One way to keep the contents of a garage from becoming too cold on a night when a severe subfreezing temperature is forecast is to put a tub of water in the garage. If the mass of the water is 148 kg and its initial temperature is 22.3°C, how much energy must the water transfer to its surroundings in order to freeze completely?

Answer:

(a) [tex]K = \frac{I}{2\pi a}[/tex]

(b) [tex]J = \frac{I}{2\pi as}[/tex]

Explanation:

(a) The surface current density of a conductor is the current flowing per unit length of the conductor.

                                   [tex]K = \frac{dI}{dL}[/tex]

Considering a wire, the current is uniformly distributed over the circumferenece of the wire.

                                   [tex]dL = 2\pi r[/tex]

The radius of the wire = a

                                    [tex]dL = 2\pi a[/tex]

The surface current density [tex]K = \frac{I}{2\pi a}[/tex]

(b) The current density is inversely proportional

                                     [tex]J \alpha  s^{-1}[/tex]    

                                     [tex]J = \frac{k}{s}[/tex]           ......(1)

k is the constant of proportionality

                                     [tex]I = \int\limits {J} \, dS[/tex]

                                     [tex]I = J \int\limits \, dS[/tex]     ........(2)

substituting (1) into (2)

                                     [tex]I = \frac{k}{s} \int\limits\, dS[/tex]

                                     [tex]I = k \int\limits^a_0 \frac{1}{s}  {s} \, dS[/tex]

                                     [tex]I = 2\pi k\int\limits\, dS[/tex]

                                     [tex]I = 2\pi ka[/tex]

                                     [tex]k = \frac{I}{2\pi a}[/tex]

substitute [tex]J = \frac{k}{s}[/tex]

                                     [tex]J = \frac{I}{2\pi as}[/tex]

In a wire with current I and radius a, the surface current density K with uniform distribution is I/(2πaL). If volume current density varies inversely with the radius, the current is more dense at the center and less dense towards the surface, described by I/(πa²L).

The subject here relates to the physical properties of the current flowing down a wire with a certain radius. (a) If the current I is uniformly distributed over the surface of the wire with a radius a, then the surface current density K can be given by the total current (I) divided by the surface area of the wire. In this context, the surface area of a cylindrical wire can be calculated by the formula 2π * a * L, where L is the length of the wire. Therefore, the surface current density K is I/(2πaL).

(b) If the current is distributed such that the volume current density J is inversely proportional to the radius, it implies that the current is more dense at the center of the wire and less dense as you approach the surface. The volume current density J can be described by the formula I/(πa²L). This complex distribution would likely require calculus to derive an exact relationship between current density and radius.

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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.

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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:

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

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:

T = 2.4 s

Explanation:

given,

angle at which ball is thrown = 29°

speed relative to ground = 24.3 m/s

ball is caught at a distance = 51.0463

acceleration due to gravity = 9.8 m/s²

time for which ball was in the air = ?

now,

velocity of ball in x-direction

V_x =  v cos θ

V_x =  24.3 x cos 29°

V_x = 21.25 m/s

velocity in y direction

V_y =  v sin θ

V_y =  24.3 x sin 29°

V_y = 11.78 m/s

distance on the ground when ball will reach maximum height

x = 51.0463/2 = 25.52 m

at top most point velocity is equal to zero

time for which the ball was in air

v = u + a t

0 = 11.78 - 9.8 t

[tex]t = \dfrac{11.78}{9.8}[/tex]

t = 1.20

this time is taken to travel half distance

total time = 2 x 1.20

T = 2.4 s

time for which ball was in air is T = 2.4 s

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:

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:

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.

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.

Because they perform specific tasks repeatedly throughout your program, as needed

Answer:

Because they perform specific tasks repeatedly throughout your program, as needed

Explanation:

Answer:

Lack of proper roof ventilation

Explanation:

The icicles hanging off the eaves of a roof are due to lack of proper roof ventilation. This means after snowfalls the attic of the roof receives warm air which melts the snow above. This is caused because the upper part of roof is above 32⁰C (which melts the snow) and lower part of your roof is at a lower temperature which refreezes the snow dripping down to form icicles.

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:

15.65 °C

Explanation:

cold temperature (Tc) = -15.5 degree C = 273.15 - 15.5 = 257.65 kelvin

minimum coefficient of performance (η) = 8.25

find the maximum hot reservoir temperature of such a generator (Th)

η = \frac{Tc}{Th-Tc}

Th = Tc x (\frac{1}{η} + 1)

Th = 257.65 x (\frac{1}{8.25} + 1)

Th = 288.8 K

Th = 288.8 - 273.15 = 15.65 °C

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.

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: 2/3 of the total volume

Explanation:

See attachment for details

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

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.

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.

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.

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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:

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

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.

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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.

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:

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:

a) v=1.81 m/s; B) v=4.95 m/s

Explanation:

using momentum conservation

m1v1+m2v1=m1v2+m2v2

A)

5.2*672+700*0=5.2*428+700v2

The initial velocity of the block is 0, solving for v2

v2=1.81 m/s

B) Now both the bullet and the block travel together

m1v1+m2v1=(m1+m2)v2

5.2*672+700*0=(5.2+700)v

v=4.95 m/s

a. To find the resulting speed of the block after the bullet strikes it, we can use the law of conservation of momentum. b. The speed of the bullet-block center of mass can be found by calculating the weighted average of the speeds of the bullet and block.

a. To find the resulting speed of the block, we can use the law of conservation of momentum. The momentum before the collision is equal to the momentum after the collision.

The initial momentum of the bullet is given by m1 * v1, and the final momentum is given by (m1 + m2) * vf, where m1 is the mass of the bullet, v1 is the initial velocity of the bullet, m2 is the mass of the block, and vf is the final velocity of the bullet and block combined.

Using these values, we can solve for vf and then find the resulting speed of the block.

b. The speed of the bullet-block center of mass can be found by calculating the weighted average of the speeds of the bullet and block. Since the mass of the bullet is much smaller than the mass of the block, the center of mass will be closer to the speed of the block.

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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