core. Scientists use various methods, including chemical and mineralogical analysis, to distinguish meteorites from terrestrial material. Lunar meteorites, for instance, can be identified by their unique chemical properties compared to Earth rocks. By studying meteorites, scientists gain valuable knowledge about the history and formation of the solar system.

Answer:

Not possible.

Explanation:

Exoplanets are an active area of modern research. The article states that the outermost planet (Planet C) goes all the way around its star in less time than the innermost planet (Planet A). Which is not possible as it will violet Kepler's third law of planetary motion.  Which says that the square of orbital period of a planet is proportional to the cube of its semi-major axis of its orbit.

Explanation:

Taking the incident light to be traveling in the + x-direction so that it is at normal incidence to the left side of the film(referred to as the "Front side"). This means the beam transmitted into the liquid is essentially as strong as the incident beam.

Almost all the light that is reflected off the back surface will get through the front surface. (But only 2.78% gets re-reflected off the the front surface back to the right) this means that there are two beams reflected to the - x-direction, one from the front surface and one from the back, and these beams are of almost equal intensity.

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Answer:

a) -1.57 rad/s²

b) 800 revolutions

Explanation:

a)In here you can use the equations of velocity as if it were a linear movement. In this case:

wf = wo + at

wo is the innitial angular velocity, that we can get this value using the fact that a revolution is 2π so:

wo = 20 * 2π = 125.66 rad/s

We have the time of 80 seconds, and the final angular speed is zero, because it's going to a rest so:

0 = 125.66 + 80a

a = -125.66 / 80

a = -1.57 rad/s²

b) In this part, we will use the following expression:

Ф = Фo + wo*t + 1/2 at²

But as this it's coming to rest then:

Ф = 1/2at²

solving we have:

Ф = 0.5 * (-1.57)*(80)²

Ф = 5,024 rad

Ф = 5024 / 2π

Ф = 800 revolutions

(a) The angular acceleration of the grinding wheel is approximately [tex]-1.57 \, \text{rad/s}^2[/tex]. (b) The grinding wheel made about 800 revolutions during the time it was coming to rest.

To solve the problem of the grinding wheel, we need to find the angular acceleration and the number of revolutions during its deceleration.

First, we convert the initial angular velocity from revolutions per second to radians per second:
[tex]\omega_0 = 20.0 \, \text{rev/s} \times 2\pi \, \text{rad/rev} = 40\pi \, \text{rad/s} \approx 125.66 \, \text{rad/s}[/tex]

Angular acceleration [tex]\alpha[/tex] can be calculated using the formula:
[tex]\alpha = \frac{\omega_f - \omega_0}{t}[/tex]
where [tex]\omega_f = 0 \, \text{rad/s}[/tex] (final angular velocity, when the wheel comes to rest).

Substituting in the values:
[tex]\alpha = \frac{0 - 125.66}{80.0} = \frac{-125.66}{80.0} \approx -1.57 \, \text{rad/s}^2[/tex]

To find how many revolutions the wheel made while coming to rest, we can use the formula for angular displacement [tex]\theta[/tex]:
[tex]\theta = \omega_0 t + \frac{1}{2} \alpha t^2[/tex]

Substituting the values:
[tex]\theta = (125.66 \, \text{rad/s}) (80.0 \, ext{s}) + \frac{1}{2} (-1.57) (80.0)^2[/tex]
[tex]\theta = 10052.8 \, \text{rad} - \frac{1}{2} (1.57) (6400)\approx 10052.8 - 5024\approx 5028.8 \, \text{rad}[/tex]

Now convert radians to revolutions:
[tex]\text{Revolutions} = \frac{\theta}{2\pi} = \frac{5028.8}{2\pi} \approx 799.8 \, ext{rev} \approx 800 \, ext{rev}[/tex]

Answer:

Explained

Explanation:

Your tutor is completely wrong here. Ampere and volt are both completely different concept. Ampere measure current in circuit, whereas volt measure the potential difference across two points in circuit. It is due to this difference in the potential that leads to flow of current in the circuit. The potential difference is the cause and current is the effect.

An ampere measures electric current, while a volt measures electrical potential difference, and they are critical in understanding electrical circuits. Ammeters are used to measure current and are wired in series, while voltmeters, which include an internal resistor, measure voltage and are connected in parallel. Confusing these concepts suggests a serious misunderstanding of basic electrical principles, thus getting a different tutor would be recommended.

If your tutor tells you that an ampere (A) and a volt (V) measure the same thing and suggests that these terms complicate a simple concept, it would be wise to consider finding a different tutor. This is because an ampere and a volt actually measure two fundamentally different electrical properties. The ampere measures electric current, which is the flow of electric charge, and is analogous to how much water flows through a pipe. In contrast, a volt measures electrical potential difference, or voltage, which is the energy available to move the charge, akin to the height from which water falls. When using tools to measure these properties, we use an ammeter to measure current, placing it in series so that all the current flows through it, and a voltmeter to measure voltage, connecting it in parallel to get a reading without significantly altering the flow of current.

Additionally, the internal design of a voltmeter includes an internal resistor and when connected in a circuit, it effectively creates a parallel resistance arrangement with the component across which the voltage is being measured. Therefore, to accurately measure and understand electrical circuits, one must recognize the difference between amperes and volts and use the appropriate measurement tools accordingly.

The angular acceleration of a ceiling fan with a net torque of 2.1 N · m and blades having a moment of inertia of 0.19 kg · m² is approximately 11.05 rad/s².

The subject of this question is Physics, specifically rotation dynamics. In rotation dynamics, angular acceleration is defined by the equation α = τ / I, where α is the angular acceleration, τ is the net torque, and I is the moment of inertia. In the given problem, a net torque of 2.1 N · m is applied to a ceiling fan with blades having a total moment of inertia of 0.19 kg · m². Substituting the given values into the equation, we can solve for the angular acceleration: α = 2.1 N · m / 0.19 kg · m² = approximately 11.05 rad/s². Hence, the angular acceleration of the ceiling fan's blades is approximately 11.05 rad/s².

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The angular acceleration of the ceiling fan blades, given a net torque of 2.1 N·m and a moment of inertia of 0.19 kg·m², is calculated using Newton's second law for rotation. The resulting angular acceleration is 11.05 rad/s².

The student's question is related to the field of Physics, specifically rotational kinematics and dynamics. The key concept here is Newton's second law for rotation, which can be expressed as τ = Iα, where τ represents the net torque, I is the moment of inertia, and α is the angular acceleration.

Given that the net torque (τ) is 2.1 N·m and the moment of inertia (I) is 0.19 kg·m², we can find the angular acceleration (α) by rearranging the equation α = τ / I. Substituting the given values into this equation: α = 2.1 N·m / 0.19 kg·m² = 11.05 rad/s². Hence, the angular acceleration of the blades of the ceiling fan is 11.05 rad/s².

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Final answer:

To calculate the pressure after a temperature change, use the equation PV = nRT, and simplifying it to P1/T1 = P2/T2. Rearranging the equation, the final pressure (P2) can be calculated as P2 = P1 * (T2 / T1). In this case, the pressure after the temperature has risen to 35.0ºC is approximately 7.33 × 10^5 Pa.

Explanation:

To calculate the pressure after the temperature change, we can use the equation PV = nRT, where P represents pressure, V represents volume, n represents the number of moles, R represents the ideal gas constant, and T represents temperature. Since the volume and moles remain constant in this scenario, we can simplify the equation to P1/T1 = P2/T2, where P1 and T1 represent the initial pressure and temperature, and P2 and T2 represent the final pressure and temperature. Rearranging the equation, we get P2 = P1 * (T2 / T1). Therefore, the pressure after the temperature has risen to 35.0ºC can be calculated as:

P2 = 7.00 × 10^5 Pa * (35.0 + 273.15) / (21.0 + 273.15)

P2 = 7.00 × 10^5 Pa * 308.15 / 294.15

P2 = 7.33 × 10^5 Pa

Answer:

option B.

Explanation:

The correct answer is option B.

The phenomenon of the curtains to pull out of the window can be explained using Bernoulli's equation.

According to Bernoulli's Principle when the speed of the moving fluid increases the pressure within the fluid decrease.

When wind flows in the outside window the pressure outside window decreases and pressure inside the room is more so, the curtain moves outside because of low pressure.

Final answer:

To find the spring constant of the car's springs, we use Hooke's Law and the given information about the car's mass, maximum amplitude, and speed. The spring constant is approximately 92638 N/m.

Explanation:

To find the spring constant of the car's springs, we need to use Hooke's Law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position. The formula for Hooke's Law is F = -kx, where F is the force, k is the spring constant, and x is the displacement.

In this case, the car bounces up and down with the maximum amplitude when traveling at 5.7 m/s. The maximum amplitude of the oscillation is half the distance between bumps, so it is 4.9 m/2 = 2.45 m. We can use this information to solve for the spring constant k using the formula:

k = mω²

where m is the mass of the car and ω is the angular frequency, which can be calculated using the formula:

ω = 2πf

where f is the frequency, which is the reciprocal of the period T.

Given that the bumps are spaced 4.9 m apart, the period of the oscillation is the time it takes the car to travel one bump, which is T = 4.9 m / 5.7 m/s = 0.859 s.

The frequency is the reciprocal of the period, so f = 1 / T = 1 / 0.859 s = 1.164 Hz.

Plugging the values into the formulas, we have:

ω = 2π(1.164) ≈ 7.294 rad/s

k = (1800 kg)(7.294 rad/s)² ≈ 92638 N/m

Therefore, the spring constant of the car's springs is approximately 92638 N/m.

Answer:

Stoma represents the interface between the environment and the plant, helping to obtain the necessary CO2.

Explanation:

Stoma are groups of two or more specialized epidermal cells whose function is to regulate gas exchange and perspiration.

The frequency or density varies widely from a few tens to thousands per mm2, due to the influence of environmental factors, leaf morphology and genetic composition.

Answer:

Q = 230.36 C

Explanation:

Given

R = 3.54 Ω

t = 30'45" = (30')*(60"/1') + 45" = 1845 s

V = 442 mV = 442*10⁻³V

Q = ?

We can use Ohm's Law in order to get I as follows

V = I*R   ⇒    I = V / R

⇒    I = 442*10⁻³V / 3.54 Ω = 0.1248 A

Finally we use the formula

I = Q / t     ⇒    Q = I*t = (0.1248 A)(1845 s)

⇒    Q = 230.36 C