An aluminum wire with a diameter of 0.115 mm has a uniform electric field of 0.235 V/m imposed along its entire length. The temperature of the wire is 55.0°C. Assume one free electron per atom. Given that at 20 degrees, rhoo = 2.82x10-8 Ωm and α = 3.9x10-3 /C. Determine:
a) the resistivity of the wire.
b) the current density in the wire.
c) the total current in the wire.
d) the potential different that must exist between the ends of a 2m length of wire if the given electric field is to be produced.

Answer:

The weight loss of object is equal to the weight of water displaced.

Explanation:

- When the object is immersed the force of Buoyancy acts against the weight and reducing the scale weight.

- The amount of Buoyancy Force is proportional to the fraction of Volume of object immersed in water; hence, the same amount is spilled/lost.

- The amount of water is proportional to the volume of object of fraction of object immersed in water will lead to the same fraction of water displaced and caught by Dr. Hewitt.  

Answer:

-14 e

Explanation:

Assuming oil drop is spherical then V = 4pi.r^3/3

density = 0.816 g/cm^3= 0.816 x 10^-3kg/cm^3= 0.816 x 10^-3/10^-6 kg/m^3= 0.816 x 10^3 kg/m^3

mass =(4 x 3.142 x (2.342 x 10^-6)^3 x 0.816 x 10^3)/3 kg

mass = (12.568 x 12.85 x 10^-18 x 0.816 x 10^3)/3 kg

m= 4.39 x 10^-14 kg

F=qE…. Eqn. 1

F=mg… Eqn. 2

Compare both eqn.1 and eqn. 2

qE=mg

q=mg/E

q = (4.39 x 10^-14 x 9.81)/1.92 x 10^5

q = 2.24 x 10^-18 C

Number of charges, n = 2.24 x 10^-18/1.62 x 10^-19

n=13.827

Charges come in integer values, nearest is 14

Number of charges is 14.

The direction of the field (downwards) is the direction a positive test charge would move. This means a positive charge would move downwards and repelled by the top plate which must be positive.

Since mg acts downwards then the other force must act up if the oil drop is suspended. This means that the charge is being attracted to the top plate which we have already determined is positive. for the charge to be attracted to the positive top plate then the charge must be negative.

Charge is electron hence the sign is minus.

-14 e

Answer:

The inductance of solenoid A is twice that of solenoid B

Explanation:

The inductance of a solenoid L is given by

L = μ₀n²Al where n = turns density, A = cross-sectional area of solenoid and l = length of solenoid.

Given that d₁ = 2d₂ and l₂ = 2l₁ and d₁ and d₂ are diameters of solenoids A and B respectively. Also, l₁ and l₂ are lengths of solenoids A and B respectively.

Since we have a cylindrical solenoid, the cross-section is a circle. So, A = πd²/4.

Let L₁ and L₂ be the inductances of solenoids A and B respectively.

So  L₁ = μ₀n²A₁l₁ = μ₀n²πd₁²l₁/4

L₂ = μ₀n²A₂l₂ = μ₀n²πd₂²l₂/4

Since d₁ = 2d₂ and l₂ = 2l₁, sub

L₁/L₂ = μ₀n²πd₁²l₁/4 ÷ μ₀n²πd₂²l₂/4 = d₁²/d₂² × l₁/l₂ = (2d₂)²/d₂² × l₁/2l₁ = 4d₂²/d₂²  × l₁/2l₁ = 4 × 1/2 = 2

L₁/L₂ = 2

L₁ = 2L₂

So, the inductance of solenoid A is twice that of solenoid B

Answer:

a. v = 1.679 × 10⁹ m/s b. The answer of v = 1.679 × 10⁹ m/s is not reasonable

Explanation:

Here is the complete question

You read in a science magazine that on the Moon, the speed of a shell leaving the barrel of a modern tank is enough to put the shell in a circular orbit above the surface of the Moon (there is no atmosphere to slow the shell).

A.....What should be the speed for this to happen? Assume that the radius of the Moon is rM = 1.74×106m, and the mass of the Moon is mM = 7.35×1022kg.(Express your answer to two significant figures and include the appropriate units.)

B.....Is this number reasonable?

Solution

From the question, the centripetal force in orbit for the shell = gravitational force of moon on shell.

So, mv²/r = GMm/r²

So v = √(GM/r) where v = velocity of shell, G = universal gravitational constant = 6.67 × 10⁻¹¹ Nm²/kg², M = mass of moon = 7.35 × 10²² kg and r = radius of moon = 1.74 × 10⁶ m.

v = √(GM/r) = v = √(6.67 × 10⁻¹¹ Nm²/kg² × 7.35 × 10²² kg/1.74 × 10⁶ m)

v = √(49.0245/1.74 × 10¹⁷) m/s

v = √28.175 × 10¹⁷ m/s

v = √2.8175 × 10¹⁸ m/s

v = 1.679 × 10⁹ m/s

b. The answer of v = 1.679 × 10⁹ m/s is not reasonable because, it is over 1000000 km/s which is greater than the speed of light which is 300000 km/s

Answer:

b. to the right

Explanation:

Final answer:

Using the left-hand rule for a negatively charged particle like an electron, the force on an electron moving upward with the magnetic field directed into the page is to the left. The correct answer is option c, to the left.

Explanation:

To determine the direction of the resultant force acting on an electron as it moves within a magnetic field, one can use the right-hand rule or, in the case of negatively charged particles like an electron, the left-hand rule. Considering that an electron is negatively charged, we apply the left-hand rule, with the thumb in the direction of the electron's velocity (from the bottom to the top edge of the screen), and the index finger in the direction of the magnetic field (into the page). The middle finger then points in the direction of the force experienced by the electron.

By this rule, for a magnetic field directed into the page and an electron moving upward, the resultant force will be to the left of the electron's initial direction of travel. The correct answer to the question is option c, to the left. This force will cause the electron to move in a circular path due to the magnetic Lorentz force.

Answer:

a. What impulse act on the ball during its collision with the floor?

b. If the ball is in contact with the floor for 0.04 s, what is the average force of the ball on he floor?

The answers to the question are

a. The impulse acting on the ball during its collision with the floor is

7.076 kg·m/s

b. The average force of the ball on the floor with contact of 0.04 s is

176.9 N

Explanation:

Mass of the ball = 0.61 kg

Initial velocity = -7 m/s

Final velocity = 4.6 m/s

Impulse = Δp = FΔt = mΔv

Where Δt =change in time

m = mass of Average force of he the ball

Δv = velocity change

Therefore impulse = m×(Final velocity - initial velocity)

= 0.61 × (4.6-(-7)) = 0.61×11.6

= 7.076 kg·m/s

b. Average force of the ball on the floor is given by

[tex]F_{Average}[/tex]×Δt = mΔv = 7.076 kg·m/s

where Δt = change in time = 4.6 m/s

Therefore [tex]F_{Average}[/tex] =mΔv /Δt = 7.076/0.04 = 176.9 kg·m/s²

= 176.9 N

Answer:

[tex]\Delta \theta =11.073\ rev[/tex]

Explanation:

Given,

Speed of baseball = 93 mi/h

spin = 1510 rev/min

[tex]\Delta x = 60\ ft[/tex]

[tex]v =93\times  \dfrac{88}{60} = 136.4 ft/s[/tex]

[tex]\omega = 1510\times \dfrac{1}{60}= 25.167\ rad/s[/tex]

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

[tex]\Delta t = \dfrac{60}{136.4 }[/tex]

[tex]\Delta t = 0.44\ s[/tex]

Revolutions of ball

[tex]\Delta \theta = \omega t[/tex]

[tex]\Delta \theta = 25.167\times 0.44[/tex]

[tex]\Delta \theta =11.073\ rev[/tex]

Revolution of the ball is equal to [tex]\Delta \theta =11.073\ rev[/tex].

Answer:

The magnetic field encircles the wire in a reversal or counterclockwise direction

Explanation:

Lenz's law states that the direction of the current induced in a conductor by a changing magnetic field is such that the magnetic field created by the induced current opposes the initial changing magnetic field which produced it. According to Lenz law, the magnetic field encircles the wire in a reversal or counterclockwise direction.

Therefore, the first option is the correct answer.

Human eye could perceive this visible light and used it to look at the objects.

Explanation:

There are 3 forms of radiation emitted by the sun. They are Infrared radiation, Ultra Violet radiation as well as visible radiation.

Visible light is the type of light can perceive by the human eye and utilizes to see the objects.  

Since the sun is hotter (5800 K) than the earth, it emits mostly the radiation energy in the form of this visible light.

Answer:

[tex]n \approx 5.778\times 10^{-4}\,rev[/tex]

Explanation:

The Work-Energy Theorem is applied herein:

[tex]-\frac{1}{4}\cdot m_{cyl}\cdot R^{2}\cdot \omega^{2} = - \mu_{k}\cdot N\cdot r \cdot 2\pi \cdot n[/tex]

The number of turns needed to stop the grindstone is:

[tex]n = \frac{m_{cyl}\cdot R^{2}\cdot \omega^{2}}{4\cdot \mu_{k}\cdot N \cdot r\cdot 2\pi}[/tex]

[tex]n = \frac{(15\,kg)\cdot (0.186\,m)^{2}\cdot [(1.83\,\frac{rev}{min} )\cdot (\frac{2\pi\,rad}{1\,rev} )\cdot (\frac{1\,min}{60\,s} )]^{2}}{4\cdot (0.80)\cdot (8.82\,N)\cdot(0.186\,m)\cdot 2\pi}[/tex]

[tex]n \approx 5.778\times 10^{-4}\,rev[/tex]

Answer:

(a)  [tex]y_{max}=0.423m[/tex]

(b)  [tex]\alpha =64.3^{o}[/tex]

Explanation:

Given data

[tex]v_{i}=12km/h=3.33m/s\\\alpha =60^{o}\\g=9.8m/s^{2}\\Required\\(a)y_{max}\\(b)Angle[/tex]

Solution

For Part (a)

As the velocity component in direction of y is given by:

[tex]v_{yi}=v_{i}Sin\alpha \\v_{yi}=3.33Sin60\\v_{yi}=2.88m/s[/tex]

The maximum displacement is given by:

[tex]v_{yf}^{2}=v_{yi}^{2}-2gy_{max}\\ y_{max}=\frac{(2.88)^{2}}{2(9.8)}\\ y_{max}=0.423m[/tex]

For Part (b)

To reach y=46cm =0.46m apply:

[tex]0=v_{yi}^{2}-2(9.8)(0.46)\\v_{yi}=3m/s\\As\\Sin\alpha =\frac{v_{yi}}{v_{i}}\\\alpha =Sin^{-1}(\frac{v_{yi}}{v_{i}})\\\alpha =Sin^{-1}(\frac{3}{3.33} )\\\alpha =64.3^{o}[/tex]

a) When launched at a 60° angle with a speed of 3.33 m/s, the robot cheetah can reach a maximum height of about 0.715 meters.

b) To reach a height of 0.46 meters, the launch angle needs to be approximately 31.74 degrees.

a) To find the maximum height (h_max) when the robot cheetah launches at a 60-degree angle with a speed of 3.33 m/s, we can use the following formula:

h_max = (u^2 * sin^2(θ)) / (2 * g)

Where:

u is the initial speed (3.33 m/s)

θ is the launch angle (60 degrees)

g is the acceleration due to gravity (9.8 m/s²)

First, calculate sin(60 degrees):

sin(60 degrees) = √3 / 2 ≈ 0.866

Now, plug in the values and calculate h_max:

h_max = (3.33^2 * (0.866)^2) / (2 * 9.8) ≈ 0.715 meters

b) To determine the launch angle (θ) required to reach a height of 0.46 meters (46 cm), we'll rearrange the same formula:

sin^2(θ) = (2 * g * h_desired) / u^2

Plug in the values:

sin^2(θ) = (2 * 9.8 * 0.46) / (3.33^2)

Now, find sin(θ):

sin(θ) ≈ √(0.2794) ≈ 0.5289

Finally, calculate θ:

θ ≈ arcsin(0.5289) ≈ 31.74 degrees

So, the launch angle required to reach a height of 0.46 meters is approximately 31.74 degrees.

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Answer:

Incomplete questions

Completed question, check attachment for diagram

Because the block is not moving, the sum of the y components of the forces acting on the block must be zero. Find an expression for the sum of the y components of the forces acting on the block, using coordinate system shown. Express your answer in terms of some or all of the variables

Fn, Ff, Fw and θ.

Explanation:

Check attachment for solution

Final answer:

The sum of the y components of forces on a stationary block must be zero due to Newton's second law, which results in the normal force being equal to the weight of the block.

Explanation:

In physics, when analyzing the forces acting on a stationary block, we apply Newton's second law, which implies that the net force in the y-component must be zero because the block is not moving vertically. An expression for the sum of the y components of the forces acting on the block can be deduced by considering all the vertical forces, including the weight of the block (acting downward) and the normal force (acting upward).

For a block on a frictionless surface attached to a spring, we consider the spring force and gravitational force. If the block is in equilibrium, these forces satisfy the equation mg = k Δy, where m is the mass of the block, g is the acceleration due to gravity, k is the spring constant, and Δy is the displacement from the equilibrium position. Therefore, the sum of the y components equates to zero: normal force - weight = 0, which also indicates that the normal force is equal to the weight.

Answer:

critical value is known as threshold

Explanation:

solution

when we apply electrical stimulus to the cell of muscle

then magnitude of stimulus will be strong enough for reaching the critical value

and this critical value is threshold because when the size of an stimulus change in requirement for the detection, this is called the threshold

but if change is done by without stimulation then there threshold stimulus is absolute threshold

so correct answer is threshold

Answer: Highly-elliptical-earth-orbit (heo)

Explanation: Highly-elliptical-earth-orbit (heo) satellite system has unique properties

which is used by governments for spying and by scientific agencies for observing celestial bodies. It is an extremely elongated orbit that is useful for communication satellites which creates signals between a source transmitter and a receiver at different locations on earth. They are used by government for spying, scientific agencies for observing celestial bodies, for the internet and telephone communications.

Answer:

Highly elliptical satellite orbit.

Explanation:

Highly elliptical satellite orbit is used to provide coverage over any point on the globe. The HEO is not limited to equatorial orbits like the geostationary orbit and the resulting lack of high latitude and polar coverage.

As a result of its ability to provide high latitude and polar coverage, countries such as Russia which need coverage over polar and near polar areas make significant use of highly elliptical orbits, HEO. With two satellites in any orbit, they are able to provide continuous coverage.

Answer:

Explanation:

The Big Bang theory is a cosmological model of the observable universe from the earliest known periods through its subsequent large-scale evolution.

These theories were based on the hypothesis that all the matter in the universe was created in one big bang at a particular time in the remote past.

What led to big bang theory was that free electrons would have caused light (photons) to scatter the way sunlight scatters from the water droplets in clouds," NASA stated. Over time, however, the free electrons met up with nuclei and created neutral atoms. This allowed light to shine through about 380,000 years after the Big Bang.

The best-supported theory of our universe's origin centers on an event known as the big bang. This theory was born of the observation that other galaxies are moving away from our own at great speed in all directions, as if they had all been propelled by an ancient explosive force.

Origins of the universe, explained

The most popular theory of our universe's origin centers on a cosmic cataclysm unmatched in all of history—the big bang.

The best-supported theory of our universe's origin centers on an event known as the big bang. This theory was born of the observation that other galaxies are moving away from our own at great speed in all directions, as if they had all been propelled by an ancient explosive force.

A Belgian priest named Georges Lemaître first suggested the big bang theory in the 1920s, when he theorized that the universe began from a single primordial atom. The idea received major boosts from Edwin Hubble's observations that galaxies are speeding away from us in all directions, as well as from the 1960s discovery of cosmic microwave radiation—interpreted as echoes of the big bang—by Arno Penzias and Robert Wilson.

Further work has helped clarify the big bang's tempo. Here’s the theory: In the first 10^-43 seconds of its existence, the universe was very compact, less than a million billion billionth the size of a single atom.

It's thought that at such an incomprehensibly dense, energetic state, the four fundamental forces—gravity, electromagnetism, and the strong and weak nuclear forces—were forged into a single force, but our current theories haven't yet figured out how a single, unified force would work. To pull this off, we'd need to know how gravity works on the subatomic scale, but we currently don't.

Answer: Tympanum

Explanation: A Tympanum could be described as the semicircular space above the doorway or window or entrance of a building. The space is usually designed using elaborate sculptural designs, Rocky costumes and ornaments. The tympanum could also be triangular-shaped and attributed to classical Greece and Roman architecture. It is usually located between the portals archivolt and the lintel. The tympanum is commonly observed in the churches and temples of ancient Rome and Greece.

The semicircular space above a doorway in a Romanesque church portal is called a tympanum and it was often decorated with intricate carvings relating to religious themes.

The prominent semicircular space above a doorway in a Romanesque church portal is referred to as a tympanum. These were often covered in elaborate carvings that represented religious imagery or important biblical stories. The Romanesque style of architecture, prevalent in Europe from the 9th to 12th centuries, was known for its massive quality, thick walls, and robust pillars. This style also romanticized elaborate decorative details, among them the beautifully carved tympanum.

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Answer:

[tex]a. C=8X\\\\b. A=\frac{16x^2}{\pi}[/tex]

Explanation:

Given length is [tex]8x[/tex]

Circumference of a circle is given as:

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

a.But the circumference is equal to length of the wire. Therefore circumference as a function of [tex]x[/tex] is:

[tex]C=8x[/tex]

b.Area as function of [tex]x[/tex]

Area is calculated as[tex]A=\pi r^2[/tex]

Rewrite the circumference equation to make r the subject of the formula.

[tex]2\pi r=8x\\r=\frac{4x}{\pi}[/tex]

To express area as a function of [tex]x[/tex]:-

[tex]A=\pi r^2\\=\pi (\frac{4x}{\pi})^2\\=\frac{16x^2}{\pi}[/tex]

Therefore area of circle as a function of [tex]x[/tex] is [tex]\frac{16x^2}{\pi}[/tex]

The circumference of the circle, represented as function of x, is C(x) = 8x. The area of the circle, represented as function of x, is A(x) = (16x²) / π.

The given length of the wire bent into a circle is 8x. This is equivalent to the circumference of this circle because a circle's circumference is the distance around it.

So, the function of the circumference, C, in terms of x is C(x) = 8x.

For the area of the circle, we must understand that the formula for the area of a circle is πr² where r is the radius of the circle. The radius is half the diameter, and since the circumference of a circle is πD where D is the diameter, we can find that r = circumference / (2π), or r = 8x / (2π).  

So, substituting r into the formula for the area, we get A(x) = π(8x / (2π))² = π(4x / π)² = π((4x)² / π²) = (16x²) / π.

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Answer: Rolling friction

Explanation:

Rolling friction is said to act when an object rolls over a surface. Machines often have moving parts. These moving parts roll over each other as the machine works. Ball bearings are commonly used to reduce friction between the two surfaces in contact as the machine parts roll over each other. This is a typical example of rolling friction as applied to machine parts.

Answer:

Rolling friction.

Explanation:

Rolling friction is the force resisting the motion when a body ( such as a ball, tires, wheel) rolls on a surface. It is applicable for bodies whose point of contact keeps changing. It is the force that opposes the motion of a body which is rolling over the surface of another.

Rolling resistance, sometimes called rolling friction or rolling drag, is the force resisting the motion when a body rolls on a surface. It is mainly caused by non-elastic effects; that is, not all the energy needed for deformation of the wheel, roadbed, etc. is recovered when the pressure is removed.

Tech B is correct.

Explanation:

Generally the electromagnet for a coil of wire, which allow the  system to transform electric energy into mechanical energy is understood as a solenoid, by generating  magnetic field from electric current and induces linear motion by utilizing the magnetic field. Every modern starters depend on the solenoid to use the flywheel ring gear to enable the start drive. When the solenoid is rejuvenated, a plunger or lever is controlled which pushes the ring gear into mesh with the pinion. A standard starter solenoid has one small adapter for the starter control wire and two major terminals: one for the positive battery cable, and another one for the thick wire that drive the starter motor by its own.

The correct answer is that both Tech A and Tech B are correct.

In a vehicle's starting system, the solenoid serves two main functions:

1. Switching High Current: When the ignition key is turned to start the engine, a small current flows through the solenoid coil, creating an electromagnetic field that pulls the solenoid plunger inward. This action closes a pair of heavy contacts, allowing a high current to flow from the battery to the starter motor. This is what Tech A is referring to when they mention that the solenoid switches the high current on and off.

2. Engaging the Starter Motor with the Ring Gear: The movement of the solenoid plunger also pushes a lever that engages the starter motor's pinion gear with the ring gear on the engine's flywheel. This engagement is necessary to turn the engine over during the starting process. This is the function that Tech B is describing.

Therefore, the solenoid is responsible for both switching the high current to the starter motor and engaging the starter motor with the ring gear. Both technicians are correct in their statements about the functions of the solenoid in the starting system.

Answer:

For further investigation see also the most recent World Population Data ... and Latin America and the Caribbean, and the regions of Melanesia, ... While Germany's death rate exceeds its birth rate, its population ... Population growth accelerated.

Answer:

an ice cream machine produced 44 ice cream per minute.

Now, after reconditioning it  speeds up to 55 ice cream per minute.

=> 55 - 44 = 11

=> 11 / 44 = 0.25

=> 0.25 * 100% = 25%.

thus it increased it production to 25%.

Explanation:

Answer:

25%

Explanation:

The way to find this answer is to:

Subtract 44 from 55 (11)

Then, you can put 11 over 44

Simplified, this is equal to 1/4.

1/4 as a percentage is 25%.

Good luck with your RSM work!

Answer:

They both intercept,focus and determine the intensity of an incoming radiation but at different degree.

Explanation:

Radio telescope is much larger than optical telescope because radio wavelengths are much longer than optical wavelengths. The longer the wavelengths implies that the radio waves has a lower energy than optical light waves. So, in order to collect enough radio photons to detect a signal, the radio dishes must be very large.

Answer: 1.25

Explanation:

The ratio of the amplitude of the sound can be calculated using the wave intensity by squaring the amplitude of the two wave particles.

Let the sound level be S2 and S1 and intensities be I1 and I2

Difference in sound level(S) = S2 - S1 = 2dB

Using the relationship between difference in sound level and Intensity

S2 - S1 = 10log(I2 ÷ I1)

Note : Intensity is the square of the amplitude of sound

Therefore,

I1 = A1^2 and I2 = A2^2

Substituting the values into the equation:

S2 - S1 = 10log (I2 ÷ I1)

2dB = 10log (A2^2 ÷ A1^2)

2dB = 10log(A2 ÷ A1)^2

2 dB= 20log(A2 ÷ A1)

2÷20 = log (A2 ÷ A1)

0.1 = log (A2 ÷ A1)

(A2 ÷ A1) = 10^0.1

A2/A1 = 1.25

Answer:

This is because, the flywheel has a very large moment of Inertia and hence sudden piston torques have negligible effect on the flywheel, but every piston combined has a significant torque. This smoothens out the vibrations.

Explanation:

Final answer:

A flywheel reduces engine vibrations by utilizing its angular momentum to smooth out the intermittent power delivery from piston firings, thus ensuring steady rotation of the crankshaft and maintaining engine speed during periods when power is not supplied.

Explanation:

The primary reason why a flywheel reduces engine vibrations in conventional piston engines is due to its ability to store rotational energy. When the pistons fire, they impart energy to the crankshaft, causing the engine to turn. This energy, however, is delivered in pulses rather than smoothly, which can lead to uneven rotation and vibrations. The flywheel, being a heavy rotating disk, has significant angular momentum. This momentum ensures that the flywheel continues to spin between these pulses of power, effectively smoothing out the rotation of the engine's crankshaft. This results in a reduction of the vibrations that occur due to the intermittent nature of power delivery from individual piston firings.

Flywheels also help maintain engine speed during the periods when no power is supplied, such as between combustion events in a four-stroke engine. This steady rotation is crucial for the engine's performance and longevity. Additionally, flywheels play a role in energy conservation, as they can store energy and release it when needed, which is particularly important in stopping and starting scenarios.

Answer: night vision goggles

Explanation: These goggles use technology to enhance all light, including the infrared rays, which aren't normally visible to the naked eye. This way you can see any type of light that is surrounding you.

please give brainliest!

Nothing does. That's why we can't see it without some sort of external imaging device.

Answer:

Weight = 734.46 N

Explanation:

Given:

Initial height of the pole-vaulter is, [tex]h_i=5.31\ m[/tex]

Final height of the pole-vaulter is, [tex]h_f=0\ m[/tex]

Change in the vaulter's potential energy is, [tex]\Delta U=-3900\ J[/tex]

We know that, change in potential energy is given as:

[tex]\Delta U=mg(h_f-h_i)[/tex]

Where, 'm' is the mass of the object, 'g' is acceleration due to gravity and has a value of 9.8 m/s².

Now, weight of the object is given as the product of its mass and acceleration due to gravity. So, replace 'mg' by weight 'w'. So, the equation becomes,

[tex]\Delta U = w(h_f-h_i)[/tex]

Now, rewriting in terms of 'w', we get:

[tex]w=\dfrac{\Delta U}{(h_f-h_i)}[/tex]

Now, plug in all the given values and solve for 'w'. This gives,

[tex]w=\dfrac{-3900\ J}{(0-5.31)\ m}\\\\\\w=\dfrac{3900}{5.31}\ N\\\\\\w=734.46\ N[/tex]

Therefore, weight of the vaulter is 734.46 N.

The weight of the pole-vaulter is calculated using the principle of conservation of mechanical energy and the equation for gravitational potential energy, resulting in a value of approximately 734.46 Newtons.

The question asked concerns the calculation of the weight of a pole-vaulter given a change in potential energy as the vaulter falls. The calculation can be made using the principle of conservation of mechanical energy, and the equation for gravitational potential energy: PE = mgh, where PE is potential energy, m is mass, g is the acceleration due to gravity, and h is the change in height.

The change in the vaulter's potential energy is given in the problem as -3900 J, which is negative because potential energy decreases as height decreases. Assuming that the entire change in potential energy is converted into kinetic energy, we can arrange the equation: -PE = mgh = weight * h for the weight of the vaulter, giving: weight = -PE / h.

Substituting the given values into this equation gives weight = (-(-3900 J)) / (5.31 m) = 734.46 N. So, the weight of the pole-vaulter is approximately 734.46 Newtons.

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Answer:

Force(F) = -80,955.01 N

Explanation:

We need to first determine the impulse that the truck driver received from the car during the collision

So; m₁v₁ - m₂v₂ = (m₁m₂)v₀

where;

m₁ = mass of the truck = 4280 kg

v₁ = v₂ =  speed of the each vehicle = 7.69 m/s

m₂ = mass of the car = 810 kg

Substituting our data; we have:

(4280×7.69) - (810×7.69) = (4280+810)v₀

32913.2 - 6228.9 = (5090)v₀

26684.1 =  (5090)v₀

v₀ = [tex]\frac{26684.1}{5090}[/tex]

v₀ = 5.25 m/s

NOW, Impulse on the truck = m (v₀ - v)

= 4280 × (5.25 - 7.69)

= 4280 ×  (-2.44)

= -10,443.2 kg. m/s

Force that the seat belt exert on the truck driver can be calculated as:

Impulse = Force × Time

-10,443.2 kg. m/s = F (0.129)

F = [tex]\frac{-10,443.2}{0.129}[/tex]

Force(F) = -80,955.01 N

Thus, the Force that the seat belt exert on the truck driver = -80,955.01 N

your question is missing the given conditions, here is the complete question;

Two machines, A and B, each working at a constant rate, can complete a certain task working together in 6 days. In how many days, working alone, can machine A complete the task?

(1) The average time A and B can complete the task working alone is 12.5 days.

(2) It would take machine A 5 more days to complete the task alone than it would take machine B to complete the task

Answer:

Machine A, working alone, can complete the task in 15 days.

Explanation:

As the average is given as 12.5 so,

A+B=2*12.5

A+ B=25

second condition says machine A takes 5 more days to complete the task alone than B so

A=B+5........Eq1

Now from the question statement we can get that

1/A+1/B=1/6, where A is time needed for A to do the task alone and B is the time needed for B to complete the task alone

thus, simplyfing above equation we get as

AB/A+B=6; \\ putting A+B=25 we get

AB/25=6

AB=6*25

AB=150; \\ putting Eq1 we get

(B+5)B=150

B^2+5B-150=0

simplifying the quadratic equation above we get B=10

putting B=10 in Eq1, we get

A+10=25

A=15

Thus, Machine A, working alone, can complete the task in 15 days.

The ratio of the work delivered by the turbine to the work consumed by the pump in the steam power plant is 1.

To determine the ratio of the work delivered by the turbine to the work consumed by the pump in the steam power plant, we need to consider the energy conversions that occur in the cycle. The work done by the turbine is equal to the area under the pressure-volume curve in the turbine phase, while the work consumed by the pump is equal to the area under the pressure-volume curve in the pump phase. Since the process is reversible and heat losses are negligible, the amount of work done in the turbine is equal to the amount of work consumed by the pump. Therefore, the ratio of the work delivered by the turbine to the work consumed by the pump is 1.

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Answer:

The ratio of moment of inertia of larger sphere to that of smaller sphere = 4

Explanation:

The moment of inertia of solid sphere is given by I = 2/5MR² where M = mass of sphere and R = radius of sphere.

Radius of smaller sphere = D/2

Radius of larger sphere = 2D/2 = D.

Moment of inertia of smaller sphere I₁ = 2/5M × D²/4 = MD²/10

Moment of inertia of larger sphere I₂ = 2/5M × D² = 2MD²/5

The ratio of moment of inertia of larger sphere to that of smaller sphere = I₂/I₁ = 2MD²/5 ÷ MD²/10 = 10 × 2/5 = 4