A man on the 14 th floor of a building sees a bucket (dropped by a window washer) passing his window and notes that it hits the ground 1 second later. Assuming a floor is 4.9 meters high (and neglecting air friction), from what floor was the bucket dropped?

Answer:

qa/qb = 0.3125

Explanation:

Let the distance of the point from first charge (qa) be ra.

Likewise, let the distance of the point from the second charge (qb) be ra

Now, from the question, ra=0.15m

While rb = 0.48m

Normally, we know that:

The electric potential due to a point charge, q, at a point located at a distance, r, away from it is given by the equation;

V = q/(4π(ϵo)r)

We know that 1/(4π(ϵo)) cam be said to ne K.

Therefore, V = Kq/r

Where K = 9 × 10^(9) V.m/C

Now, since from the question, the electric potential at the point is the same due to each of the charges, their electric potential will be the same, thus;

Va = Vb

So, (Kqa) / ra = (Kqb) / rb

This gives us; qa / ra = qb / rb

So rearranging, we get;

qa/qb = ra/rb = 0.15/0.48 = 0.3125

The ratio qB/qA of the charges is 3.2.

The electric potential owing to a point charge Q at a distance r from the charge is given as:

V = kQ / r

where k is the electrostatic constant.  

Since the potentials due to charges A and B are equal at the given spot, we can write:

VA = VB

Substituting the values:

kQA / 0.15 = kBQB / 0.48

Simplifying:

qB/qA = 0.48 / 0.15 = 3.2

Answer:

C. It decreases

Explanation:

The pressure law states that for a constant volume of gas in a sealed container the temperature of the gas is directly proportional to its pressure. This can be easily understood by visualizing the particles of gas in the container moving with a greater energy when the temperature is increased.

A common example is cooking gas when refilled, there is a perceptible change in the temperature of the cylinder.

Answer:

How much energy does it take to melt a 16.87 g ice cube? ΔHfus = 6.02 kJ/mol How much energy does it take to melt a 16.87 g ice cube? = 6.02 kJ/mol

A. 108 kJ

B. 102 kJ

C. 5.64 kJ

D. 936 kJ

E. none of the above

5.64 kJ

Explanation:

The Heat of fusion is the heat energy required to dissolve a given mass of ice at melting point.

The heat energy required to dissolve ice can be calculated using the expression below;

Q = ΔH[tex]_{f}[/tex] x m ...............................................1

where Q is the heat energy required;

           ΔH[tex]_{f}[/tex]  is the heat of fusion for ice;

           m is the mole

All the parameters above are provided in the question except m, so to get m we use the molar mass of water (also for ice) which is 18.01528 g/mol .

This means that 18.01528 g of ice is contained in one mole, therefore the mole for 16.87 g of ice is given as;

[tex]m = \frac{16.87g}{18.015g/mol}[/tex]

m = 0.9364 mole of ices

Now the parameters are complete, we are given;

ΔH[tex]_{f}[/tex]  = 6.02 kJ/mol

m = 0.9364 mol

Q =?

Substituting into equation 1, we have

Q =  6.02 kJ/mol x 0.9364 mol

Q = 5.64 kJ

Therefore, the energy required to melt 16.87 g of ice is 5.64 kJ

The energy required to melt a 16.87 g ice cube can be calculated by first converting the mass to moles and then multiplying by the enthalpy of fusion. The calculated energy is 5.64 kJ.

The amount of energy required to melt an ice cube can be calculated using the enthalpy of fusion, which is given as 6.02 kJ/mol for ice. In order to make the conversion, we need to convert the mass of the ice cube from grams to moles. Since the molecular weight of water is approximately 18.015 g/mol, the 16.87 g ice cube amounts to 0.937 mol of ice. We then multiply this amount by the enthalpy of fusion to obtain the required energy. Thus, Energy = (0.937 mol) * (6.02 kJ/mol) = 5.64 kJ. Therefore, it would take about 5.64 kJ of energy to melt the 16.87 g ice cube.

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Answer: Separately derived system

Explanation: A separately derived system is used to describe a premise wiring system whose power is derived from a source of electrical energy such as transformer, solar photovoltaic cell or generator. A separately derived system has no direct connection to any conductor from another system or doesn't generate it's power from any direct connection to a conductor from another system or source except those from established from bonding or grounding connections. Separately derived systems usually generate it's power on it's own.

An isolated power system is isolated from other systems, using bonding or grounding for safety, and may include an isolation transformer. Electrical safety devices like circuit breakers or fuses prevent thermal hazards, and a three-wire system enhances both thermal and shock safety.

The student's question refers to an "isolated power system" which is a type of electrical distribution system. An isolated power system is unique because it is separated from other power systems. It has no direct connection with the circuit conductors of another system, with the exception of connections through bonding or grounding. This premise of design is intended to enhance safety, and it usually involves the use of an isolation transformer to prevent shock. Moreover, it avoids a sudden increase in the voltage that could disrupt the power supply.

Electrical safety devices, such as circuit breakers and fuses, are critical in such systems to interrupt excessive currents and prevent thermal hazards. The three-wire system, which is essential for safety in modern household and industrial wiring, utilizes live/hot, neutral, and earth/ground wires. The neutral wire and the case of any connected appliance are both grounded, which means they are connected to the earth to ensure they exist at zero volts, providing an alternative return path for the current through the earth, thereby guarding against thermal and shock hazards.

Answer:

= 4.96cm

Explanation:

distance between objects of moon = 5.20km = 5.2 × 10³ m

Wavelength of light, λ = 550nm = 5.50 × 10⁻⁷m

distance of moon, L = 384000 km = 3.84 × 10⁸m

formula for resolving power of two objects

d = (1.22 × λ ×L) / D

D = (1.22 × λ ×L) / d

D = (1.22 × 5.50 × 10⁻⁷ ×3.84 × 10⁸) / 5.2 × 10³

D = 4.96cm

Answer:

E) are almost circular, with low eccentricities.

Explanation:

Kepler's laws establish that:

All the planets revolve around the Sun in an elliptic orbit, with the Sun in one of the focus (Kepler's first law).

A planet describes equal areas in equal times (Kepler's second law).

The square of the period of a planet will be proportional to the cube of the semi-major axis of its orbit (Kepler's third law).

[tex]T^{2} = a^{3}[/tex]

Where T is the period of revolution and a is the semi-major axis.

Planets orbit around the Sun in an ellipse with the Sun in one of the focus. Because of that, it is not possible to the Sun to be at the center of the orbit, as the statement on option "C" says.

However, those orbits have low eccentricities (remember that an eccentricity = 0 corresponds to a circle)

In some moments of their orbit, planets will be closer to the Sun (known as perihelion). According with Kepler's second law to complete the same area in the same time, they have to speed up at their perihelion and slow down at their aphelion (point farther from the Sun in their orbit).

Therefore, option A and B can not be true.

In the celestial sphere, the path that the Sun moves in a period of a year is called ecliptic, and planets pass very closely to that path.  

Answer:

a. Rotational inertia: 5.21kgm²

b. Magnitude of it's angular momentum: 123.32kgm²/s

Explanation:

Length of the rod = 3.46m

Weight of the rod = 12.8 N

Angular velocity of the rod= 226 rev/min

a. Rotational Inertia (I) about its axis

The formula for rotational inertia =

I = (1/12×m×L²) + m × ( L ÷ 2)²

Where L = length of the rod

m = mass of the rod

Mass of the rod is calculated by dividing the weight of the rod with the acceleration due to gravity.

Acceleration due to gravity = 9.81m/s²

Mass of the rod = 12.8N/ 9.81m/s²

Mass of the rod = 1.305kg

Rotational Inertia =

(1/12× 1.305 × 3.46²)+ 1.305 ( 3.46÷2)²

Rotational Inertia =  1.3019115 + 3.9057345

Rotational Inertia = 5.207646kgm²

Approximately = 5.21kgm²

b. The magnitude of the rod's angular momentum about the rotational axis is calculated as

Rotational Inertia about its axis × angular speed of the rod.

Angular speed of the rod is calculated as= (Angular velocity of the rod × 2π)/60

= (226×2π) /60

= 23.67 rad/s

Rotational Inertia = 5.21kgm²

The magnitude of the rod's angular momentum about the rotational axis

= 5.21kgm²× 23.67 rad/s

= 123.3207kgm²/s

Approximately = 123.32kgm²/s

Answer:

a. the work done by the gravitational force on Block A is less than the work done by the gravitational force on Block B.

b. the speed of Block A is equal to the speed of Block B.

c. the momentum of Block A is less than the momentum of Block B.

Explanation:

a. The  work done by the gravitational force is equal to:

w = m*g*h

where m is mass, g is the standard gravitational acceleration and h is height. Given that both blocks are released from rest at the same height, then, the bigger the mass, the bigger the work done.

b. With ramps frictionless, the final speed of the blocs is:

v = √(2*g*h)

which is independent of the mass of the blocks.

c. The momentum is calculated as follows:

momentum = m*v

Given that both bocks has the same speed, then, the bigger the mass, the bigger the momentum.

The work done by gravitational force on blocks A and B is equal as the work is independent of the path. Both blocks have the same speed when they reach the final height due to the conversion of potential energy into kinetic energy. However, the momentum of Block B is greater due to its larger mass.

This question is about the principles of work, energy and momentum in physics. Let's address each part of it:

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Explanation:

It is given that the number of electrons passing through the cross-sectional area in 1 s is [tex]3.4 \times 10^{18}[/tex]. Also, we know that charge on an electron is [tex]-1.60 \times 10^{-19} C[/tex], then negative charge crossing to the left per second is  as follows.

         I- = [tex]3.4 \times 10^{18} electrons \times -1.6 x 10^{-19} C/electrons[/tex]

         I- = 0.544 A

As it is given that the number of protons crossing per second is [tex]1.4 \times 10^{18}[/tex], as the charge on the proton is [tex]+1.60 \times 10^{-19} C[/tex], then positive charge crossing to the right per second is calculated as follows.

          I+ = [tex]1.4 \times 10^{18} electrons \times 1.6 \times 10^{-19} electrons/C[/tex]

            I+ = 0.224 A

          I = l I+ l + l I- l

So,    I = 0.544 + 0.224

            = 0.768 A

Thus, we can conclude that the current in given hydrogen discharge tube is 0.768 A.

Answer:

Horizontal velocity is 14 m/s

Vertical velocity is 28.3 m/s

Explanation:

Hello dear friend, you have not mentioned the type of speed that you require for this problem.

In this case, there are three possibilities with which the slingshot can be fired i.e. Horizontally, Vertically straight up and vertically straight down. Below is the explanation / answer to all three possibilities

Fired horizontally:

initial conditions:  

Vertical Velocity = 0 ; Horizontal Velocity = 14m/s

final conditions:

Vertical Velocity  (v²  = u² + 2gs) but initial vertical velocity is zero

v²  =  2gs so v²  = 2(9.8)(31) = 607

v = 24.6m/s

but Horizontal Velocity is still  = 14m/s

Resultant velocity from these two velocity components (Pythagoras theorem)

V² = (v horizontal)² + (v vertical)² = 14² + 24.6²

V = 28.3m/s

angle = tan ⁻¹(24.3/14) = 60.1⁰

V = 28.3m/s at angle of 60.1⁰ to the horizontal

Fired Vertically  Straight Up

distance before the pebble reaches maximum height from top of building

v²  = u² + 2gs

where, v is zero at maximum height

g is minus for upward motion.

v²  = u² + 2gs

0  = 14² -  2(9.8)s

s = 196/19.6 = 10.0m

totals distance from maximum height to the ground = 10.0 m + 31.0 m = 41.0m

v²  = u² + 2gs

now u from maximum height is 0 and g is positive for downward motion

v²  =  2gs

v²  =  2(9.8)(41.0)

v = 28.3m/s

v = 28.3m/s vertically straight up

Fired Vertically Straight Down

v²  = u² + 2gs

u = 14m/s, g = 9.8m/s², s = 31.0m

v²  = 14² + 2(9.8)(31.0)

v = 28.3m/s

v = 28.3m/s vertically straight down

Answer:

a) [tex]I = 113.014\,kg\cdot m^{2}[/tex], b) [tex]m = 2075.556\,kg[/tex]

Explanation:

a) The turntable has the following physical model by using Newton's laws:

[tex]F \cdot R = I \cdot \alpha[/tex]

The moment of inertia is:

[tex]I = \frac{F\cdot R}{\alpha}[/tex]

[tex]I = \frac{(300\,N)\cdot(0.33\,m)}{0.876\,\frac{rad}{s^{2}} }[/tex]

[tex]I = 113.014\,kg\cdot m^{2}[/tex]

b) The moment of inertia for a solid cylinder:

[tex]I = \frac{1}{2}\cdot m \cdot R^{2}[/tex]

The mass of the turntable is:

[tex]m = \frac{2 \cdot I}{R^{2}}[/tex]

[tex]m = \frac{(2)\cdot (113.014\,kg\cdot m^{2})}{(0.33\,m)^{2}}[/tex]

[tex]m = 2075.556\,kg[/tex]

Answer:

a) Q = 80,000 cal

b) Q = 100,000 cal

c) Q = 540,000 cal

d) Q = 720,000 cal

Explanation:

a)1 kg from 0⁰ Ice to 0⁰ water, the heat produced is latent heat of fusion

[tex]Q_{l} = ML_{f}[/tex] = 1 * 80

[tex]Q_{l}[/tex] = 80 kCal = 80,000 cal

b) 1 kg of O°C ice water to 1 kg of 100°C boiling water

Specific heat capacity, c =  1000cal/kg.C

[tex]Q_{c} = mc \delta T\\Q_{c} = 1 * 1000 * (100 - 0)\\Q_{c} =100000 cal[/tex]

c) 1 kg of 100°C boiling water to 1 kg of 100°C steam

Latent heat of vaporization is needed for this conversion

[tex]Q_{v} = ML_{v} \\L_{v} = 540 kCal/kg\\Q_{v} =1* 540 \\Q_{v} = 540 kCal = 540000 cal[/tex]

d)  1 kg of O°C ice to 1 kg of 100°C steam.

Q = [tex]Q_{L} + Q_{c} + Q_{v}[/tex]

Q = 80,000 + 100,000 + 540,000

Q = 720,000 cal

Final answer:

To change 1 kg of ice at 0°C to water at 0°C, 80 kcal of energy is required. To change 1 kg of water at 0°C to boiling water at 100°C, 100 cal of energy is required. To change 1 kg of boiling water at 100°C to steam, 540 kcal of energy is required.

Explanation:

The quantity of heat required to change the phase of a substance is given by the equation Q = mL, where m is the mass of the substance and L is the heat of fusion or heat of vaporization. For example, to change 1 kg of ice at 0°C to water at 0°C, the energy required is Q = (1 kg)(80 kcal/kg) = 80 kcal. To change 1 kg of water at 0°C to boiling water at 100°C, the energy required is Q = (1 kg)(1 cal/g °C)(100°C) = 100 cal. To change 1 kg of boiling water at 100°C to steam, the energy required is Q = (1 kg)(540 kcal/kg) = 540 kcal.

Augmented reality has the potential to superimpose digital data over real photos so that GPS maps can be combined with real pictures of stores and streets to help people locate their position.

Explanation:

An engaging perception of an original globe atmosphere, where by computer-generated perceptual knowledge the transformation of real-world entities take place and also by multiple sensory modalities, involving somatosensory, visual, auditory, haptic and olfactory forms, thus known as augmented reality.

AR app uses GPS and camera from a smartphone to deploy an augmented reality-enabled GPS navigation system. As in the web, AR tool termed as Real View Navigation is accessible to all Android and iOS clients. Google is brought its first virtual reality walking directions, now recognized as Live Experience on Google Maps.

Answer:

[tex] W = 5.94 \cdot 10^{15} N [/tex]      

Explanation:  

To calculate the weight on the surface of a neutron star we can use the following equation:

[tex] W = m*g [/tex]

Where:

W: is the weight of the person

m: is the mass of the person

g: is the gravity of the neutron star

Hence, first we need to find m and g. The mass is equal to:

[tex]m = \frac{W}{g} = \frac{685 N}{9.81 m/s^{2}} = 69.83 kg[/tex]

Now, the gravity of the neutron star can be found using the followig equation:    

[tex]F = \frac{G*m*M}{r^{2}} = m*g \rightarrow g = \frac{G*M}{r^{2}}[/tex]

Where:

G: is the gravitational constant = 6.67x10⁻¹¹ m³ kg⁻¹ s⁻²    

M: is the mass of the neutron star = 1.99x10³⁰ kg

r : is the distance between the person and the surface of the neutron star = 25/2 = 12.5 km  

[tex] g = \frac{6.67 \cdot 10^{-11} m^{3}kg^{-1}s^{-2}*1.99 \cdot 10^{30} kg}{(12.5 \cdot 10^{3} m)^{2}} = 8.50 \cdot 10^{13} m/s^{2} [/tex]  

Now, we can find the weight on the surface of the neutron star:

[tex]W = m*g = 69.83 kg * 8.50 \cdot 10^{13} m/s^{2} = 5.94 \cdot 10^{15} N[/tex]      

I hope it helps you!

Your weight on a neutron star with the same mass as the Sun and a diameter of 25.0 km would be approximately 5.95 × 10¹⁴ N. This is due to the extremely high gravitational acceleration on the neutron star's surface. Such high gravity results from the star's compactness and mass.

To determine your weight on the surface of a neutron star, we need to calculate the gravitational acceleration on its surface and then use this to find the weight force.

Step-by-Step Solution:

Summary: Your weight on a neutron star with the same mass as the Sun and a diameter of 25.0 km would be approximately 5.95 × 10¹⁴N, which is significantly more than your weight on Earth.

Answer:

height of tower= 78.48 meters

Explanation:

So here are your givens:

time(t)= 4 s.

initial velocity(u) = 0 m/s

acceleration due to gravity (g)= 9.81 m/s^2

distance(s)=s meters

using one of Newton's equation of motion ;

[tex]s=ut+\frac{1}{2} gt^{2} \\s=0(4)+\frac{1}{2}(9.81)(4)^{2} \\s=\frac{1}{2} (9.81)(16)\\s=\frac{156.96}{2} \\s=78.48[/tex]

height of the tower from the ground=total distance covered by bearing

height of tower= 78.48 meters

Final answer:

The shot tower needs to be at least 78.4 meters tall for a ball bearing to solidify in 4.0 seconds given the acceleration due to gravity.

Explanation:

Calculating the Height of the Shot Tower

To determine how high the tower must be for a ball bearing to solidify in 4.0 seconds, we can use the kinematic equation for free-fall motion without initial velocity, which is h = 1/2gt², where h is the height, g is the acceleration due to gravity (9.8 m/s² on Earth), and t is the time in seconds. For t = 4.0 seconds, we get:

h = 1/2 * 9.8 m/s² * (4.0 s)²

h = 1/2 * 9.8 * 16

h = 4.9 * 16

h = 78.4 meters

Therefore, the shot tower must be at least 78.4 meters tall to allow a ball bearing to solidify in mid-air within 4.0 seconds before impact.

Using physics concepts of Ohm's law, resistance calculation, and electric field magnitude calculation, we can find the current in copper and silver sections, the electric field magnitudes, and the potential difference in silver section. The potential difference across the silver section will be the same as that applied across the entire wire due to copper's negligible resistance.

The student's question is related to electricity and magnetism, a branch of physics. In the scenario described, the resistance (R) of each wire section can be found using the formula R = ρL/A, where ρ is resistivity, L is length, and A is cross-sectional area. Here, resistivity needs to be known from Table 27.2.

Once the resistance of each wire section is known, Ohm's law (V = IR) can be used to find the current (I) in each section. The same current will flow in both sections of the wire since it is a series circuit. The potential difference across each section can then be calculated using Ohm's law.

The magnitude of the electric field E in each section can be calculated from E = V/d, where V is the potential difference across the section and d is its length.

The potential difference across the silver section is the same as the potential difference applied across the entire wire because the copper wire has negligible resistance compared to silver.

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Answer:

Definitely Spinning permanent magnets within an array of fixed permanent magnets

Explanation:

Any relative motion between magnets (be they permanent or electromagnetic) and a coil of wire will induce an electric current in the coil.

What will not induce an electric current is the relative motion between the two coils of wire (because there is no change in magnetic field), or the relative motion between two magnets (there are no coils of wire to induce the current into).

Therefore, spinning permanent magnets within an array of fixed permanent magnets does not induce an electric current.

Answer:

Spinning permanent magnets within an array of fixed permanent magnets

Explanation:

Answer:

The magnitude of air = 392N

Explanation:

We use Newton's 2nd law. The sum of the vertical forces must be equal to zero because at terminal speed , the acceleration is zero. Solving for the air resistance force,F(air ) gives:

EFvertical = mg - F(air)= ma

F(air) = mg = 40 × 9.8 = 392N

Answer: 392N

Explanation:

Newton's second law of motion states that "The second law states that the acceleration of an object is dependent upon two variables - the net force acting upon the object and the mass of the object."

the sum of vertical forces has to be equal to zero because by the time the terminal speed has been attained, the acceleration is zero. Now, we solve for air resistance force.

summation of F(vertical) = mg - F(air) = ma

a = 0 m/s²

thus, F(air) = mg

F(air) = 40kg*9.8m/s²

F(air) = 392N

Explanation:

Below is an attachment containing the solution.

The distance covered by a freely falling object in a certain time is calculated by the formula d = 1/2 * g * t^2 where d is the distance, g is acceleration due to gravity and t is time. When plugging in the values g = 32 ft/sec^2 and t = 5 sec, we find that the object would have fallen 400 ft in the first 5 seconds.

In physics, the distance that a free-falling object covers is given by the formula d = 1/2 * g * t^2, where g is the acceleration due to gravity. In typical physics problems, g is approximated as 32 feet/second^2 on Earth. If we plug t = 5 sec into the equation, we get:

d = 1/2 * 32 ft/sec^2 * (5 sec)^2 = 400 ft.

Therefore, the object would have fallen 400 ft in the first 5 seconds of free fall.

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Explanation:

Below is an attachment containing the solution.

Answer:

Carrier Wave

Explanation:

A carrier wave is described or known as the continuous electromagnetic radiation, of constant amplitude and frequency, which is being given out or released by a transmitter. It is modulated in direct proportion to the signal,that is voice or music, which is meant to be transmitted or broadcasted.

It is mostly used for the transmission of information such as speech and music which can be seen in radio communication.

Answer:

The acceleration of the refrigerator is [tex]a= 0.056 ms^{-2}[/tex]

Explanation:

The expression of the equation of the net force acting on the refrigerator is as follows;

F-f= ma

Here, F is the applied force, f is the force of friction, m is the mass and a is the acceleration.

It is given in the problem that you're having a hard time pushing a refrigerator having mass 355 kg across the kitchen floor. The force of your own push is 993 N. The force of friction opposing your own push is 973 N.

Put F= 993, f= 973 N and m = 355 kg in the above expression of the equation to calculate the acceleration of the refrigerator.

993 - 973 = (355)a

20 = 355 a

[tex]a= 0.056 ms^{-2}[/tex]

Therefore, the acceleration of the refrigerator is [tex]a= 0.056 ms^{-2}[/tex].

The refrigerator's acceleration is 0.0563 m/s², calculated by subtracting the force of friction from the pushing force and then dividing by the refrigerator's mass.

To find the acceleration of the refrigerator, we first need to calculate the net force acting on it. The net force is the difference between the force of the push and the force of friction.

Step 1: Calculate the Net Force

Net Force = Force of the push - Force of friction
Net Force = 993 N - 973 N
Net Force = 20 N

Step 2: Apply Newton's Second Law of Motion

According to Newton's Second Law of Motion, the acceleration (a) can be calculated using the formula:

a = Net Force / Mass

Substituting the known values:

a = 20 N / 355 kg
a ≈ 0.0563 m/s²

The refrigerator's acceleration when being pushed across the kitchen floor is approximately 0.0563 meters per second squared.

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Answer:

Total angle through which the wheel has turned 58.9s after it begins rotating is 1709.52 rad

Explanation:

The image attached would offer a better explanation

Answer:

The answer to the question is;

The total angle through which the wheel has turned 58.9 s after it begins rotating is approximately 1709.67 rad.

Explanation:

To solve the question we note the equation for the motion of the flywheel as

ω₂ = ω₁ + α·t

Where:

ω₁ = Initial angular velocity = 0 rad/s as the body is initially at rest

ω₂ = Final angular velocity

α = angular acceleration = 1.35 rad/s²

t = Time = 28.3 s

Plugging in the values, we find ω₂

ω₂ = 0 + 1.35 rad/s²× 28.3 s = 38.205 rad/s

Since the acceleration is constant, only the mean velocity is required to determine the angle traveled during the first 28.3 seconds thus

Average velocity

ω[tex]_{average}[/tex]= [tex]\frac{Final .Velocity +Initial . Velocity}{2} = \frac{\omega_2+\omega_1}{2} = \frac{38.205 rad/s+0 rad/s}{2}[/tex]

= 19.1025 rad/s

The total angle traveled in 28.3 s is ω[tex]_{average}[/tex] × time

= 19.1025 rad/s × 28.3 s = 540.60075 rad

After this the remaining time left is

58.9 s - 28.3 s = 30.6 s

Since the flywheel is moving at a constant velocity of 38.205 rad/s during the last 30.6 s we have

Angle traveled in 30.6 s at an angular velocity of 38.205 rad/s is given by

Angle traveled = Time × Angular velocity = 30.6 s × 38.205 rad/s

= 1169.073 rad

Therefore, the total angle traveled by the flywheel in 58.9 s is given by

540.60075 rad + 1169.073 rad = 1709.67375 rad ≈1709.67 rad.

the total angle traveled by the flywheel in 58.9 s ≈ 1709.67 rad.

Answer:

11 m/s²

Explanation:

Deceleration: This can be defined as the rate of decrease of velocity. The S.I unit of deceleration is m/s².

From the question,

F = md ..................... Equation 1

Where F = Force acting on the dummy towards the rear of the car, m = mass of the dummy, d = deceleration of the dummy.

make d the subject of the equation

d = F/m............... Equation 2

Given: F = 825 N, m = 75 kg.

substitute into equation 2

d = 825/75

d = 11 m/s²

Answer:

11 m/s^2.

Explanation:

Given:

Mass = 75 kg

Force = 825 N

F = m × a

a = 825 ÷ 75

= 11 m/s^2.

Answer:

True, check attachment for code

Explanation:

To convert java strings of text to upper or lower case, we can use and inbuilt methods To Uppercase and To lower case.

The first two lines of code will set up a String variable to hold the text "text to change", and then we print it out.

The third line sets of a second String variable called result.

The fourth line is where the conversion is done.

We can compare the string

We can compare one string to another. (When comparing, Java will use the hexadecimal values rather than the letters themselves.) For example, if we wanted to compare the word "Fat" with the word "App" to see which should come first, you can use an inbuilt string method called compareTo.

Check attachment for the code

Answer:

The correct frequenvy of the second fork is; ν2 = 566Hz

Explanation:

First of all, when two wave sources with slightly differing frequencies ν1 and ν2 generate waves at the same time and are superposed, then an interference effect will occur in time.

The intensity will be found to oscillate with time with a frequency (ν) called the beat frequency. It is depicted by:

ν = ± (ν1 −ν2).

In this question, there are two tuning forks, one with a frequency of let's say ν1=560Hz

The beat frequency is ν=6Hz

Therefore,

ν2=560 - 6 or ν2=560 + 6

i.e ν2=554 or ν2=566

For us to know the correct frequency, if the 560 Hz fork is loaded with wax, the increased inertia will lower its frequency.

Then it is found that the beat frequency increases. This can only mean that the other fork has a higher frequency. Hence the unkown frequency of the second fork must be,

ν2 = 566Hz

Answer:

Explanation:

Potential energy Is given as.

U=kq1q2/r

Where k is a constant

q1 is charge

And q2 is also a charge

r is the distant between the two charges

When distance between the two charges is infinity then, the potential energy will b zero

U=kq1q2/∞

Therefore

U=0

Thus, the potential energy is zero when charged particles are separated by an infinite distance.

Let considered that both charges are positive.

Then U becomes

U=k(+q1)(+q2)/r

This shows that the energy is positive when the charges are positively charge. Also if the charges are also both negative charged the total energy will also be positive

U=k(-q1)(-q2)/r.

Both when their are opposite charges, the energy will be negative

U=k(-q1)(+q2)/r

U will be negative

Answer:

The answers to the questions are as follows;

(a) The rate of change of T at (1, 2, 2) in the direction toward the point (4, 1, 3) is  [tex]\frac{160\sqrt{11} }{33}[/tex]

(b) The direction of the gradient is in the direction of greatest increase and it is towards the origin.

Explanation:

To solve the question, we note that the shape of the ball is that of a sphere.

Therefore the distance of a point from the center is given by

f(x, y, z)  = [tex]\sqrt{x^2+y^2+z^2}[/tex]

The temperature T in a metal ball is inversely proportional to the distance from the center of the ball

Therefore T ∝ [tex]\frac{1}{\sqrt{x^2+y^2+z^2}}[/tex] or T = [tex]\frac{C}{\sqrt{x^2+y^2+z^2}}[/tex]

Where

C = Constant of proportionality

x, y, and z are the x, y and z coordinates values

To find C, we note that at point (1, 2, 2), T = 160 °C.

Therefore 160 °C = [tex]\frac{C}{\sqrt{1^2+2^2+2^2}}[/tex] = [tex]\frac{C}{\sqrt{9}}[/tex] = [tex]\frac{C}{3}}[/tex]

Therefore C = 160 × 3 = 480 °C·(Unit length)

We therefore have the general equation as

T = [tex]\frac{480}{\sqrt{x^2+y^2+z^2}}[/tex]

The vector from points  (1, 2, 2) to point (4, 1, 3) is given by

1·i + 2·j +2·k - (4·i + 1·j +3·k) = -3·i + j -k

From which we find the unit vector given by

u = [tex]\frac{1}{\sqrt{(-3)^2+1^2+(-)^2} } (-3, 1, -1)= \frac{1}{\sqrt{11} } (-3, 1, -1)[/tex]  

From which we have the gradient equal to

∇T(x, y, z) = -480×(x²+y²+z²)[tex]^-{\frac{3}{2}}[/tex] in (x, y, z)

This gives D[tex]_u[/tex] = ∇T·u

                       = -480×(x²+y²+z²)[tex]^-{\frac{3}{2}}[/tex] in (x, y, z)·[tex]\frac{1}{\sqrt{11} } (-3, 1, -1)[/tex]

That is

[tex]-\frac{480}{\sqrt{11} }[/tex](x²+y²+z²)[tex]^-{\frac{3}{2}}[/tex] (-3·x + y - z)

From where D[tex]_u[/tex]Tat point (1, 2, 2) is  = [tex]\frac{160\sqrt{11} }{33}[/tex]  

(b) The direction of greatest increase in temperature is in the direction of the gradient and the direction of the gradient is opposite to the direction of {x, y, z}, which is away from the origin.

Hence the direction of the greatest increase in temperature is towards the origin.

Answer:

Using lighter material in car construction, improving energy efficiency by enhancing engine design or replacing the engine with more efficient technologies.

Explanation:

Using lighter materials in the car construction, reducing the potential energy required to accelerate and to move the car, as well as energy losses due to rolling friction. There is evidence of such benefits by replacing steel and aluminium parts with components made of composite materials.  

Improving the design of internal combustion engines to minimize energy losses and accordingly, improving energy efficiency. A more radical approach is replacing internal combustion engines with electric engines, which offer higher efficiencies. Such conclusions can be easily inferred from model based on Work-Energy Theorem and Principle of Energy Conservation:

[tex]\eta_{engine} \cdot U_{engine} = \frac{1}{2} \cdot m_{car} \cdot v^{2} + \mu_{r} \cdot m_{car} \cdot g \cdot \Delta s[/tex]

Answer:

3.1216 m/s.

Explanation:

Given:

M1 = 0.153 kg

v1 = 0.7 m/s

M2 = 0.308 kg

v2 = -2.16 m/s

M1v1 + M2v2 = M1V1 + M2V2

0.153 × 0.7 + 0.308 × -2.16 = 0.153 × V1 + 0.308 × V2

= 0.1071 - 0.66528 = 0.153 × V1 + 0.308 × V2

0.153V1 + 0.308V2 = -0.55818. i

For the velocities,

v1 - v2 = -(V1 - V2)

0.7 - (-2.16) = -(V1 - V2)

-(V1 - V2) = 2.86

V2 - V1 = 2.86. ii

Solving equation i and ii simultaneously,

V1 = 3.1216 m/s

V2 = 0.2616 m/s