A block of mass 2 kg is traveling in the positive direction at 3 m/s. Another block of mass 1.5 kg, traveling in the same direction at 4 m/s, collides elastically with the first block. Find the final velocities of the blocks. How much kinetic energy did the system lose

Answer:

Electric flux

Explanation:

The electric flux measures the amount of electric field passing through a surface. For any closed surface, the electric field passing through it (electric flux) is given by Guass law. The mathematical relation between electric flux and the enclosed charge is known as Gauss law for the electric field. Electric flux may also be visualised as the amount of electric lines of force passing through an area.

Answer:

Cover-braking technique

Explanation:

Cover braking involves the technique of taking off the foot from the accelerator and hovering it over the braking pedal. The foot must not be placed on the braking pedal to avoid the wear of brake unnecessarily.

It is done usually when an obstacle is expected in front of the moving car. This provides an edge in the reaction time of application of the brakes hence reducing the stopping time.

Regenerative braking and engine braking are techniques used for a smooth transition from acceleration to braking. These techniques convert kinetic and potential energy into electrical energy or use engine power to slow down the vehicle, respectively.

The technique that provides a smooth transition from acceleration to braking is commonly recognized in physics and engineering called regenerative braking. Regenerative braking is a central component of the operation of hybrid and electric vehicles. It functions by converting a vehicle's kinetic and gravitational potential energy into electrical energy that recharges the vehicle's battery when deceleration is initiated.

Another method is engine braking, usually applied in larger vehicles like trucks to avoid overheating of brakes specially when traveling downhill.

Both methods, whether it is engine braking or regenerative, provide a smooth progression from accelerated motion to a decrease in speed, or braking. This way, they manage the transition smoothly while conserving and efficiently using energy.

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Incomplete question as we have not told which quantity to find.So the complete question is here

A solenoid used to produce magnetic fields for research purposes is 2.2 mm long, with an inner radius of 25 cmcm and 1300 turns of wire. When running, the solenoid produced a field of 1.5 TT in the center.Given this, how large a current does it carry?

Answer:

[tex]I=2.021A[/tex]

Explanation:

Magnetic field B=1.5 T

Length L=2.2mm =0.0022m

Number of turns N=1300 turns

To find

Current I

Solution

From the magnetic at the center of loop we know that:

[tex]B=uI\frac{N}{L}[/tex]

Substitute the given values

[tex]B=uI\frac{N}{L}\\ as\\u=4\pi *10^{-7} T.A/m\\So\\B=uI\frac{N}{L}\\I=\frac{LB}{Nu}\\ I=\frac{0.0022m(1.5T)}{(1300)(4\pi *10^{-7} T.A/m)}\\I=2.021A[/tex]

Answer:

59.84 N

Explanation:

The net force is responsible for the upward acceleration of the bowling ball.

The net force acting on a body accelerates the body in the same direction as that in which the resultant is applied.

Net force = ma

ma = F - mg

In the first case,

F = 71.6 N, a = a m/s²

ma = 71.6 - mg (eqn 1)

In the second case,

F = 82.3 N, a = 1.91a m/s²

m(1.91a) = 82.3 - mg

1.91 ma = 82.3 - mg (eqn 2)

Substitute for ma in (eqn 2)

1.91 (71.6 - mg) = 82.3 - mg

136.756 - 1.91 mg = 82.3 - mg

136.756 - 82.3 = 1.91 mg - mg

0.91 mg = 54.456

mg = 54.456/0.91

mg = 59.84 N

Hence, the weight of the bowling ball = 59.84 N

Hope this Helps!!!

The weight of the bowling ball is 59.84 N

The net force should be held responsible where there is the upward acceleration of the bowling ball. When it should be acted on the body so it should be in a similar direction.

We know that

Net force = ma

So,

ma = F - mg

Now

In the first case,

F = 71.6 N, a = a m/s²

ma = 71.6 - mg (eqn 1)

And,

In the second case,

F = 82.3 N, a = 1.91a m/s²

m(1.91a) = 82.3 - mg

So,

1.91 ma = 82.3 - mg (eqn 2)

Now

1.91 (71.6 - mg) = 82.3 - mg

136.756 - 1.91 mg = 82.3 - mg

136.756 - 82.3 = 1.91 mg - mg

0.91 mg = 54.456

mg = 54.456/0.91

mg = 59.84 N

Hence, the weight of the bowling ball = 59.84 N

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Answer: 20m

Explanation:

We will solve this question by applying the law of conservation of energy which states that the sum of potential energy and kinetic energy is always the same.

The PE is 0 at surface and maximum at top while the KE is maximum at surface and 0 at top.

From the question,

PE = mgh = 50 J -(1)

mg* 10 = 50

mg = 50/10

mg = 5

The total energy at that point = PE + KE = 50 + 50 = 100 J

Therefore, at topmost point, the PE will be 100 J

mgH = 100J , H is the needed height

Using the value of mg obtained above, we have

H= 100/5

H = 20 m

Answer: B) Light

Explanation: light waves are Electromagnetic waves. Visible light is one of the many types of electromagnetic waves. The others are mechanical waves.

Answer:

dehydration reactions

Final answer:

Dehydration reactions decrease entropy within a cell by building larger molecules from smaller units, unlike catabolic reactions like digestion and respiration which increase entropy by breaking down molecules.

Explanation:

The type of reaction that would decrease the entropy within a cell are dehydration reaction. Entropy is a measure of disorder or randomness in a system, and dehydration reactions are anabolic processes that build larger molecules from smaller ones, thus decreasing entropy. In contrast, catabolic reactions, such as digestion, hydrolysis, and respiration, generally increase entropy in a system by breaking down complex molecules into simpler ones and releasing energy in the process.

The radius R of the turn is 1.984 km.

Explanation:

As the falcon is experiencing a centripetal motion, the acceleration exhibited by the falcon will be centripetal acceleration. The formula for centripetal acceleration is

                 [tex]a=\frac{v^{2} }{R}[/tex]

Here a is the acceleration for centripetal motion, v is the velocity and R is the radius of the circular path.

As the centripetal acceleration is given as 0.6 g, the velocity is given as 108 m/s, then the radius of the path can be determined as

       [tex]0.6 \times 9.8=\frac{(108)^{2}}{R}[/tex]

      [tex]R=\frac{(108)^{2}}{0.6 \times 9.8}=\frac{11664}{5.88}=1983.67\ \mathrm{m}[/tex]

So, the radius of the turn is 1.984 km.

Answer:

Explanation:

Given that we have two cars

First car has mass =m

Second car has mass = 4m

They are driving at constant speed

Given that the radius of curve is R

Both cars maintain the same acceleration.

Let velocity of small car be vS

Velocity of big car be vL

From centripetal acceleration

a=V²/R

V²=aR

Then since both car have the same accelerating and bashing through the same curve of radius R

Then, We can say, V² is constant

vL² = vS²

Then taking square root of both side

vL=vS

The speed of the small car vS is greater than the speed of the large car vL as they round the curve due to the difference in their masses and the application of the same acceleration.

The speed of the small car vS is greater than the speed of the large car vL as they round the curve. This is because both cars have the same acceleration a, but the small car has less mass than the large car. According to Newton's second law, F = ma, the force required to maintain the same acceleration is greater for the larger car, which means it has a greater speed as it rounds the curve.

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Answer:0.754m

Explanation:

F=kq1q2/r^2

R^2= kq1q2/f

R^2= 9*10^9*7.9*10^-6*6.0*10^-6/0.75

R^2= 9*7.9*6*10^-3/0.75

R^2=0.4266/0.75

R^2=0.5688

R=√0.5688

R=0.754m

Answer:

Coefficient of friction between the book and floor is 0.582.

Explanation:

Using the velocity formula;

v^2 = 2as

a = v^2/(2s)

a = 1.6^2/(2*0.9)

a = 2.56/1.8

a = 1.42 m/s^2

the force necessary to give the book the acceleration is  

F = ma = 3.5*1.42 (m is mass of the book i.e. 3.5 kg)

F = 4.98 N

The difference in the force is the friction force, which is

Ff = 25 - 4.98 = 20 N

Ff = mgμ

where μ is coefficient of friction and g is acceleration due to gravity that is 9.8 m/s^2

μ = Ff/mg

μ = 20/(3.5*9.81)

μ = 0.582

Coefficient of friction between the book and floor is 0.582.

This question involves the concepts of the equation of motion and Newton's second law of motion.

The coefficient of kinetic friction between the book and the floor is "".

First, we will find the acceleration of the block by using the third equation of motion:

[tex]2as = v_f^2-v_i^2[/tex]

where,

a = acceleration = ?

s = distance covered = 0.9 m

vf = final speed = 1.6 m/s

vi = initial speed = 0 m/s

Therefore

[tex]a=\frac{(1.6\ m/s)^2-(0\ m/s)^2}{2(0.9\ m)}\\\\a=1.42\ m/s^2[/tex]

Hence, from Newton's second law of motion:

[tex]Net\ Force = Frictional\ Force + F\\Net\ Force = \mu mg+ma[/tex]

where,

Net Force = 25 N

μ = coefficient of kinetic friction = ?

m = mass of the book = 3.5 kg

g = acceleration due to gravity = 9.81 m/s²

Therefore,

[tex]25\ N = \mu(3.5\ kg)(9.81\ m/s^2)+(3.5\ kg)(1.42\ m/s^2)\\\\\mu=\frac{25\ N - 4.98\ N}{34.33\ N}\\\\\mu = 0.58[/tex]

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The attached picture shows Newton's Second Law of Motion.

Answer:

True

Explanation:

If there's no preference over the string case (upper case or lower case), one can convert both strings to upper case or to lowercase and then compare the converted strings to test if they're equal or not.

An Illustration is

string a = "Boy"

string b = 'bOy"

if(a.ToUpper() == b.ToUpper() || a.ToLower() == b.ToLower())

{

Print "Equal Strings"

}

else

{

Print "Strings are not equal";

}

The above will first convert both strings and then compare.

Since they are the same (after conversion), the statement "Equal Strings" will be printed, without the quotes

The statement is true. Most programming languages include methods to convert strings to either lower or upper case. This feature is useful to make comparisons case-insensitive.

This statement is true. In many programming languages, there are methods to convert a string to either lower case or upper case. These methods are often utilized to make string comparisons case-insensitive, eliminating any discrepancy caused by case differences.

For example, in Java, the methods are toLowerCase() and toUpperCase(), while in Python, they are lower() and upper(). This is particularly useful when a program is designed to interact with human input, as it allows the program to accept input regardless of the case used.

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The situation can be modeled with a differential equation taking into account the inflow and outflow rates of carbon dioxide. By resolving this equation, we obtain a function representing the CO2 quantity over time. This can be easily converted into percentage by dividing by the room's volume and multiplying by 100.

This problem can be solved using a mathematical model called a differential equation. The percentage of carbon dioxide in the room changes over time due to the input of fresher air and the removal of mixed air.

Let's denote the quantity (not the percentage, the actual quantity) of carbon dioxide in the room at time t by Q(t). Initially, we have Q(0) = 0.0025 * 180 = 0.45 m³.

Carbon dioxide flows into the room at a rate of 0.0005 * 2 = 0.001 m³/min and flows out at the rate proportional to the total quantity present, which is (Q(t) / 180) * 2 = (Q(t) / 90) m³/min. Therefore the situation can be modelled by the differential equation dQ/dt = 0.001 - Q(t) / 90. Here, 0.001 represents the rate on inflow of carbon dioxide, and Q(t) / 90 represents the rate of outflow.

By solving this differential equation, we can obtain the function Q(t) which gives the quantity of carbon dioxide in the room at each moment, and the percentage of carbon dioxide can be obtained by dividing Q(t) by the volume of the room and multiplying by 100 to get a percentage, i.e., p(t) = Q(t)/180 * 100.

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The percentage of carbon dioxide in the room over time can be calculated using differential equations. The resulting function is[tex]p(t) = 0.005 * e^{(t/90)} + 0.02 * e^{(-t/90)}[/tex]. This takes into account both the inflow of fresh air and the mixture exiting the room.

To determine the percentage p of carbon dioxide in the room as a function of time t (in minutes), we need to use principles from differential equations to model the mixing process.

Initially, the volume of the room is 180 m³ containing 0.25% carbon dioxide. Fresh air with 0.05% carbon dioxide flows into the room at 2 m³/min.

Let's denote the amount of carbon dioxide in the room at time t by C(t), measured in cubic meters. The concentration of carbon dioxide p(t) is given by:

The rate of change of the carbon dioxide in the room can be written as:

The inflow of carbon dioxide is:

The outflow of carbon dioxide depends on the concentration in the room:

Thus, the differential equation becomes:

This simplifies to:

[tex]or, dC/dt = 0.001 - (C/90)[/tex]

To solve this, we use an integrating factor. The integrating factor is:

Multiplying both sides by the integrating factor:

This simplifies to:

Integrate both sides:

Hence,

To find K, use the initial condition C(0):

Initial amount of CO2:

Thus,

Therefore, [tex]K = 0.36[/tex].

The solution is:

The percentage of CO2 is:

This simplifies to:

Hence:

[tex]p(t) = 0.005 * e^{(t/90)} + 0.02 * e^{(-t/90)}[/tex]

Answer:

1 V / div

Explanation:

Solution:

- The vertical scale has eight divisions.  

- If each division is set to equal 1 volt, the display will show 0 to 8 volts.  

- This is okay in a 0 to 5 volt variable sensor such as a throttle position (TP) sensor.  

- The volts per division (V/div) should be set so that the entire anticipated waveform can be viewed.

Answer:

The energy stored in this new capacitor is [tex]4.4514\times10^{-9}\ J[/tex]

Explanation:

Suppose, Two parallel plates, each having area A = 2180 cm² are connected to the terminals of a battery of voltage [tex]V_{b}= 6\ V[/tex] as shown. The plates are separated by a distance d = 0.39 cm.

We need to calculate the charge

Using formula of capacitance

[tex]C=\dfrac{Q}{V}[/tex]

[tex]\dfrac{Q}{V}=\dfrac{\epsilon_{0}A}{d}[/tex]

[tex]Q=V\times\dfrac{\epsilon_{0}A}{d}[/tex]

Put the value into the formula

[tex]Q=6\times\dfrac{8.85\times10^{-12}\times2180\times10^{-4}}{0.39\times10^{-2}}[/tex]

[tex]Q=2.968\times10^{-9}\ C[/tex]

The distance between the plates is doubled.

We need to calculate the new capacitance

Using formula of capacitance

[tex]C'=\dfrac{\epsilon_{0}A}{d}[/tex]

Put the value into the formula

[tex]C'=\dfrac{8.85\times10^{-12}\times2180\times10^{-4}}{0.78\times10^{-2}}[/tex]

[tex]C'=2.473\times10^{-10}\ F[/tex]

We need to calculate the energy stored in this new capacitor

Using formula of energy

[tex]U=\dfrac{1}{2}C'V^2[/tex]

Put the value into the formula

[tex]U=\dfrac{1}{2}\times2.473\times10^{-10}\times(6)^2[/tex]

[tex]U=4.4514\times10^{-9}\ J[/tex]

Hence, The energy stored in this new capacitor is [tex]4.4514\times10^{-9}\ J[/tex]

Answer:

Smoky Mountains specific spots--such as a factory's smokestacks--where large quantities of pollution are discharged

Explanation:

Point source pollution is characterized by the following components:

From the options, Smoky Mountains specific spots--such as a factory's smokestacks--where large quantities of pollution are discharged ticked all the necessary box for a point source pollution.

Answer:

In chemical compounds, atoms tends to have the electron configuration of a noble gas.

Explanation:

The noble gases are unreactive because of their electron configurations. This noble gas neon has the electron configuration of 1s22s22p6 . It has a full outer shell and cannot incorporate any more electrons into the valence shell.

The octet rule states that atoms tend to form compounds in ways that give them eight valence electrons and thus the electron configuration of a noble gas. An exception to an octet of electrons is in the case of the first noble gas, helium, which only has two valence electrons.

The octet rule states that atoms (excluding some exceptions like hydrogen and helium) in a compound strive for eight electrons in their valence shell, making it stable. This is achieved by sharing, accepting or donating electrons. For instance, oxygen in a water molecule gains two electrons from two hydrogen atoms through covalent bonding.

The octet rule is a principle in chemistry which states that atoms in chemical compounds tend to achieve a stable electron configuration with eight electrons, a complete 'octet', in their valence shell. Atoms will donate, accept, or share electrons to fulfill this rule. For example, oxygen, which has six electrons in its valence shell, will react with other atoms so as to gain two more electrons, completing its octet. This is achieved through covalent bonding, where electrons are shared between atoms, such as in a water molecule H2O. It is important to note that there are exceptions to this rule, notably hydrogen and helium which are stable with two and helium with two electrons in their valence shell respectively.

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Answer:

Protein molecules

Explanation:

Ribosomes are the cell organelles that are responsible for the synthesis of protein in the cell. Proteins are the fundamental building blocks and help in repair and damage of cell in the body.

Ribosome is a complex which is made up of protein and RNA. Ribosomes can be found floating within the cytoplasm or attached to the endoplasmic reticulum.

Answer:

The first eagle hear a frequency of 4.23kHz and the second eagle hear a frequency of 3.56kHz

Explanation:

Given that

both eagle are flying towards one another

speed of the first eagle v1 = 15m/s

speed of the second eagle v2 = 20m/s

frequency emitted by the first eagle f1= 3200Hz

frequency emitted by the second eagle f2 = 3800Hz

speed of sound v = 330m/s

[tex]F_1 = (\frac{v + v_2}{v - v_1} )f_1\\F_1 = (\frac{330 + 20}{330 - 15} )(3200)\\= 3.56 \times 10^3Hz\\= 3.56kHz\\[/tex]

the second part

[tex]F_1 = (\frac{v + v_2}{v - v_1} )f_1\\F_1 = (\frac{330 + 15}{330 - 20} )(3800)\\= 4.23 \times 10^3Hz\\= 4.23kHz\\[/tex]

The first eagle hear a frequency of 4.23kHz and the second eagle hear a frequency of 3.56kHz

Answer:

(a) increase

Explanation:

On a line graph; we have the x-axis to the positive side and the negative side .In a positive x-axis direction, the force is usually positive, vice versa the negative side as well.

The change in the potential energy of a charge field-system can be given as:

[tex]\delta U= -q(EdsCos \theta)[/tex]

where;

q = positive test charge

E = Electric field

ds = displacement between thee charge positions

θ  = Angle between the electric field and the displacement.

Given that:

Charge of the particle = -q

displacement = (60.0 -20.0)cm = 40.0 cm

θ = 0

Replacing our values in the above equation, we have:

[tex]\delta U = -(-q)(60Cos 0)[/tex]

[tex]\delta U = qEds[/tex]

Since the potential energy of the system is positive, therefor the electric potential energy also increases.

The electric potential energy of a system consisting of a negatively charged particle in a uniform electric field increases when the particle is moved in the same direction as the field.

The electric potential energy of the charge-field system increases as a negatively charged particle is moved in the same direction as the electric field. This is because work is done to overcome the force of the electric field, which opposes the movement of the negatively charged particle. The uniform electric field produces a constant force, and since work is force times distance, the amount of work (and hence energy) increases.

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Answer:

a) [tex]v=313.209\ m.s^{-1}[/tex]

b) [tex]v_t=3751.79\ m.s^{-1}[/tex]

Explanation:

Given:

a)

[tex]v=\sqrt{2g.h}[/tex]

[tex]v=\sqrt{2\times 9.81\times 5000}[/tex]

[tex]v=313.209\ m.s^{-1}[/tex]

b)

given that:

diameter of the drop, [tex]d=4\ mm=0.004\ m[/tex]

density of the air, [tex]\rho=1.18\ kg.m^{-3}[/tex]

the terminal velocity is given as:

[tex]v_t=\sqrt{\frac{2m.g}{\rho.A.c_d} }[/tex]

where:

m = mass

g = acceleration due to gravity

[tex]\rho=[/tex] density of the medium through which the drop is falling (here air)

A = area normal to the velocity of fall

[tex]c_d=[/tex] coefficient of drag = 0.47 for spherical body

[tex]v_t=\sqrt{\frac{2\times 5\times 9.81}{1.18\times \pi\times 0.002^2\times 0.47} }[/tex]

[tex]v_t=3751.79\ m.s^{-1}[/tex]

Answer:

[tex]372.3 J/^{\circ}C[/tex]

Explanation:

First of all, we need to calculate the total energy supplied to the calorimeter.

We know that:

V = 3.6 V is the voltage applied

I = 2.6 A is the current

So, the power delivered is

[tex]P=VI=(3.6)(2.6)=9.36 W[/tex]

Then, this power is delivered for a time of

t = 350 s

Therefore, the energy supplied is

[tex]E=Pt=(9.36)(350)=3276 J[/tex]

Finally, the change in temperature of an object is related to the energy supplied by

[tex]E=C\Delta T[/tex]

where in this problem:

E = 3276 J is the energy supplied

C is the heat capacity of the object

[tex]\Delta T =29.1^{\circ}-20.3^{\circ}=8.8^{\circ}C[/tex] is the change in temperature

Solving for C, we find:

[tex]C=\frac{E}{\Delta T}=\frac{3276}{8.8}=372.3 J/^{\circ}C[/tex]

Final answer:

The heat capacity of the calorimeter, determined by applying a constant voltage and measuring the temperature change, is calculated to be 372.3 J/°C.

Explanation:

To calculate the heat capacity of the calorimeter, we first need to understand the amount of heat (q) added to the system. This can be determined using the formula q = IVt, where I is the current (2.6 A), V is the voltage (3.6 V), and t is the time (350 seconds). So, the heat added to the system is q = 3.6 V * 2.6 A * 350 s = 3276 J. The temperature change (ΔT) observed in the calorimeter is from 20.3°C to 29.1°C, which is a change of 8.8°C. The heat capacity (C) of the calorimeter can then be calculated as C = q/ΔT = 3276 J / 8.8 °C = 372.3 J/°C. This indicates the amount of heat required to raise the temperature of the calorimeter by one degree Celsius.

Answer:

Ensures land is used for its designated purposes hence avoiding misuse of land.

Explanation:

The process of urban planning ensures that different land uses are shown such as commercial, residential, public land, forestry and agricultural and institutional lands. This process helps in designing for essential services such as roads, sewarage and water, gas and electricity. In the process, encroachment is controlled and land utilized as planned. Therefore, land is properly utilized while minimizing environmental pollution, leading to sustainable development.

Answer:

Both

A. Low tides are lowest at both full moon and new moon.

B. High tides are highest at both full moon and new moon.

Explanation:

Tides are formed as a consequence of the differentiation of gravity due to the moon across to the Earth sphere.

Since gravity variate with the distance:

[tex]F = G\frac{m1\cdot m2}{r^{2}}[/tex]  (1)

Where m1 and m2 are the masses of the two objects that are interacting and r is the distance Where m1 and m2 are the masses of the two objects that are interacting and r is the distance between them.

For example, see the image below, point A is closer to the moon than point b and at the same time the center of mass of the Earth will feel more attracted to the moon than point B. Therefore, that creates a tidal bulge in point A and point B.

On the other hand, a full moon it gets when Sun, the Earth and the moon are in a line and the moon is reflecting the sunlight.

When the Moon is between the Earth and the Sun it will be illuminated in its back, so it is not possible to see it from the Earth (that is called new moon).

In those two cases mentioned above, the Sun tidal force contributes to the tidal force of the moon over the earth making high tides higher and low tides lower.  

Explanation:

The field at the center of circular current can be calculated by

B = [tex]\frac{\mu _0 I}{r}[/tex]

here μ₀ is permeability constant and is equal to 4π x 10⁻⁷

I is the current in circular path and r is the radius of circle

Thus I =[tex]\frac{90x10^-^1^2x12x10^-^2}{4\pi x 10^-^7 }[/tex] = 8.8 x 10⁻⁵ A

Answer:

k = 1755 N/m

Explanation:

Given:

- The length of the cord L = 23.4 m

- Weight of the student W = 818 N

- The elevation of balloon H = 31.3 m

Find:

Calculate the required force constant of the cord if the student is to stop safely 2.74 m above the river.

Solution:

- We know the potential energy of the student changes by  

                      ΔP.E = m*g*( H - 2.74 )

                      mg*(31.3 - 2.74) = 818*28.56 = 23362.08 J

- When he stops at 2.74 m above ground his KE = 0 so ALL his lost potential energy must be stored in the extended or stretched bungee cord.

- He falls 23.4 m before the bungee cord starts to stretch. That means it doesn't start stretching until he is 31.3 - 23.4 = 7.9 m above the ground.  

- It has to stop  stretching at 2.74 m above the ground so the

                                total stretch = 7.9 - 2.74 = 5.16 m

- Therefore his PE from 31.3 m to 2.74 m is stored in a 5.16 m stretch of the bungee cord.                      

                                ½kx² =  ΔP.E

                                k = 2*ΔP.E / x^2

                                k = 2*23362.08 / 5.16^2

                                k = 1755 N/m

Answer:

Time spent on the greenway road  = 4.5 hours

Time spent on the 2 lane road = 1.5 hours

Explanation:

The distance of the trip  is 360 miles and the initial speed of the car is 62 miles/hr and after the road became 2 lane highway the car slowed to 54 miles/hr.

Let us divide the trip into two

Greenway

speed = distance/time

speed = 62 mph

time = a

distance = speed × time

distance = 62a

2 lane highway

speed = distance/time

speed = 54 mph

time = b

distance = speed × time

distance = 54b

Total distance

62a + 54b = 360......................(i)

Total time

a + b = 6..............................(ii)

a = 6-b

insert a in equation (i)

62(6-b) + 54b = 360

372  - 62b + 54b = 360

-8b = 360-372

-8b = - 12

b = 12/8

b = 1.5

from equation (ii)

a + 1.5 = 6

a = 6 - 1.5

a = 4.5

Explanation:

When coil is placed in the magnetic field , the flux attached with it can be found by the relation . Flux Ф = the dot product of magnetic field and area of coil .

Thus Ф = B A cosθ

here B is magnetic field strength and A is the area of coil .

The angle θ is the angle between coil and field direction .

When coil rotates , the angle varies . By which the flux varies . The emf is produced in coil due to variation of flux . The relation for this is

The emf produced ξ = - [tex]\frac{d\phi}{dt}[/tex] =  B A sinθ [tex]\frac{d\theta}{dt}[/tex]

Now in the given problem

5 = 0.38 x A x [tex]\frac{d\theta}{dt}[/tex]                            I

Now if the magnetic field is 0.55 T and all the other terms are same , the emf produced

ξ = 0.55 x A x [tex]\frac{d\theta}{dt}[/tex]                              Ii

dividing II by I , we have

[tex]\frac{\xi}{5}[/tex] = [tex]\frac{0.55}{0.38}[/tex] = 1.45

or ξ = 7.2 V

Answer:

In 3 hours, the cars will be 297 miles apart.

Explanation:

Speed=Distance/Time

Distance= Speed X Time

Speed of 1st Car=44 miles/hr

Distance=44 X Time taken = 44t

Speed of 2nd Car=55 miles/hr

Distance=55 X Time taken = 55t

Total Distance Covered by both Cars = 44t + 55t = 99t

The cars are 297 miles apart, therefore:

99t = 297

t = 3 hours

It means that in 3 hours, the distance between the cars is 297 miles.

Answer:

 = 238N

Explanation:

mass = 0.14g = 14 × 10⁻⁵kg

initial velocity = 218m/s

final velocity = 0

penetration depth (distance) = 14mm = 14 × 10⁻³m

v²(final) = v²(initial) + 2aΔx

0² = (218)² + 2(14 × 10⁻³)a

a = -(218)² /  2(14 × 10⁻³)

a = 16.97 × 10⁵m/s²

F = ma

 = (14 × 10⁻⁵)(16.97 × 10⁵)

 = 237.58N

 ≅ 238N

Explanation:

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