What is heat?
A. A measure of the movement of molecules inside an object
B. The transfer of energy from a hot object to a cold object
C. The force exerted on an area by an object
D. A measure of mass per unit volume of an object

Complete Question

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Answer:

The total pressure is  [tex]P_T = 10.79*10^{5} N/m^2[/tex]

The temperature at the bottom is [tex]T_b = 284.2 \ K[/tex]

Explanation:

From the question we are told that

    The length of the glass tube is  [tex]L = 1.50 \ m[/tex]

      The length of water  rise at the bottom of the lake  [tex]d = 1.33 \ m[/tex]

     The depth of the lake is  [tex]h = 100 \ m[/tex]

     The air temperature is [tex]T_a = 27 ^oC = 27 +273 = 300 \ K[/tex]

      The atmospheric pressure is  [tex]P_a = 1.01 *10^{5} N/m[/tex]

      The density of water is [tex]\rho = 998 \ kg/m^3[/tex]

The total pressure at the bottom of the lake is mathematically represented as

                 [tex]P_T = P_a + \rho g h[/tex]

substituting values

               [tex]P_T = 1.01*10^{5} + 998 * 9.8 * 100[/tex]

               [tex]P_T = 10.79*10^{5} N/m^2[/tex]

According to ideal gas law

         At the surface the glass tube not covered by water at surface

             [tex]P_a V_a = nRT_a[/tex]

Where is the volume of

             [tex]P_a *A * L = nRT_a[/tex]

 At the bottom of the lake  

           [tex]P_T V_b = nRT_b[/tex]

Where [tex]V_b[/tex] is the volume of the glass tube not covered by water at bottom

          and  [tex]T_b[/tex] i the temperature at the bottom

  So the ratio between the temperature  at the surface to the temperature at the bottom is mathematically represented as

             [tex]\frac{T_b}{T_a} = \frac{d * P_T}{P_a * h}[/tex]

substituting values

           [tex]\frac{T_b}{27} = \frac{0.133 * 10.79 *10^5}{1.01 *10^{5} * 1.5}[/tex]

   =>     [tex]T_b = 284.2 \ K[/tex]

Answer:

1.3*10^14 J

Explanation:

The energy of the satellite that orbits the earth is given by the second Newton law:

[tex]F=ma_c\\\\-G\frac{mM_s}{r^2}=m\frac{v^2}{r}\\\\v^2=\frac{GM}{r}\\\\E_T=K+U=G\frac{mM_s}{2r}-G\frac{mM}{r}=-G\frac{mM}{2r}[/tex]

where you have taken into account the centripetal acceleration of the satellite.

m: mass of the satellite

M_s: mass of the sun = 1.98*10^30 kg

G: Cavendish's constant = 6.67*10^-11 m^3/kg s^2

r: distance to the center of the Earth = Earth radius + distance satellite-Earth surface

To find the needed energy, you first compute the energy for a constant altitude of 99km:

r = 6.371*10^6m + 99*10^3m = 6.47*10^6 m

[tex]E_T=-(6.67*10^-11 m^3 /kg.s^2)\frac{(969kg)(1.98*10^{30}kg)}{2(6.47*10^6)}\\\\E_T=-9.88*10^{15} \ J[/tex]

Next, you calculate the energy for an altitude of 195km:

r = 6.371*10^6m + 195*10^{3}m = 6.56*10^6 m

[tex]E_T=-(6.67*10^-11 m^3 /kg.s^2)\frac{(969kg)(1.98*10^{30}kg)}{2(6.56*10^6)}\\\\E_T=-9.75*10^{15} \ J[/tex]

Finally, the energy required to put the satellite in the new orbit is:

-9.75*10^15 J - (-9.88*10^15 J) = 1.3*10^14 J

Answer:1960j

Explanation:

total input energy=2000j

98% of total input energy is useful

98% of 2000

98/100 x 2000

(98 x 2000) ➗ 100

196000 ➗ 100=1960

1960j is useful

The amount of useful transferred energy is  1960 J.

A body's capacity for work is measured in terms of energy. It cannot be produced or eliminated. There are numerous types of energy, including thermal, electrical, fusion, electrical, and nuclear. Energy has the ability to change its forms.

Efficiency is essentially a measurement of the amount of labour or energy that can be saved throughout a process. In other words, it's similar to comparing the energy input and output in any particular system. For instance, we observe that many processes result in the loss of effort or energy like vibration or waste heat.

Given parameters:

Total input energy; I =2000 Joule.

efficiency of the kettle; η = 98%.

We have to find useful output energy of the kettle: O = ?

We know that: output energy = efficiency × input energy

= 98% ×  2000 J.

 = 98/100 x 2000 J.

= (98 x 2000) ÷ 100 J.

= 196000 ÷ 100 J

= 1960 J.

Hence, the useful transferred energy is  1960 J.

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Answer:

Explanation:

On both sides of the film , the mediums have lower refractive index.

for interfering pattern from above , for constructive interference of reflected wave from both sides of the film , the condition is

2μt = ( 2n +1 ) λ / 2

μ is refractive index of film ,t is thickness of film λ is wavelength of light

n is order of fringe

for minimum thickness

n = 0

2μt =  λ / 2

t =  λ / 4μ

= 670 / 1.75 x 4

= 95.71 nm .

Answer:

9.2 amperes

Explanation:

Ohm's law states that the voltage V across a conductor of resistance R is given by [tex]V = R I[/tex]

Here, voltage V is proportional to the current I.

For voltage, unit is volts (V)

For current, unit is amperes (A)

For resistance, unit is Ohms (Ω)

Put R = 12.5 and V = 115 in V=RI

[tex]115=12.5I\\I=\frac{115}{12.5}\\ =9.2\,\,amperes[/tex]

Correct question is;

To regulate the intensity of light reaching our retinas, our pupils1 change diameter anywhere from 2 mm in bright light to 8 mm in dim light. Find the angular resolution of the eye for 550 nm wavelength light at those extremes. In which light can you see more sharply, dim or bright?

Answer:

We'll see more sharply in dim light

Explanation:

If we consider diffraction through a circular aperture, then angular resolution is given by;

θ = 1.22λ/D

where:

θ is the angular resolution (radians) λ is the wavelength of light

D is the diameter of the lens' aperture.

Thus,

at diameter = 2mm = 2 x 10^(-3) m = 2 x 10^(6) nm

θ = (1.22 * 550)/(2 x 10^(6))

θ = 335.5 x 10^(-6) radians

Now, we need to convert this to arc seconds.

Thus;

1 arc second = 4.85 x 10^(-6) radians

So,θ = 335.5 x 10^(-6) radians = [335.5 x 10^(-6)]/[4.85 x 10^(-6)]

= 69.18 arc seconds

at diameter = 8mm = 8 x 10^(-3) m = 8 x 10^(6) nm

θ = (1.22 * 550)/(8 x 10^(6))

θ = 83.875 x 10^(-6) radians

Now, we need to convert this to arc seconds.

Thus;

1 arc second = 4.85 x 10^(-6) radians

So,θ = 83.875 x 10^(-6) radians = [83.875 x 10^(-6)]/[4.85 x 10^(-6)]

= 17.3 arc seconds

From the values of angular resolution gotten, we see that sharpness of image increases with increasing angular resolution. Thus, objects are sharper in dim light.

Answer:

c. electric attraction is a force that can act at a distance.

Explanation:

stuisland

Final answer:

A negatively charged balloon attracting positively charged hair strands without contact illustrates that c. electric attraction can act at a distance.

Explanation:

When Katie rubs the balloon against her hair, electrons move from her hair to the balloon, resulting in the balloon having a negative charge and her hair having a positive charge. If the negatively charged balloon is brought near Katie's hair and the hair strands move toward it without direct contact, this demonstrates electric attraction as a force that can act at a distance.

Therefore, electric attraction is a force that can act at a distance. This example, similar to the effect observed when someone touches a Van de Graaff generator, shows charge separation and induction. It validates the scientific concept that electric forces can operate between charged objects even when they are not in physical contact.

Answer:

a) 423.64 KJ / mole

Explanation:

The pictures below explains it all in the calculation and i hope it helps you

An impulse is the product of force and the time interval during which that force is applied, resulting in a change of an object's momentum. It can be described both mathematically (J = F⋅Δt) and visually (area under the force-time curve). An impulse leads to an object's acceleration or deceleration and affects both speed and direction.

An impulse acting on an object is a concept in physics that describes the effect of a force applied over a period of time. It is the product of the average force and the time duration during which the force acts, resulting in a change in the object's momentum. The impulse experienced by an object can result in acceleration or deceleration, dependent on the direction of the force. Moreover, impulse is not just about the magnitude of force, but also the duration over which it is applied. A key point is that an impulse can be delivered either by a large force over a short period or a smaller force over a longer period, tailored to the specifics of a situation.

Impulse is measured as the change in momentum, which is the mass of the object multiplied by its velocity (mv). The formula for impulse is typically represented as J = F⋅Δt, where J represents impulse, F the force, and Δt the change in time. If you graph force versus time, the area under the curve represents the impulse, visually demonstrating the relationship between force, time, and momentum change.

It is essential to understand that impulse not only influences the speed of an object but also its direction of motion. For example, when a tennis player hits a ball, the racket imparts an impulse to the ball changing its momentum. The total impulse given by multiple forces is considered the net impulse, which is the sum of all individual impulses over a specified time.

Answer:

The magnetic field required required for the beam not to be deflected  is [tex]B = 0.0036T[/tex]

Explanation:

From the question we are told that

    The charge on the particle is [tex]q = +2e[/tex]

    The mass of the particle is  [tex]m = 6.64 *10^{-27} kg[/tex]

    The potential difference is [tex]V_a = 1.8 kV = 1.8 *10^{3} V[/tex]

    The potential difference between the two parallel plate is  [tex]V_b = 120 V[/tex]

    The separation between the plate is  [tex]d = 8 mm = \frac{8}{1000} = 8*10^{-3}m[/tex]

The Kinetic energy experienced by the beam before entering the region of the parallel plate is equivalent to the potential energy of the beam  after the region having a potential difference of 1.8kV

               [tex]KE_b = PE_b[/tex]

Generelly

              [tex]KE_b = \frac{1}{2} m v^2[/tex]

And      [tex]PE_b = q V_a[/tex]

 Equating this two formulas

              [tex]\frac{1}{2} mv^2 = q V_a[/tex]

making v the subject

           [tex]v = \sqrt{\frac{q V_a}{2 m} }[/tex]

Substituting value  

           [tex]v = \sqrt{\frac{ 2* 1.602 *10^{-19} * 1.8 *10^{3}}{2 * 6.64 *10^{-27}} }[/tex]

           [tex]v = 41.65*10^4 m/s[/tex]

Generally the electric field between the plates is mathematically represented as

                 [tex]E = \frac{V_b}{d}[/tex]  

Substituting value  

                 [tex]E = \frac{120}{8*10^{-3}}[/tex]              

                [tex]E = 15 *10^3 NC^{-1}[/tex]

the magnetic field  is mathematically evaluate    

                     [tex]B = \frac{E}{v}[/tex]

                   [tex]B = \frac{15 *10^{3}}{41.65 *10^4}[/tex]

                    [tex]B = 0.0036T[/tex]

Answer:

a) v3 = 1 m/s

c) K3 < K1

d) p3 = p1

Explanation:

a) To solve this problem you use the conservation of the linear momentum in elastic collision.

In the first case you have:

[tex]p_i=p_f\\\\m_1v_{1i}+m_2v_{2i}=m_1v_{1f}+m_2v_{2f}[/tex]

but the second block is at rest, then v2i = 0m/s:

[tex]m_1v_{1i}=m_1v_{1f}+m_2v_{2f}[/tex]

Furthermore, you can assume that the first object stops just after the collision with the second one. From this last expression you obtain the value of the second object:

[tex]v_{2f}=\frac{m_1v_{1i}}{m_2}\\\\m_2=2m_1\\\\v_{2f}=\frac{m_1(4m/s)}{2m_1}=2\ m/s[/tex]

Then, you use the conservation of momentum for the second case, in which the second objects impact the third one:

[tex]m_2v'_{2i}+m_3v_{3i}=m_2v'_{2f}+m_3v_{3f}\\\\v_{3i}=0\\\\m_2v'_{2i}=m_2v'_{2f}+m_3v_{3f}\\\\v_{2f}=0\\\\m_2v'_{2i}=m_3v_{3f}\\\\v_{3f}=\frac{m_2v'_{2i}}{m_3}[/tex]

where again it has assumed that the second object stops, just after the impact with the third object. v'_2i = v_2f (in order to distinguish). BY using the fact m3 = 2m2 you obtain:

[tex]v_{3f}=\frac{m_2(2m/s)}{2m_2}=1\ m/s[/tex]

Then, you obtain that v3 < v2 < v1

c) The kinetic energy is given by:

[tex]K=\frac{1}{2}mv^2[/tex]

you compute for all the three objects:

[tex]K_1=\frac{1}{2}m_1(4m/s)^2=8m_1\ m^2/s^2\\\\K_2=\frac{1}{2}m_2(2m/s)^2=\frac{1}{2}(2m_1)(4m^2/s^2)=4m_1\ m^2/s^2\\\\K_3=\frac{1}{2}m_3=(1m/s)^2=\frac{1}{2}(2m_2)(1\ m^2/s^2)=\frac{1}{2}(2(2m_1))(1 m^2/s^2)=2m_1\ m^2/s^2[/tex]

then, k3 < k2 < k1

d) For the momentum you have:

[tex]p_1=4m_1\ m/s\\\\p_2=m_2(2m/s)=(2m_1)(2m/s)=4m_1\ m/s\\\\p_3=m_3(1m/s)=(2m_2)(1m/s)=(2(2m_1))(1m/s)=4m_1\ m/s[/tex]

p1 = p2 = p3

A) the item required for the experiment is a stopwatch.

B) You are looking for time savings. To get this, divide the time by 10. The result is the period. The formula is given as

F  =  [tex]\frac{1}{T}[/tex] Where F is the frequency i.e. the number of cycles per second and T is the number of seconds per cycle.

C) One parameter of the pendulum that can be altered in order to affect the frequency of the pendulum is its length.  A pendulum with a longer string will have a lower frequency.

The one with a shorter length will have a higher frequency

D) In an environment that is thermally insulated perfectly, it means that any heat generated within the room is trapped within it. As the pendulum comes to rest, the room will experience a slight increase in temperature due to the conversion of mechanical energy to thermal energy.

Understanding the physics of pendulums helps one to get a better grasp of gravity, inertia, and centripetal force.

Pendulums are used for the construction or engineering of clocks, metronomes, sismometers, amusement park rides.

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The simple pendulum above consists of a bob hanging from a light string the experiments is :

A. Stopwatch

B. You are looking for time savings. To get this, divide the time by 10.

C. The one parameter of the pendulum that can be modified in arrange to influence the recurrence of the pendulum is its length.

D. In an environment that's thermally protects superbly

Answer A:

Answer B:

The experimental procedure that you would use is :

Where :

Answer C:

Answer D:

Uses of the pendulum experiments :

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The correct statements are: (b) All these technologies use radio waves, including high-frequency microwaves. (d) Microwave ovens emit in the same frequency band as some wireless Internet devices.

The correct statements that describe the various applications listed above are:

Statement a.) is incorrect because not all technologies listed use low-frequency microwaves. Statement c.) is incorrect because not all technologies listed use a combination of infrared waves and high-frequency microwaves. Statement e.) is incorrect because wireless Internet devices do not have the shortest wavelength among the technologies listed. Statement f.) is incorrect because the wavelengths of the technologies listed vary. Statement g.) is incorrect because the wavelengths of the technologies listed also vary.

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The correct answers are option (a) and option (d). All these technologies use radio waves, including low-frequency microwaves and Microwave ovens emit in the same frequency band as some wireless Internet devices.

The electromagnetic (EM) spectrum includes a wide range of frequencies, which are used in various modern technologies. Here are analyses correlating with the provided frequency ranges:

Answer:

Explanation:

Let θ be the inclination

downward acceleration on an inclined plane

= g sinθ

= 32 x sin6

a =  3.345 ft /s

a ) for knowing the speed at point B

v² = u² + 2 a s , v is final velocity , u is initial velocity , a is acceleration and s is distance travelled .

v² = 0 + 2 x 3.345 x 500

= 3345

v = 57.8 ft /s

from point B to C , the car decelerates so we shall find deceleration

v² = u² + 2 a s

0 = 3345 + 2 x a x 70      ( v becomes u here )

a = - 23.9 m /s²

net force on car during deceleration

= μmgcosθ - mg sinθ     where  μ is coefficient of static friction ,

= mg ( μcosθ -  sinθ )

deceleration = g ( μcosθ -  sinθ )

g ( μcosθ -  sinθ )  = 23.9

( μcosθ -  sinθ ) = .74

μcosθ = .74 + .104

= .8445

μ = .8445 / .9945

= .85 .

Final answer:

To calculate the maximum deceleration of a car heading down a 6° slope under different road conditions, we can use the coefficient of static friction. On dry concrete, the deceleration is approximately 2.12 m/s². On wet concrete, the deceleration is approximately 1.62 m/s². On ice, the deceleration is approximately 2.04 m/s².

Explanation:

To calculate the maximum deceleration of a car heading down a 6° slope, we need to consider the road conditions. Assuming the weight of the car is evenly distributed on all four tires, and that the tires are not allowed to slip during the deceleration, we can calculate the deceleration for different road conditions.

(a) On dry concrete, the coefficient of static friction can be calculated using the equation μs = tan(θ), where θ is the angle of the slope. In this case, the coefficient of static friction is approximately 0.105 and the maximum deceleration is approximately 2.12 m/s².

(b) On wet concrete, the coefficient of static friction is typically lower than on dry concrete. Let's assume a coefficient of 0.08. In this case, the maximum deceleration is approximately 1.62 m/s².

(c) On ice, assuming a coefficient of static friction of 0.100, the same as for shoes on ice, the maximum deceleration is approximately 2.04 m/s².

Answer:

The question above is repeated twice.

Removing the repetition, we have:  A plane flies toward a stationary siren at 1/4 the speed of sound. Then the plane stands still on the ground and the siren is driven toward it at 1/4 the speed of sound. In both cases, a person sitting in the plane will hear the same frequency of sound from the siren. True or False?

The correct answer to the question is "False"

Explanation:

The question above, illustrates a phenomenon referred to as "Doppler effect"

The Doppler effect only changes the frequency of the sound which explains how wavelength changes when a wave source is moving toward or away from an object. The Doppler effect occurs when a source of waves and/or observer move relative to each other.

When a sound source is moving toward the observer (a person sitting in the plane) in the case above,  the observer will hear a higher pitch as the source approaches. That is, the plane stands still on the ground and the siren is driven toward it.This is due to a decrease in the amplitude of the sound wave.

However, If the observer moves toward the stationary source, the observed frequency is higher than the source frequency. In this case, A plane flies toward a stationary siren.

λ = v/f = vT,

where T is the period,

The relationship  between frequency, speed, and wavelength is:

f = v/λ

v represents the speed of sound through the medium.

Doppler effect depends on things moving, as the observer moves, the frequency becomes higher as the distance decreases. If the observer moves and the distance becomes larger, it means that the sound frequency becomes lower.

Final answer:

The Doppler effect explains why a person sitting in a plane moving toward or away from a stationary siren at 1/4 the speed of sound perceives the same frequency of sound. This phenomenon is true due to the relative motion between the source of sound and the observer.

Explanation:

True

The phenomenon described in the question is related to the Doppler effect in physics. When a source of sound and an observer are in motion relative to each other, the frequency of the sound waves changes due to this motion. In this case, when the plane is moving toward or away from the siren at 1/4 the speed of sound, the observer perceives the same frequency of sound from the siren.

Answer: A BIRD BRAINLIEST PLEASE

Explanation: If a plane was traveling at the same velocity as a bird, which would have the most kinetic energy (assuming the plane has more mass)? ... So if a 747 weighs 750,000 times as much as a bird, at the same velocity it will have 750,000 times the kinetic energy.

The two objects have the same speed, thus the plane will have more kinetic energy compared to the bird.

Kinetic energy is the energy acquired by a body during its motion. This kinetic energy depends on the speed and mass of the object.

The formula for estimating kinetic energy is given as;

K.E = ¹/₂mv²

where;

The mass of the plane should be greater than the mass of the bird. Since the two objects have the same speed, we can conclude that the plane will have more kinetic energy compared to the bird.

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Answer:

8 minutes sooner

Explanation:

Average speed of snail= 4cm/min

Distance to be covered = 160cm

Time taken for the journey = distance/speed

Time taken for the journey = 160/4

Time taken for the journey = 40 min

If it crawed an average speed of 5cm/min

Distance = 160 cm

Time for the journey = distance/speed

Time for the journey = 160/5

Time for the journey = 32 min

Its going to take the snail 40 min - 32 min to Kno how sooner it will taje it if the average speed is 5cm/min

40 min - 32 min = 8 min

Complete question:

A person uses 25.0 J of kinetic energy to push an object for 11.0 s How are work and power affected if the person uses the same amount of kinetic energy to push the object in less time ?

Answer:

The power will increase, and the amount of work will remain the same

Explanation:

Given;

Kinetic energy, K = 25.0 J

time of work, t = 11.0 s

Power = work / time = Energy / time

This equation shows that power is inversely proportional to time

Also, Energy is directly proportional to work (both are measured in Joules)

Since the person will use the same amount of kinetic energy to push the object in less time.

It means that energy will be constant (work done will not change) and the time will be reduced.

Power and time are inversely proportional, decrease in time means increase in power.

Thus, the power will increase, and the amount of work will remain the same

Complete Question

The spaceship Intergalactica lands on the surface of the uninhabited Pink Planet, which orbits a rather average star in the distant Garbanzo Galaxy. A scouting party sets out to explore. The party's leader–a physicist, naturally–immediately makes a determination of the acceleration due to gravity on the Pink Planet's surface by means of a simple pendulum of length 1.08m. She sets the pendulum swinging, and her collaborators carefully count 101 complete cycles of oscillation during 2.00×102 s. What is the result? acceleration due to gravity:acceleration due to gravity: m/s2

Answer:

The acceleration due to gravity is  [tex]g = 167.2 \ m/s^2[/tex]  

Explanation:

From the question we are told that

     The length of the simple pendulum is [tex]L = 1.081.08 \ m[/tex]

      The number of cycles is  [tex]N = 101[/tex]

       The time take is  [tex]t = 2.00 *10^{2 \ }s[/tex]

Generally the period of this oscillation is mathematically evaluated as

         [tex]T = \frac{N}{t }[/tex]

substituting values

         [tex]T = \frac{101}{2.0*10^2 }[/tex]

        [tex]T = 0.505 \ s[/tex]

The period of this oscillation is mathematically represented  as

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

making g the subject of the formula we have

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

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

Substituting values

               [tex]g = \frac{4 * 3.142 ^2 * 1.08 }{505.505^2 }[/tex]

               [tex]g = \frac{4 * 3.142 ^2 * 1.08 }{0.505^2 }[/tex]  

              [tex]g = 167.2 \ m/s^2[/tex]  

Answer:

1*10^6 N/m^2

Explanation:

Coefficient of Linear Expansion for Concrete = α = 1.2 x 10^-5 (°C)^-1

Change in temperature = ΔT

ΔT= T2 - T1

ΔT = 33 - 21

ΔT = 12°C

ΔL = α * L(i) * ΔT

ΔL = (1.2 x 10^-5 (°C)^-1) * L(i) * (12°C)

ΔL = 1.44 x 10^-4

Stress = F / A

Strain = ΔL / L

Strain = (1.44*10^-4) * (L) / L

Strain = 1.44*10^-4

Y = Stress / Strain

Stress = Y * Strain

Stress = (7.00*10^9 N/m^2) * (1.44*10^-4)

Stress = 1*10^6 N/m^2

Thus, the stress in the cement on a hot day of 33° is 1*10^6 N/m^2

Answer:

Tension maximum =1131.9 N

Tension minimum =868.28 N

Tension at 3/4= 1065.995 N

Explanation:

a)

Given Mass of wrecking ball M1=88.6 Kg

Mass of the chain M2=26.9 Kg

Maximum Tension Tension max=(M1+M2) × (9.8 m/s²)

=(88.6+26.9) × (9.8 m/s²)

=115.5 × 9.8 m/s²

Tension maximum =1131.9 N

b)

Minimum Tension Tension minimum=Mass of the wrecking ball only × 9.8 m/s²

=88.6 × 9.8 m/s²

Tension minimum =868.28 N

c)

Tension at 3/4 from the bottom of the chain =In this part you have to use 75% of the chain so you have to take 3/4 of 26.9

= (3/4 × 26.9)+88.9) × 9.8 m/s²

= (20.175+88.6) × 9.8 m/s²

=(108.775) × 9.8 m/s²

=1065.995 N

Final answer:

The maximum tension in the chain is 1131.9 N, occurring at the top, while the minimum tension is 263.62 N at the bottom. The tension at a point three-fourths the way up from the bottom is 935.465 N.

Explanation:

To find the maximum and minimum tension in the chain, we need to consider the system's configuration, and the force due to gravity. The maximum tension occurs at the top of the chain, where it supports the entire weight of the wrecking ball and the chain. The minimum tension occurs at the bottom of the chain, where it only needs to support the chain's weight. To find the tension at a point three-fourths of the way up from the bottom, we need to consider the weight of the portion of the chain below that point and the wrecking ball's weight.

Maximum tension (Tmax) is the sum of the weight of the wrecking ball and the entire chain:
Tmax = (mass of ball + mass of chain) × gravitational acceleration
Tmax = (88.6 kg + 26.9 kg) × 9.80 m/s²
Tmax = 115.5 kg × 9.80 m/s²
Tmax = 1131.9 N

Minimum tension (Tmin) is just the weight of the chain:
Tmin = mass of chain × gravitational acceleration
Tmin = 26.9 kg × 9.80 m/s²
Tmin = 263.62 N

Tension at three-fourths the way up:
We calculate the weight of the top one-fourth of the chain plus the wrecking ball:
Tension at three-fourths the way up = (mass of one-fourth of the chain + mass of ball) × gravitational acceleration
Tension at three-fourths = ((26.9 kg / 4) + 88.6 kg) × 9.80 m/s²
Tension at three-fourths = (6.725 kg + 88.6 kg) × 9.80 m/s²
Tension at three-fourths = 935.465 N

Answer:

D. The object will continue to move with a constant velocity

Explanation:

According to Newton's first law also known as law of inertia, states that an object at rest will remain at rest or, if in motion, will remain in motion at constant velocity unless acted on by a net external force.

Therefore, An object moving in the absence of a net force will continue to move at a constant velocity

In the absence of a net force, an object will continue to move with a constant velocity.

The correct answer is D. The object will continue to move with a constant velocity. In the absence of a net force, an object will continue to move at a constant velocity. This means that the object will continue to move in a straight line at the same speed without slowing down or changing direction.

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The unit vector forms of the given vectors is required.

The required vectors are [tex]A=-8.93\hat{i}+15.16\hat{j}[/tex] and [tex]B=-10.75\hat{i}-18.84\hat{j}[/tex]

Magnitude of vector A = [tex]|A|=17.6[/tex]

Angle vector A makes with positive x axis counter clockwise = [tex]\theta_1=120.5^{\circ}[/tex]

Magnitude of vector B = [tex]|B|=21.7[/tex]

Angle vector B makes with positive x axis counter clockwise = [tex]\theta_2=240.3^{\circ}[/tex]

The vectors need to be resolved in order to write in the unit vector forms.

The vectors are

[tex]A=|A|(\cos\theta_1\hat{i}+\sin\theta_1\hat{j})\\\Rightarrow A=17.6(\cos120.5\hat{i}+\sin120.5\hat{j})\\\Rightarrow A=-8.93\hat{i}+15.16\hat{j}[/tex]

[tex]B=|B|(\cos\theta_2\hat{i}+\sin\theta_2\hat{j})\\\Rightarrow B=21.7(\cos240.3\hat{i}+\sin240.3\hat{j})\\\Rightarrow B=-10.75\hat{i}-18.84\hat{j}[/tex]

Learn more about vectors:

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Final answer:

To resolve the vectors into components, apply trigonometric functions -- cosine for x components and sine for y components -- to their magnitudes and angles, then express them in unit vector form with i and j.

Explanation:

When resolving vectors A and B into their components in the x-y plane, the general method involves using trigonometry, specifically, the cosine and sine functions for the x and y components, respectively. Given that vector A has a magnitude of 17.6 and an angle of 120.5° from the x-axis, its components can be calculated as follows:

Ax = A * cos(θ) = 17.6 * cos(120.5°)

Ay = A * sin(θ) = 17.6 * sin(120.5°)

Similarly, vector B with a magnitude of 21.7 and an angle of 240.3° from the x-axis has components:

Bx = B * cos(θ) = 21.7 * cos(240.3°)

By = B * sin(θ) = 21.7 * sin(240.3°)

The resulting components should then be written in unit vector form by attaching the unit vectors i (for the x-axis) and j (for the y-axis) to the respective components.

Answer:

The number of molecules in the volume is  [tex]N_v = 2.27109* 10^{12}[/tex] molecules

Explanation:

From the question we are told that

    The pressure of the ultrahigh vacuum is [tex]P = 8.4*10^{-11} torr = 8.4*10^{-11} * 133 = 1.1172 *10^{-8}Pa[/tex]

     The molecular diameter of the gas molecules [tex]d = 2.2*10^{-10} m[/tex]

      The temperature is  [tex]T = 310 \ K[/tex]

      Avogadro's number is [tex]N = 6.02214 *10^{23}\ l/mol[/tex]

        The volume of the gas is [tex]V = 0.87 m^3[/tex]

From the ideal gas law[[tex]PV = nRT[/tex]] that the number of mole is mathematically represented as

           [tex]n = \frac{PV}{RT}[/tex]

Where R is the gas constant with a value  [tex]R = 8.314\ J/mol[/tex]

  Substituting values

              [tex]n = \frac{1.1172 *10^{-8} * 0.87}{8.314 * 310}[/tex]

             [tex]n = 3.771*10^{-12} \ mole[/tex]

The number of molecules is mathematically represented as

               [tex]N_v = n * N[/tex]

  Substituting values

              [tex]N_v = 3.771*10^{-12} * 6.02214 *10^{23}[/tex]

             [tex]N_v = 2.27109* 10^{12}[/tex] molecules

The speed of the train can be calculated using the formula for the Doppler effect. Using the given frequencies and the speed of sound in air, the student can calculate the speed of the train to be approximately 8.7 m/s.

To calculate the speed of the train, we can use the formula for the Doppler effect. The formula is given by:

Δf/f = v/c

Where Δf is the change in frequency, f is the frequency observed when the train is at rest, v is the speed of the train, and c is the speed of sound in air.

Using the given frequencies of 491 Hz and 472 Hz, and the speed of sound in air of 343 m/s, we can calculate the speed of the train:

v = (Δf/f) * c = (491 - 472) / 491 * 343 = 8.7 m/s

Therefore, the student finds that the speed of the train is approximately 8.7 m/s.

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Given the observed frequencies of 491 Hz when approaching and 472 Hz when receding, the calculated speed of the train is approximately 6.66 m/s. This calculation assumes the speed of sound in air is 343 m/s.

The question involves using the Doppler Effect to calculate the speed of the train. The Doppler Effect formula for a source moving towards a stationary observer is:

[tex]f'_{approach} = f \times (v + v_o)/(v - v_s)[/tex]

and when the source is moving away:

[tex]f'_{recede} = f \times (v - v_o)/(v + v_s)[/tex]

where:

Given:

First, solve for the source frequency (f) using both equations.

For the approaching train:

[tex]491 = f \times (343) / (343 - v_s)[/tex]

For the receding train:

[tex]472 = f \times (343) / (343 + v_s)[/tex]

Divide the two frequency equations to eliminate f:

(491 / 472) = (343 + [tex]v_s[/tex]) / (343 - [tex]v_s[/tex])

Cross-multiplying and solving for [tex]v_s[/tex]:

491 × (343 - [tex]v_s[/tex]) = 472 × (343 + [tex]v_s[/tex])

491 × 343 - 491 × [tex]v_s[/tex] = 472 × 343 + 472 × [tex]v_s[/tex]

168313 - 491 × [tex]v_s[/tex] = 161896 + 472 × [tex]v_s[/tex]

168313 - 161896 = 491 × [tex]v_s[/tex] + 472 × [tex]v_s[/tex]

6417 = 963 × [tex]v_s[/tex]

[tex]v_s[/tex] = 6417 / 963

[tex]v_s[/tex] ≈ 6.66 m/s

Therefore, the student calculates the speed of the train to be approximately 6.66 m/s.

The horizontal distance (d) a block travels after being released from a slide is limited by the initial velocity from the slide and the time of flight from the table. Mathematical considerations of kinetic energy and projectile motion demonstrate why the distances h1 and h2 are crucial factors. On the Moon, the block would travel further due to reduced gravity.

The horizontal distance (d) that a block travels after sliding down a slide and falling off a table is dependent on both the vertical height dropped and the velocity with which it leaves the table. If we make height h1 (the slide) very small, the velocity of the block at the bottom of the slide and consequently at the end of the table would be small because it would have converted a smaller amount of potential energy into kinetic energy. This would result in a small horizontal distance (d) even though height h2 (the table) is large. Conversely, making height h2 (the table) very small would mean that the block doesn't have much height to fall from, which limits the total time it has to move horizontally, again resulting in a small d.

In analyzing both scenarios mathematically, the relationship between the horizontal distance and the heights would involve equations of motion and energy conservation. The step that supports reasoning in part (a)i would involve the equation for kinetic energy at the end of the slide (KE = 1/2 m[tex]v^2[/tex]), which is maximized when h1 is large. Similarly, the step supporting part (a)ii is Newton's equations of motion for projectile motion (particularly, time of flight = sqrt(2h2/g)), where increasing h2 increases the time the block spends in air and thus d.

When repeating the experiment on the Moon, the new landing distance d will be greater than the landing distance when performed on Earth. This is because the acceleration due to gravity on the Moon is less than on Earth, which increases the time the block spends in the air.

Complete Question

If a sound with frequency fs is produced by a source traveling along a line with speed vs and an observer is traveling with speed vo along the same line from the opposite direction toward the source, then the frequency of the sound heard by the observer is

f_o = [(c+v_o)/(c-v_s)] f_s

where c is the speed of sound, about 332 m/s. (This is the Doppler effect). Suppose that, at a particular moment, you are in a train traveling at 34 m/s and accelerating at 1.2 m/s^2. A train is approaching you from the opposite direction on the other track at 40 m/s, accelerating at 1.4 m/s^2, and sounds its whistle, which has a frequency of 460Hz. At that instant, what is the perceived frequency that you hear and how fast is it changing?

Answer:

The frequency the person hears is  [tex]f_o = 557 Hz[/tex]

The speed at which it is changing is [tex]\frac{df_o}{dt} = 4.655 Hz/s[/tex]

Explanation:

Form the question we are told that

       The frequency of the sound produced by source is  [tex]f_s[/tex]

        The speed of the source is  [tex]v_s[/tex]

         The speed of the observer

         The frequency of sound heard by observer  [tex]f_o =[ \frac{c + v_o }{c - v_s} ] * f_s[/tex]

          The speed of sound is  c  with value [tex]c = 332 m/s[/tex]

Looking the question we can deduce that the person in the first train is the observer so the

            [tex]v_o = 34 m/s[/tex]

and the acceleration is  [tex]\frac{dv_o}{dt} = 1.2 m/s^2[/tex]

The train the travelling in the opposite direction the blew the whistle

is the source

    So   [tex]v_s = 40 m/s[/tex]

    and  [tex]f_s = 460 Hz[/tex]

and the acceleration is  [tex]\frac{dv_s}{dt} = 1.4 m/s^2[/tex]  

   We are told that

           [tex]f_o =[ \frac{c + v_o }{c - v_s} ] * f_s[/tex]

Substituting values we have that  

          [tex]f_o =[ \frac{332 + 34 }{332 - v40} ] * 460[/tex]

        [tex]f_o = 557 Hz[/tex]

  Differentiating [tex]f_o[/tex]  using chain rule we have that

         [tex]\frac{d f_o}{dt} = \frac{df_o}{dt } * \frac{dv_o}{dt} + \frac{d f_o}{dv_s} * \frac{dv_s}{dt}[/tex]    

Now  

           [tex]\frac{df_o}{dt } = \frac{f_s}{c- v_s}[/tex]

           [tex]\frac{df_o}{dv_s} = \frac{c+ v_o}{c-v_s} f_s[/tex]

Substituting this into the equation

         [tex]\frac{df_o}{dt} = \frac{f_s}{c-v_s} * \frac{d v_o}{dt} + \frac{c+v_o}{(c-v_s)^2} f_s * \frac{dv_s}{dt}[/tex]

Now substituting values

         [tex]\frac{df_o}{dt} = \frac{460}{332 - 40} * (1.2) + \frac{332+ 34}{(332- 40)^2} 460 * 1.4[/tex]

          [tex]\frac{df_o}{dt} = 4.655 Hz/s[/tex]

Answer:

7.44 m/s

Explanation:

Units

The first thing you must do is get the units.

The distance is in meters.

The time is in seconds.

Therefore the speed is going to be in meters/second.

Givens

d = 2345 meters

t = 315 seconds

Solution

s = d/t

s = 2345/315

s = 7.44 meters/second

Answer:

741 J/kg°C

Explanation:

Given that

Initial temperature of glass, T(g) = 72° C

Specific heat capacity of glass, c(g) = 840 J/kg°C

Temperature of liquid, T(l)= 40° C

Final temperature, T(2) = 57° C

Specific heat capacity of the liquid, c(l) = ?

Using the relation

Heat gained by the liquid = Heat lost by the glass

m(l).C(l).ΔT(l) = m(g).C(g).ΔT(g)

Since their mass are the same, then

C(l)ΔT(l) = C(g)ΔT(g)

C(l) = C(g)ΔT(g) / ΔT(l)

C(l) = 840 * (72 - 57) / (57 - 40)

C(l) = 12600 / 17

C(l) = 741 J/kg°C