The acceleration vector of a particle in uniform circular motion __________.

Answer: 2/3 of the total volume

Explanation:

See attachment for details

Answer

Given,

Frequency of the ultrasonic pulse = 30 kHz

Speed of the sound = v = 343 m/s

wavelength of the wave emitted = ?

using formula

     [tex]v = \nu \lambda[/tex]                    

     [tex]\lambda= \dfrac{v}{\nu}[/tex]                  

     [tex]\lambda= \dfrac{343}{30\times 10^3}[/tex]

     [tex]\lambda=11.43 \times 10^{-3}\ m[/tex]          

     [tex]\lambda=11.43\ mm[/tex]                    

time taken for a pulse  that reflects off an object 3.0 m away to make a round trip                                                

   [tex]time = \dfrac{\Delta x}{\Delta v}[/tex]

   [tex]time = \dfrac{2\times 3}{343}[/tex]

            t = 0.01749 s

            t = 17.49 ms

The motion detector uses ultrasonic waves to measure distance by timing the round trip of a sound wave. Distance is calculated using the speed of sound and the time taken for the echo to return, and the calculation requires a division by 2 to account for the round trip. Calibration is important for accuracy as the speed of sound changes with temperature.

The motion detector described is a classic example of how ultrasonic waves can be used to measure distance. A similar principle is applied in an automatic focus camera, which generates ultrasonic sound waves, captures their reflections off objects, and calculates the distance based on the time delay of the returning waves. The speed of sound in air at 20 ℃ is approximately 344 m/s. Therefore, if a sound wave returns after 0.150 seconds, we can calculate the distance to the object as follows:

Distance = Speed of Sound × Time / 2
Distance = 344 m/s × 0.150 s / 2
Distance = 25.8 meters
This calculation takes into account that the sound wave must travel to the object and back, making the total distance twice the distance we want to measure, hence the division by 2.

The ultrasonic range finder and technologies such as radar and Doppler shift applications in traffic law enforcement rely on similar concepts of wave reflection and frequency shifts to measure distance and speed.

To understand the effects of temperature on the calibration of such devices, the room temperature is required because the speed of sound in air changes with temperature, potentially influencing the accuracy of these measurements.

Answer:

1964.8 J

[tex]5.12894\times 10^{-6}\ m^3[/tex]

1150 Joules

Explanation:

m = Mass of bullet = 0.5 kg

[tex]\Delta T[/tex] = Change in temperature = (327-20)

c = Specific heat of lead = 128 J/kg °C

[tex]\beta[/tex] = [tex]84\times 10^{-6}\ /^{\circ}C[/tex]

[tex]L_f[/tex] = Latent heat of fusion of lead = [tex]23000\ J/kg^{\circ}C[/tex]

(Values taken from properties of lead table)

Heat is given by

[tex]Q=mc\Delta T\\\Rightarrow Q=0.05\times 128\times (327-20)\\\Rightarrow Q=1964.8\ J[/tex]

The heat needed to raise the bullet to its final temperature is 1964.8 J

Change in volume is given by

[tex]\Delta V=V_0\beta \Delta T\\\Rightarrow \Delta V=5\times 10^{-6}\times 84\times 10^{-6}\times (327-20)\\\Rightarrow \Delta V=1.2894\times 10^{-7}\ m^3[/tex]

[tex]V=V_0+\Delta V\\\Rightarrow V=5\times 10^{-6}+1.2894\times 10^{-7}\\\Rightarrow V=5.12894\times 10^{-6}\ m^3[/tex]

The volume of the bullet when it comes to rest is [tex]5.12894\times 10^{-6}\ m^3[/tex]

Heat needed for melting

[tex]Q=mL_f\\\Rightarrow Q=0.05\times 23\times 10^3\\\Rightarrow Q=1150\ J[/tex]

The additional heat needed to melt the bullet is 1150 Joules

Final answer:

The calculation involves determining the heat required to increase the bullet's temperature, calculating the change in volume due to thermal expansion, and the additional heat required to melt the bullet, using the specific heat capacity, coefficient of thermal expansion, and latent heat of fusion for lead.

Explanation:

To solve this problem, we will use the specific heat capacity formula and the properties of lead to calculate the heat needed for temperature change and melting.

Heat required to raise the bullet's temperature: The heat (Q) needed can be calculated using the specific heat capacity equation Q = mcΔT, where 'm' is mass, 'c' is specific heat capacity, and ΔT is the change in temperature. For lead, the specific heat capacity (c) is approximately 128 J/(kg·°C).

Volume: To find the volume at the final temperature, we use the formula V = V_0(1+ αΔT), where V_0 is the initial volume, α is the coefficient of thermal expansion for lead, and ΔT is the change in temperature.

Additional heat to melt the bullet: To calculate the additional heat (Q_m) required to melt the bullet, we use the formula Q_m = mL_f, where 'm' is the mass of the bullet and L_f is the latent heat of fusion for lead.

To calculate these values, we also need the initial temperature (T_i), final temperature (T_f), and coefficient of thermal expansion for lead, which is 29.3 × 10⁻⁶ °C-1. For melting lead, the latent heat of fusion (L_f) is 24.7 kJ/kg.

Answer:

Magnetometer

Explanation:

Magnetometer technique is not using by scientists for studying the ocean floor.The scientists currently is using SONAR ( sound navigation and ragging) technique for studying the ocean floor.SONAR is used sound waves sound waves for studying the ocean floor or we can say that SONAR is based on sound propagation.

Therefore answer is Magnetometer

Answer:

(B) be extremely unlikely and therefore violate the 2nd law of thermodynamics.

Explanation:

This process is highly unlikely and if happens would violet the 2nd law of thermodynamics.

The laws of motion do not rule out a move to one side of the room of all the air molecules. But it would be extremely unlikely to happen that. The second law of thermodynamics states that the universe responds to circumstances that become more and more likely, not improbable.

Final Answer:

The angle θ at which the wheel comes to rest is approximately θ = tan^(-1)(μ), where μ is the coefficient of static friction. The minimum coefficient of static friction required to prevent slipping is μ = tan^(-1)(m_wheel / m_cylinder), where m_wheel is the mass of the wheel and m_cylinder is the mass of the cylinder.

Explanation:

In this scenario, the forces involved include the gravitational force acting on both the wheel and the cylinder and the tension in the cord. The component of the gravitational force parallel to the incline causes the wheel to roll, and the frictional force opposes slipping. At the point where the wheel comes to rest, the net force along the incline is zero.

Using the equilibrium condition, the gravitational force component along the incline is balanced by the frictional force. This gives us the equation: m_wheel * g * sin(θ) = μ * m_wheel * g * cos(θ), where g is the acceleration due to gravity. Simplifying, we find μ = tan(θ).

To find the minimum coefficient of static friction, we can substitute the masses of the wheel and cylinder: μ_min = tan^(-1)(m_wheel / m_cylinder). This represents the point where the wheel will come to rest without slipping. The tan^(-1) function gives the angle at which the static friction is just sufficient to prevent slipping, and this corresponds to the minimum coefficient of static friction required.

Answer:

  λ₂ = 1,219 10⁻⁷ m , λ₃ = 1.028 10⁻⁷ m ,   λ₄ = 0.9741 10⁻⁷ m , λ₅ = 0.9510 10⁻⁷ m and  λ₆ = 0.9395 10⁻⁷ m

Explanation:

To calculate the lines of the hydrogen liman series, we can use the Bohr atom equation

           En = -13.606 / n²       [eV]

n       En

1       -13,606

2       -13.606 / 4 =    -3.4015

3       -13.606 / 9 =    -1.5118

4       -13.606 / 16 =  -0.8504

5       -13.606 / 25 = -0.5442

6       -13.606 / 36 = -0.3779

The lyma series are transitions where the state is fundamental (E1), let's calculate the first five transitions

State

initial final energy

6           1      -0.3779 - (- 13.606) =  13.23 eV

5           1      -0.5442 - (- 13.606) =  13.06 eV

4           1      -0.8504- (-13.606) =   12.76 eV

3            1      -1.5118 - (- 13.606) =   12.09 eV

2            1      -3.4015 - (- 13.606) = 10.20 eV

Let's use the relationship between the speed of light and the wavelength and the frequency

      c = λ  f

      f = c / λ  

Planck's relationship for energy

     E = h f

     E = h c / λ

    λ = hc / E

We calculate for each energy

E = 10.20 eV

      λ  = 6.63 10⁻³⁴ 3 10⁸ / (10.20 1.6 10⁻¹⁹)

      λ  = 12.43 10⁻⁷ / 10.20

      λ₂ = 1,219 10⁻⁷ m

E = 12.09 eV

     λ₃ = 12.43 10⁻⁷ / 12.09

     λ₃ = 1.028 10⁻⁷ m

E = 12.76 eV

      λ₄ = 12.43 10⁻⁷ /12.76

      λ₄ = 0.9741 10⁻⁷ m

E = 13.06 ev

      λ₅=  12.43 10⁻⁷ /13.06

       λ₅ = 0.9510 10⁻⁷ m

E = 13.23 eV

      λ₆ = 12.43 10⁻⁷ / 13.23

      λ₆ = 0.9395 10⁻⁷ m

Answer:

Vo = 4m/s

Explanation:

By conservation of energy:

[tex]1/2*m*Vf^2-1/2*m*Vo^2-m*g*h=0[/tex]

Solving for the initial speed:

[tex]Vo = \sqrt{2*(Vf^2/2-g*h)}[/tex]

[tex]Vo = \sqrt{2*(6^2/2-10*1)}[/tex]

Vo=4m/s

The interference principle is responsible for alternating light and dark bands when light passes through two or more narrow slits.

The phenomenon in which two or more waves combine to generate a new wave with a larger, smaller, or equal amplitude. It depends on the alignment of the peaks and troughs of the overlapping waves.

When two or more waves collide, this is known as interference. They may add up, or they may partially or completely cancel each other,

When two waves with the same frequency. We will see varying intensities of light at different points on the screen owing to their superposition.

Hence interference principle is responsible for alternating light and dark bands when light passes through two or more narrow slits.

To learn more about the interference refer to the link;

https://brainly.com/question/16098226

Final answer:

The speed of light in air depends on both the wavelength and the frequency of light. Increasing or decreasing the frequency of light leads to changes in the amount of delay.

Explanation:

The speed of light in air depends on both the wavelength and the frequency of light. This relationship is defined by the equation c = fλ, where c is the speed of light, f is the frequency, and λ is the wavelength.

When the frequency of light increases, the wavelength decreases, and vice versa. This means that as you make the frequency higher or lower, there is a corresponding change in the amount of delay.

For example, if you increase the frequency, the wavelength becomes smaller, which leads to a shorter delay. On the other hand, if you decrease the frequency, the wavelength becomes larger, resulting in a longer delay.

Sound waves in air and water are longitudinal waves characterized by pressure differences. Sound in solids can have both longitudinal and transverse components.

Sound waves in air and water are longitudinal waves characterized by pressure differences. When sound waves propagate through a fluid like air or water, the disturbances are periodic variations in pressure, resulting in compressions (high-pressure regions) and rarefactions (low-pressure regions).

Fluids do not have appreciable shear strength, so the sound waves in them must be longitudinal or compressional. On the other hand, sound in solids can have both longitudinal and transverse components. For example, seismic waves generated by earthquakes have both longitudinal (compressional or P-waves) and transverse (shear or S-waves) components.

Answer:

l=24.8 cm

Explanation:

The period of a simple pendulum is given by

[tex]T= 2\pi\sqrt{\frac{l}{g} }[/tex]

l= length of pendulum

g= acceleration due to gravity

taking square on both the sides we get

[tex]T^2= 4\pi^2\frac{l}{g}[/tex]

This can be rewritten as

[tex]l = \frac{T^2}{g}4\pi^2[/tex]

now substituting T= 1 and g= 9.8

[tex]l = \frac{1^2}{9.8}4\pi^2[/tex]

l= 0.248 m = 24.8 cm

Final answer:

The length of a pendulum with a period of 1.00 s can be calculated using the formula L = (T^2/g)π^2, resulting in a length of approximately 0.999 m or 99.9 cm.

Explanation:

The period of a pendulum is determined by its length and the acceleration due to gravity, and it is independent of factors such as mass or amplitude. The period is given by the formula T = 2π√(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.

In the given question, the period of the pendulum is 1.00 s. To find the length of the pendulum, we can rearrange the formula and solve for L: L = (T^2/g)π^2.

Using a standard value for acceleration due to gravity of 9.8 m/s^2, we can substitute the values to find the length of the pendulum: L = (1.00 s^2 / 9.8 m/s^2)π^2. Evaluating this expression, we find that the length of the pendulum is approximately 0.999 m, or 99.9 cm.

Answer:

Gold, Platinum and Uranium

Explanation:

A star is nothing but a huge ball of gas. Specifically, Hydrogen, the simplest element of nature. A star is in equilibrium because its immense mass causes it to collapse towards itself, squeezing those hydrogen nuclei or protons, and the union of the protons in its nucleus causes the star to explode, releasing energy. As long as these nuclear reactions exist (the same ones that human beings can cause with their hydrogen bombs), the star will remain in equilibrium.

Protons have a positive charge and tend to repel. But inside the stars they are so tight (there is a lot of pressure and temperature), that they can't avoid crashing. At that time, the electromagnetic force is defeated by what physicists call Strong Force, which holds together protons and neutrons forming more complex atoms. In a typical star, the protons join to form the next element in the periodic table: Helium, consisting of 2 protons and two neutrons. It is a rare element on Earth and was discovered in the Sun rather than on our planet. Hence his name, from the Greek Helios, the sun god.

However, the mass of the sum of the protons that bind to form Helium is less than the total mass of Helium. What happen? Are the laws of physics inside the stars not fulfilled? What happens is impossible to understand if one is born before Albert Einstein, but today it is very easy to explain. The mass that we lack, has actually become energy. The German physicist Albert Einstein (1879-1955) discovered that mass and energy are equivalent while formulating his Theory of Relativity. In fact, let me, for once, write a mathematical equation of an unparalleled beauty:

E = mc2

This equation tells us that the energy E is equal to the mass m times the square of a constant c; that constant c is the speed of light, approximately 300,000 km / s. That is, a very small mass, such as a proton, is equivalent to a very large energy, since the numerical factor by which the mass is multiplied is a very large number. And that energy is what the stars release, the one that our Sun emits and gives us life.

When Hydrogen is depleted, the star collapses until the pressure and temperature increase enough for Helium to fuse with itself; the cycle is repeated and the star ends up generating Carbon, Oxygen, Nitrogen, Silicon, Iron. As you can see, the stars are factories of atoms. When the star explodes, even heavier atoms are generated, such as Gold, Platinum, Uranium, elements that abound on our planet. And they abound, because the Sun is a second or third generation star: that is, it was born from the remains of other stars' explosions, along with the materials that make up our planet, the rest of the planets, the asteroids, the comets, the interstellar dust and ourselves.

Answer:

(a) 7 m

(b) 1  m

Explanation:

Given:

The magnitude of displacement  vector 'a' is 3 m

The magnitude of displacement vector 'b' is 4 m.

The vector 'c' is the vector sum of vectors 'a' and 'b'.

(a)

Now, when the angle between the vectors is 0°, it means that the vectors are in the same direction. When vectors are in the same direction, then their resultant magnitude is simply the sum of their magnitudes.

So, magnitude of 'c' when 'a' and 'b' are in same direction is given as:

[tex]|\overrightarrow c|=|\overrightarrow a|+|\overrightarrow b|\\\\|\overrightarrow c|=3 + 4 = 7\ m[/tex]

Therefore, the magnitude of vector 'c' is 7 m when angle between 'a' and 'b' is 0°.

(b)

When the angle between the vectors is 180°, it means that the vectors are exactly in the opposite direction. When the vectors are in opposite direction, then their resultant magnitude is the subtraction of their magnitudes.

So, magnitude of 'c' when 'a' and 'b' are in opposite direction is:

[tex]|\overrightarrow c|=||\overrightarrow a|-|\overrightarrow b||\\\\|\overrightarrow c|=|3 - 4| = 1\ m[/tex]

Therefore, the magnitude of vector 'c' is 1 m when angle between 'a' and 'b' is 180°.

Answer:

The magnitude of torque is τ = 24.522 N*m^2

Explanation:

To find the magnitude of the torque can use the equation of the force produce by the airplane so:

τ = F * d

τ = 0.804 N * 30.5 m

τ = 24.522 N*m

Check:

Find the acceleration

I = m*r^2=0.741kg*(30.5m)^2

I = 689.32 kg*m^2

τ = I*a_c

a_c = τ /I = 24.522 N*m^2 / 689.32 kg*m^2

a_c = 0.0355 m/s^2

τ = 0.0355 m/s^2 * 689.32 kg*m^2

τ = 24.522 N*m^2

Answer:

Option (a)

Explanation:

Impulse is defined as the change in momentum of the body. It is a vector quantity and its SI unit is Kg m/s.

mass of ball, m = 0.4 kg

initial velocity, u = - 30 m/s

Final velocity, v = + 20 m/s

Initial momentum, pi = mass x initial velocity = m u = 0.4 x (- 30) = - 12 kg m/ s

Final momentum, pf = mass x final velocity = mv = 0.4 x 20 = 8 Kg m /s

Change in momentum = final momentum - initial momentum = 8 - (- 12 )

So, impulse = 20 kg m /s right

Option (a) is correct

Final answer:

The impulse of the net force on the ball during its collision with the wall is the change in momentum, coming to 32 kg·m/s to the right, leading to option E) none of the above as the correct answer.

Explanation:

The impulse of the net force on a ball during its collision with the wall can be calculated using the change in momentum of the ball, which is equal to the impulse imparted to it. If the ball has a mass of 0.40 kg and changes its velocity from 30 m/s to the left (which we can consider as a negative direction) to 20 m/s to the right (a positive direction), we need to take into account the magnitude and the direction of this change.

The initial momentum of the ball is given by the product of its mass and its initial velocity, which is -0.40 kg × 30 m/s (the negative sign indicates the initial leftward direction). The final momentum after the collision is 0.40 kg × 20 m/s. The impulse is the difference between the final and initial momentum: (0.40 kg × 20 m/s) - (-0.40 kg × 30 m/s), which equals 20 kg·m/s + 12 kg·m/s or 32 kg·m/s to the right. Therefore, the correct answer is E) none of the above.

Nuclear fusion would not occur in stars of any mass if hydrogen had the smallest mass per nuclear particle.

This is the process in which nuclear reactions between light elements form heavier elements.

Hydrogen won't be able to undergo nuclear fusion in stars of any mass if hydrogen had the smallest mass per nuclear particle due to the sub=atomic particles not being favorable in this condition.

Read more about Nuclear fusion here https://brainly.com/question/982293

Final answer:

The force you exert on the rock is equal in magnitude but opposite in direction to the force the rock exerts on you, in accordance with Newton's Third Law of Motion.

Explanation:

When you push a rock along level ground and make it speed up, the force you exert compares with the force the rock exerts on you in accordance with Newton's Third Law of Motion, which states that for every action, there is an equal and opposite reaction. Therefore, the force you exert on the rock is equal in magnitude but opposite in direction to the force the rock exerts on you.

The concept can be understood by considering various scenarios where different forces are applied to objects of differing masses, resulting in different levels of acceleration. For example, pushing a basketball produces a noticeable acceleration due to the basketball's low mass, whereas pushing a stalled SUV with the same force results in a much smaller acceleration due to the SUV's greater mass.

Friction can also affect how much force is needed to move an object. When pushing a heavy crate, you must overcome static friction, which matches the force you apply up to the point where the crate begins to move. Once in motion, dynamic friction takes over, which is generally lower than static friction, making it easier to keep the object moving.

Answer:

Zero work is done when a vertical force acts on an object moving horizontally

Explanation:

Word is the dot product of force and displacement.

             W = F . s

             W = Fs cosθ

θ is the angle between force and displacement,

We need to find how much work is done when a vertical force acts on an object moving horizontally.

That is angle between force and displacement = 90°

                θ = = 90°

Substituting

              W = Fs cos90 = Fs x 0 = 0

Zero work is done when a vertical force acts on an object moving horizontally    

Answer:

D. Nothing will happen; the seesaw will still be balanced.

Explanation:

D. Nothing will happen; the seesaw will still be balanced. Since both toruqes or momentums respect to the center have changed in the same amount (one-half their original distance) the seesaw will remain balanced, if the children change distance in a different amount then it will be out of balance

D. Nothing will happen; the seesaw will still be balanced.

The force acting on a system with static equilibrium is 0

[tex] \large {\boxed {\bold {\sum F = 0}} [/tex]

(forces acting as translational motion only, not including rotational forces)

[tex] \displaystyle \sum F_x = 0 \\\\\ sum F_y = 0 [/tex]

For objects undergoing rotation, the equilibrium must be met

[tex] \large {\boxed {\bold {\sum \tau = 0}} [/tex]

A heavy boy (Hb) and a lightweight girl (Lg) are balanced on a mass-less seesaw

Because there is a balance of rotation, the torque equation:

Στ = 0

Hb.r1-Lg.r2 = 0

Hb.r1 = Lg.r2 (equation 1)

If they both move forward so that they are one-half their original distance from the pivot point, then the distance of the two children to the pivot point is reduced to half

Then the torque equation:

[tex]\rm Hb\times \dfrac{r_1}{2}= Lg\times \dfrac{r_2}{2}\\\\Hb\times r_1=Lg\times r_2[/tex]

This equation remains the same as equation 1, so the seesaw will still be balanced.

tangential force

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displacement of a skateboarder

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The distance of the elevator

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Answer:

14 billion years

Explanation:

The Hubble – Lemaître law, previously called the Hubble law, is a law of physics that states that the redshift of a galaxy is proportional to the distance it is, which is the same as, the further one galaxy is found from another, more quickly it seems to move away from it.

The Hubble constant is the value that measures the rate at which the expansion speed of the Universe varies with distance, and is one of the fundamental parameters of the Universe and allows, in particular, to determine the age of the Universe as we will see.

Answer:

Flow; Impressed

Explanation:

The electric charge can be think of as the flow rate of electrons in a certain area or point. Voltage is a difference in electrical potential, it makes charges to move in the electrical conductor, therefore it is impressed across a circuit

Answer:

a) Suzie’s average acceleration = -6.46 m/s²

b) Force exerted to stop Suzie = 271.52 N

Explanation:

a) We have equation of motion, v = u + at

     Final velocity, v = 0 m/s

     Initial velocity, u = 32 mph = 14.22 m/s

     Time, t =2.2 s

Substituting

     0 = 14.22 + a x 2.2

     a = -6.46 m/s²

Suzie’s average acceleration = -6.46 m/s²

b) Mass of Suzie = 42 kg

   Force = Mass x Acceleration

   F = Ma

   F = 42 x -6.46 =-271.52 N

   Force exerted to stop Suzie = 271.52 N

Answer:

a)

1.35 kg

b)

2.67 ms⁻¹

Explanation:

a)

[tex]m_{1}[/tex] = mass of first body = 2.7 kg

[tex]m_{2}[/tex] = mass of second body = ?

[tex]v_{1i}[/tex] = initial velocity of the first body before collision = [tex]v[/tex]

[tex]v_{2i}[/tex] = initial velocity of the second body before collision = 0 m/s

[tex]v_{1f}[/tex] = final velocity of the first body after collision =

using conservation of momentum equation

[tex]m_{1} v_{1i} + m_{2} v_{2i} = m_{1} v_{1f} + m_{2} v_{2f}\\(2.7) v + m_{2} (0) = (2.7) (\frac{v}{3} ) + m_{2} v_{2f}\\(2.7) (\frac{2v}{3} ) = m_{2} v_{2f}\\v_{2f} = \frac{1.8v}{m_{2}}[/tex]

Using conservation of kinetic energy

[tex]m_{1} v_{1i}^{2}+ m_{2} v_{2i}^{2} = m_{1} v_{1f}^{2} + m_{2} v_{2f}^{2} \\(2.7) v^{2} + m_{2} (0)^{2} = (2.7) (\frac{v}{3} )^{2} + m_{2} (\frac{1.8v}{m_{2}})^{2} \\(2.7) = (0.3) + \frac{3.24}{m_{2}}\\m_{2} = 1.35[/tex]

b)

[tex]m_{1}[/tex] = mass of first body = 2.7 kg

[tex]m_{2}[/tex] = mass of second body = 1.35 kg

[tex]v_{1i}[/tex] = initial velocity of the first body before collision = 4 ms⁻¹

[tex]v_{2i}[/tex] = initial velocity of the second body before collision = 0 m/s

Speed of the center of mass of two-body system is given as

[tex]v_{cm} = \frac{(m_{1} v_{1i} + m_{2} v_{2i})}{(m_{1} + m_{2})}\\v_{cm} = \frac{((2.7) (4) + (1.35) (0))}{(2.7 + 1.35)}\\\\v_{cm} = 2.67[/tex] ms⁻¹

Answer:

vB = 15.4 m/s

Explanation:

Principle of conservation of energy:

Because there is no friction the mechanical energy is conserve

ΔE = 0

ΔE : mechanical energy change (J)

K : Kinetic energy (J)

U: Potential energy (J)

K = (1/2)mv²

U = m*g*h

Where :

m: mass (kg)

v : speed (m/s)

h : hight (m)

Ef - Ei = 0

(K+U)final - (K+U)initial =0

(K+U)final = (K+U)initial

((1/2)mv²+m*g*h)final = ((1/2)mv²+m*g*h)initial , We divided by m both sides of the equation:

((1/2)vB² + g*hB = (1/2 )vA²+ g*hA

(1/2) (vB)² + (9.8)*(14.7) =  0 + (9.8)(26.8 )

(1/2) (vB)² = (9.8)(26.8 ) - (9.8)*(14.7)

(vB)² = (2)(9.8)(26.8 - 14.7)

(vB)² = 237.16

[tex]v_{B} = \sqrt{237.16}[/tex]

vB = 15.4 m/s : speed of the cart at B

Answer:

the guy above me is correct

Explanation:

Answer:

121 Joules

6.16717 m

Explanation:

m = Mass of the rocket = 2 kg

k = Spring constant = 800 N/m

x = Compression of spring = 0.55 m

Here, the kinetic energy of the spring and rocket will balance each other

[tex]\frac{1}{2}mu^2=\frac{1}{2}kx^2\\\Rightarrow u=\sqrt{\frac{kx^2}{m}}\\\Rightarrow u=\sqrt{\frac{800\times 0.55^2}{2}}\\\Rightarrow u=11\ m/s[/tex]

The initial velocity of the rocket is 11 m/s = u.

v = Final velocity

s = Displacement

a = Acceleration due to gravity = 9.81 m/s² = g

[tex]v^2-u^2=2as\\\Rightarrow s=\frac{v^2-u^2}{2a}\\\Rightarrow s=\frac{0^2-11^2}{2\times -9.81}\\\Rightarrow s=6.16717\ m[/tex]

The maximum height of the rocket will be 6.16717 m

Potential energy is given by

[tex]P=mgh\\\Rightarrow P=2\times 9.81\times \frac{0^2-11^2}{2\times -9.81}\\\Rightarrow P=121\ J[/tex]

The potential energy of the rocket at the maximum height will be 121 Joules

Answer:a) Each is at same temperature

Explanation:

According to the zeroth law of thermodynamics when two objects are in thermal equilibrium with the third one then they are at thermal equilibrium with each other thus they all are at the same temperature.

Here Also objects are in thermal Equilibrium then they should be at the same temperature.

As Internal Energy is an Extensive Property that depends on the amount of gas Present thus two gases at thermal Equilibrium can have different Temperatures.        

Final answer:

Objects at thermal equilibrium are at the same temperature, by the principle of thermal equilibrium and the Zeroth law of thermodynamics. This equilibrium does not require the objects to have the same internal energy or heat content.

Explanation:

For objects at thermal equilibrium, the correct statement is that each is at the same temperature. This is directly derived from the principle of thermal equilibrium, which states when two or more objects are in thermal contact and no heat flows between them, they are considered to be in thermal equilibrium. According to the Zeroth law of thermodynamics, if object A is in thermal equilibrium with object B, and object A is also in thermal equilibrium with object C, then objects B and C are in thermal equilibrium with one another. This invariably leads to the understanding that all objects at thermal equilibrium share the same temperature, but not necessarily the same internal energy or the same amount of heat.

While the law of conservation of energy ensures that the total energy in an isolated system remains constant, how this energy is distributed among objects (in terms of internal energy or heat) can vary significantly based on each object's specific heat capacity, mass, and other factors. Therefore, the correct answer to the question is: a. Each is at the same temperature.

Answer:

Adjusted forecast for January is 640

Explanation:

given,                                                                  

Demand forecast of a certain product = 800 units      

averaged over all months = 12 months                            

January monthly index = 0.8                                              

We have to find seasonally-adjustment sales for January

Adjusted forecast = ( Demand ) x ( monthly index )

                              =   800 x 0.8                              

                              =  640                                  

Adjusted forecast for January is 640

10 m/sec² acceleration is required for the tow truck to move this vehicle.

The rate at which an item changes its velocity is known as acceleration, a vector quantity. If an object's velocity is changing, it is acceleration.

The net acceleration that objects get as a result of the combined action of gravity and centrifugal force is known as the Earth's gravity, or g. It is a vector quantity whose strength or magnitude is determined by the norm and whose direction correlates with a plumb bob.

force = mass*acceleration

acceleration = force/mass

acceleration = 15000/1500

acceleration = 10 m/sec²

10 m/sec² acceleration is required for the tow truck to move this vehicle.

To learn more about acceleration refer to the link:

brainly.com/question/12550364

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The free-fall acceleration at the surface of Jupiter is approximately 24.79 m/s², which is more than two and two thirds times the gravitational pull experienced on Earth. A person weighing 150 pounds on Earth would weigh around 400 pounds on Jupiter.

The free-fall acceleration at the surface of Jupiter is approximately 24.79 m/s². This value is derived from using Newton's Law of Universal Gravitation and considering Jupiter's mass and radius. Jupiter has a mass about 300 times that of Earth and a radius approximately 11 times larger. The gravitational acceleration (g) at a planet's surface is given by the formula:

g = G x (mass of the planet) / (radius of the planet)²,

where G is the gravitational constant. Since the mass of Jupiter is much greater than that of Earth, and despite its larger radius, the acceleration due to gravity would be significantly higher on Jupiter. Therefore, an astronaut entering Jupiter's atmosphere would fall faster compared to falling through the Earth's atmosphere. If an astronaut who weighs 150 pounds on Earth were to stand on a scale on Jupiter, she would weigh approximately 400 pounds, which is more than two and two thirds times her weight on Earth. However, this value may vary slightly depending on whether she is near Jupiter's pole or equator, due to its oblateness.