A spring of force constant 1500 Nm-l is acted
upon by a constant force of 75 N. Calculate
the potential energy stored in the spring.​

a) Speed on the second floor is equal to 3.90 m/s

b) Water pressure on the second floor is 240000 Pa.

In fluid dynamics, Bernoulli's principle can be described as an increase in the speed of fluid occurring simultaneously with a decrease in static pressure or the fluid's potential energy.

The constant can be normalized in the Bernoulli equation. A common approach is total head or energy head H:

[tex]{\displaystyle H=z+{\frac {p}{\rho g}}+{\frac {v^{2}}{2g}}=h+{\frac {v^{2}}{2g}},}[/tex]

a) speed on the second floor can be calculated as:

[tex]Q_1=Q_2[/tex]

[tex]A_1V_1=A_2V_2[/tex]

[tex]\displaystyle \frac{\pi }{4}(d_1^2) \times V_1 = \frac{\pi }{4}(d_2^2) \times V_2[/tex]

[tex](2.5)^2\times 0.90 =(1.2)^2\times V_2[/tex]

V₂= 3.90 m/s

b) water pressure on the second floor can be calculated as:

[tex]{\displaystyle {\frac {P_1}{\rho g}}+{\frac {V_1^{2}}{2g}}+h_1 = {\frac {P_2}{\rho g} +{\frac {V_2^{2}}{2g}}} +h_2[/tex]

[tex]{\displaystyle {\frac {170\times 1000}{9.80\times 1000}}+{\frac {(0.90)^{2}}{2\times 9.80}}+7.6 = {\frac {P_2}{\rho g} +{\frac {(3.90)^{2}}{2\times 9.80}}}[/tex]      here  [tex]h_1-h_2 = 7.6[/tex]

[tex]{\displaystyle {\frac {P_2}{\rho g} = 24.215[/tex]

P₂ = 240000 Pa

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The total electric potential due to these charges at the  center is 9 * 10^5 J/C.

V = k × [q/r]

V = electric potential energy.

q = point charge.

r = distance between any point around the charge to the point charge.

k = Coulomb constant; k = 9.0 × 10^9 N.

at  The center (0,0)

r = 4 cm

due to Q1

v1= k ( 2.00 μC/ 4 * 10^-2) = 9.0 × 10^9 * 0.5* 10^-4 =4.5 * 10^5 J/C

due to Q2

v2 = k ( 2.00 μC/ 2 cm) = 9.0 × 10^9 * 1* 10^-4 =4.5 * 10^5 J/C

total potential at (0.0) = 9 * 10^5 J/C

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Answer:

   [tex]4 m/s^{2}[/tex]

Explanation:

You can use the formula a = (v2 - v1)/t, where a is the acceleration, v1 is the initial velocity, v2 is the final velocity, and t is the time interval.

In this case, v1 is 0 m/s (since the car starts at rest) and v2 is the final velocity of the car after it travels 100 m in 5 seconds. You can use the formula v = d/t to find the final velocity, where v is the velocity, d is the distance traveled, and t is the time taken. Plugging in the given values, you get:

v = d/t

= 100 m / 5 s

= 20 m/s

Now you can plug in the values for a, v1, v2, and t into the formula to find the acceleration:

a = (v2 - v1)/t

= (20 m/s - 0 m/s)/5 s

= [tex]4 m/s^{2}[/tex]

The wavelength of the fundamental string vibration is 0.64 m and the wavelength of the sound wave produced is 0.77 m. This difference is due to the change in speed of the sound wave in air and in the string.

Sound wave is a mechanical wave moves through a medium only. The frequency of a sound wave is called its pitch and it is the number of wave cycles obtained per unit time.

The wavelength for the fundamental frequency is = 2L

= 2 × 0.32 = 0.64 m

Now the speed of the sound waves in air = 340 m/s

frequency = 440 Hz or s⁻¹.

Thus, the  wavelength of sound wave = speed/ frequency

= ( 340 m/s)/  440 Hz = 0.77 m.

This change in wavelength from that of the  fundamental vibration is due to the change in speed of sound waves in different mediums.

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The force on the vehicle is 500000 N means that a force of 500000 N is being applied to the vehicle and its momentum is changing at a rate of 500k kg m/s²

Well, we all know Force is equal to the product of mass and acceleration. Force is nothing but, a measure of the rate of change of momentum of an object. When we say the force acting on any particle is x newtons, we mean that the particle is accelerating at x/m meter per square second at that instant  (where m is the mass of the particle). In this case, we have been given that the force applied on the vehicle is 500000 newtons. 500000 newtons can be also written as 500k Newtons. So when we are applying a force of 500k Newtons on the vehicle, in this case, we can't really find the acceleration of the vehicle as no mass is given. But we can tell one thing here, that is, a force of 500k Newtons on the vehicle means that at that particular instant the rate of change of momentum is

500k kg m/s².

So, basically, a force of 500k Newtons means that the rate of change of momentum is 500k kg m/s².

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The area on contact between the surfaces and the type of the bodies both affect how much friction there . Rolling has a smaller area of contact than sliding does, and rolling friction is lower than sliding friction.

For kids, what does sliding friction mean?

When things slide over a surface, there is friction called sliding friction. Static friction is more powerful than sliding friction. Because of this, it's simpler to move a furniture item once it's started moving that it is to stop it from moving.

What is the name for a sliding force?

There may still be friction between the surfaces even when they are moving past one another; this sliding friction is known as a kinetic friction coefficient.

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Answer:

The formula of acceleration (a) = velocity (v)- initial velocity (u) /time taken(t)

Alpha particles have a charge +2e decay is far and away from the foremost common sort of cluster decay, where the parent atom ejects an outlined daughter collection of nucleons, leaving another defined product behind. Like in case of other cluster decays, Alpha decay is also a fundamentally quantum tunnelling process.

Understanding Q Value in Alpha Decay:

In Physics, the Q-value is defined as the difference between the sum of the rest masses of original reactants and the sum of final product of masses. In simpler terms, we can say that the Q-value is the difference between the final and initial mass energy of the decayed products.

For the alpha decay equations, this Q-value is,

Q = (mX – mY – mHe) c2 (he-helium)

The energy Q derived from this decay is divided equally into the total transformed nucleus and the Helium nucleus.  

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Answer: alpha decay, type of radioactive disintegration in which some unstable atomic nuclei dissipate excess energy by spontaneously ejecting an alpha particle.

Explanation:

Minimum operating frequency or the cut off frequency for a rectangular waveguide is given by: f c = c 2 m 2 a 2 + n 2 b 2. a = length of the waveguide. b = height of the waveguide. m,n = modes of operation.

What is a wavelength?

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A concussion can be caused by the forces from a header with a light soccer ball if the ball is struck with a high level of force.

When a soccer ball is struck with a high level of force, it can create a shock wave that travels through the ball and into the head of the player who struck the ball. This shock wave can cause the brain to rapidly move back and forth inside the skull, resulting in trauma to the brain tissue.

The likelihood of a concussion occurring from a header with a light soccer ball depends on a variety of factors, including the speed and angle at which the ball is struck, the size and mass of the ball, and the position of the player's head when the ball is struck.

Players who are struck in the head by a soccer ball, particularly at high speeds or with high levels of force, are at risk of sustaining a concussion or other head injury. It is important for players to be aware of the potential for concussion and to take precautions to protect themselves from injury.

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Answer:

Therefore, the potential energy of 300 kg of water as it starts the descent from the top of the 30 m waterfall is 294.3 Joules.

Explanation:

In this case, you are given that the mass of the water is 300 kg, and the height of the waterfall is 30 m. The acceleration due to gravity is given as 9.81 m/s2. Plugging these values into the formula, you can find the potential energy of the water as it starts the descent from the top of the waterfall:

PE = 300 kg * 9.81 m/s2 * 30 m

= 294.3 kg * m^2/s^2

= 294.3 Joules

The potential energy of 300 kg of water as it starts the descent from the top of the 30 m waterfall is 294.3 Joules.

Potential energy is a form of stored energy that is dependent on the relationship between different system components. When a spring is compressed or stretched, its potential energy increases. If a steel ball is raised above the ground as opposed to falling to the ground, it has more potential energy.

Given parameters:

Mass of the water: m = 300 kg.

Acceleration due to gravity: g = 9.81 m/s²

Height: h = 30 m.

Hence, potential energy of the water at the top of the waterfall =

mass × acceleration due to gravity × height

= 300 kg × 9.81 m/s² ×30 m

= 294.3 kg-m²/s²

= 294.3 Joules

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If the coefficient of kinetic friction between a 26 kg crate and the floor is 0.34, the required horizontal force to move the crate at a steady speed is 86.6 Newton.

Steady speed means the acceleration is zero.

According to the Newton's first law of motion, to produce a motion with zero acceleration, the net force must be equal to zero.

In the problem, the forces are the horizontal force and the friction force.

Hence, the net force is:

∑F = 0

Fh - friction = 0

Fh - μ . mg = 0

Where:

Fh = horizaontal force

m = mass of the crate = 26 kg

g = acceleration due to gravity = 9.8 m/s²

μ = coefficient of kinetic friction = 0.34

Plug all the parameters into the equation,

Fh - 0.34 x 26 x 9.8 = 0

Fh = 86.6 N

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The work done by the vacuum cleaner which produced a force of 62 N is 268.77 J

The force produced by the vacuum cleaner = 62 N

The distance traveled by the vacuum cleaner = 5 m

The angle at which the vacuum cleaner is kept = 30°

The work done by the vacuum cleaner can be found using the formula,

           W = Fdcosθ

where W is the work done

           F is the force

           d is the distance traveled

           θ is the angle at which the vacuum cleaner is kept

Let us substitute the known values in the above equation, we get

        W = 62 x 5 x cos 30°

            =  310 x 0.867

            = 268.77 J

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Answer:

SONAR is short for Sound Navigation And Ranging. One of the earliest SONAR-like devices was invented by naval architect Lewis Nixon in 1906. It was designed to detect icebergs underwater to help ships navigate around them. This detection system became more important after the sinking of the in 1912.

Explanation:

"A change of phase takes place at a constant temperature."

A substance changing its phase by a physical process is called a phase change. The shift often happens when heat is applied or removed at a specific temperature, also referred to as the substance's melting or boiling point.

Both when the system receives enough energy and when the pressure on the system changes, these changes take place.

The energy that is given during a change in the state of matter is used to alter the binding energies rather than boost the kinetic energy of the molecules. As a result, the temperature doesn't change.

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Answer:

A simple microscope is simple in structure It was invented by Robert Hook It is less convenient to use it can only helps us to detect the virus but not bacteria It is cheap compared to other microscope

The binding energy per nucleon for ¹⁴N is 7.48 MeV.

The binding energy per nucleon for ⁵⁶Fe is 8.79 MeV.

The binding energy per nucleon for ²⁰⁷Pb is 7.87 MeV.

The formula to calculate the mass defect for [tex]^A_Z X[/tex]

ΔM = (Z × mp) + (N × mn) - m

To calculate the binding energy per nucleon

BE = (ΔM × 931.5 MeV) ÷ A

For [tex]^{14}_7 N[/tex]

For [tex]^{56}_{26} Fe[/tex]

For [tex]^{207}_{82} Pb[/tex]

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The length of the semi-major axis of the new planet will be 22.3 AU.

As per Kepler's law of period:

The square of a planet's period of revolution around the sun in an elliptical orbit is precisely equal to the cube of its semi-major axis.

Mathematically, we can write it as:

The period of a planet's orbit (P) squared is equal to the size of the semi-major axis of the orbit (a) cubed when it is stated in astronomical units because [tex]P^2 = a^3[/tex] according to Kepler's Third Law.

For earth T=1 year

r=1 AU

let us assume that [tex]r_p[/tex] is the radius of the new planet.

For new planet; [tex]T_p[/tex] = 105 years

Using Kepler's 3rd law:,

We can write it as:

[tex]\frac{T^2}{T_p^2}=\frac{r^3}{r_p^3} \\\\\Rightarrow\left(\frac{1}{105}\right)^2=\frac{(1)^3}{\left(r_p\right)^3}=0.0000907 \\\\\Rightarrow r_p=\left(\frac{1}{0.0000907}\right)^{\frac{1}{3}}\\\\=22.257 \mathrm{AU} \\[/tex]

Approximately 22.3 Years.

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Answer:

An atom is the smallest amount of matter that undergoes chemical changes. The accepted theory today is that the atom is composed of a positively charged nucleus made up of protons and neutrons, collectively known as a nucleon, around which is a cloud of negatively charged electrons.

Different experiences have allowed us to measure the size of atoms. Considered as a sphere, the atom has a radius of about 10-10 m and the nucleus has a radius of about 10-14 m. From this it can be deduced that the nucleus is about 10,000 times smaller than the atom.

They are organized and classified based on their atomic numbers, chemical properties, and electronic charge on the periodic table. Atoms are made up of smaller parts called subatomic particles, which include protons, neutrons, and electrons.

Explanation:

:)

Answer:

The tariff will Reduce imports into the domestic country, and since its imports represent a sizeable proportion of the world market, world demand for the product will fall.

What are tariffs?

A tariff is a type of tax that a country imposes on imported goods at its borders. Tariffs have historically been a tool for governments to generate revenue, but they are also a way governments seek to protect domestic producers.

As a protectionist measure, tariffs increase the price of imported goods. As a result, consumers choose to buy relatively cheap domestic products instead.

In today's global economy, many products that consumers buy contain components from other countries or are assembled abroad. As a result, tariffs can also hit consumers of products they believe are made in their own country.

The tariff will Reduce imports into the domestic country, and since its imports represent a sizeable proportion of the world market, world demand for the product will fall.

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It take to reach merging speed at 70mph is 10.6 s

You should be travelling at or close to the speed of the oncoming traffic when merging into the motorway. It's acceptable if you move a little more slowly, but the goal is to prevent traffic congestion. To increase your speed and enable a seamless traffic merge, take use of the time you have on the ramp or in the merging lane.

Step one:

given data

acceleration, a= 14ft/sec^2

final velocity v= 70mph

first, let is convert mph to ft/sec

1mph is 1.46667 ft/sec

70 mph is x

cross multiply we have

x= 102.7ft/s

Step two:

we are using the first equation of motion

v=u+at

initial velocity u= 0m/s

102.7=0+14*t

102.7=14t

divide both sides by 10

t=10.6seconds

Therefore It take to reach merging speed at 70mph is 10.6 s

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A majority of the an organization's overall ghgs (GHG) emissions frequently come from scope 3 emissions, also known as value chain emissions.Although not every class will be applicable to all enterprises, the GHG Protocol lists 15 types of scope 3 emissions.

In many industries (and more than 90% in many global corporations, according to CDP reporting), scope 3 emissions, also known as "Value Chain emissions," make up the bulk of total emissions. These emissions are regarded as essential to combating climate change.

Scope 3 emission are indirect emission of greenhouse gases that are produced in the larger economy in addition to scope 2 emissions.They result from a facility's operations, but they come from sources that the facility's operations do not own or control.

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The parametric equations of the velocity as a function of time are Vx (t) = 2.4 and Vy (t) = - 2.4 · t, respectively.

Parametric equations are equations in terms of a single variable t, the velocity of the particle is the first derivative of position, whose definition is shown below:

Vx (t) = dx (t) / dt

Vy (t) = dy (t) / dt

Where:

Physically speaking, the single variable t represents time.

The derivative are found by derivative rules. If we know that x (t) = α · t and y(t) = 3 - β · t², then the velocity functions are:

Vx (t) = α

α = 2.4 m / s

Vx (t) = 2.4

Vy (t) = - 2 · β · t

β = 1.2 m / s²

Vy (t) = - 2.4 · t

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The current flowing when the charge is transfered at different rates are:

A. 4.5 A4.5 A

B. 3.2 A

C. 4.6 A

D. 3 A

E. 2 A

F. 13 A

G. 6.4 A

H. 8.8 A

I. 0.5 A

We know that charge, current and time are related by the following formula:

Charge (Q) = Electric current (I) × time (t)

Q = It

Divide by t

I = Q / t

With the above formula, we can obtain the current. Details below:

A. How do I determine the current?

I = Q / t

I = 4.5 / 1

I = 4.5 A

B. How do I determine the current?

I = Q / t

I = 192 / 60

I = 3.2 A

C. How do I determine the current?

I = Q / t

I = 16560 / 3600

I = 4.6 A

D. How do I determine the current?

I = Q / t

I = 1.8 / 0.6

I = 3 A

E. How do I determine the current?

I = Q / t

I = 3.2 / 1.6

I = 2 A

F. How do I determine the current?

I = Q / t

I = 33.8 / 2.6

I = 13 A

G. How do I determine the current?

I = Q / t

I = 147.2 / 23

I = 6.4 A

H. How do I determine the current?

I = Q / t

I = 7920 / 900

I = 8.8 A

I. How do I determine the current?

Charge (Q) = 7920 C

Time (t) = half hour = 30 mins = 30 × 60 = 1800 s

Current (I) = ?

I = Q / t

I = 900 / 1800

I = 0.5 A

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The x axis supports a proton and an electron. At x = -d, the proton is located, while at x = +d, the electron.

One of the three main types of particles within an atom is an electron that is bonded to it; the other two are protons and neutrons. The nucleus of an atom is made up of electrons, protons, and neutrons together. The positive charge of a proton balances the negative charge of an electron.

Electrons are incredibly light, negatively charged particles. These electrons move in distinct orbits around the nucleus. (ii) Protons have a mass of roughly 1 amu and are positively charged particles. These positively charged particles can be found in the nucleus, which sits in the center of the atom.

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The ball's change in momentum on the bounce will be "0.308 kg.m/s."

Since linear momentum is mv, it varies with each bounce by the same quantity, r = R. For instance, if a ball bounced 80% of its height each time, it would lose 20% of its energy.

Velocity and Motion

The answer is that the mass of a baseball is m = 0.140 m.

-1.20 m/s is the downward speed.

Upward speed, v "= 1 m/s

Since we are aware of the momentum, P = mv

The force acting downward is: = mv'

When the data are put together, Pv = 0.140 (-1.20) Pv = -0.168 kg.m/s

The forward motion is now: = mv "Pv = 0.140 kg/s/s Pv = 0.140 kg/s/s

Therefore, the modification will be: = 0.140 - (-0.168)

Pv-Pu = 0.308 kg/m/s

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The correct answer is B) partially inelastic. If the masses of the blocks and the velocities before and after being given then The collision is partially inelastic.

To determine the character of the collision, you need to compare the kinetic energy before and after the collision. If the kinetic energy is the same before and after the collision, the collision is elastic. If the kinetic energy is less after the collision, the collision is inelastic. If the kinetic energy is greater after the collision, the collision is not possible because energy cannot be created or destroyed, it can only be transformed from one form to another.

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An object's momentum may be calculated mathematically by multiplying its mass by its velocity. Mass plus velocity equals momentum.

Mass in motion, which is related to the mass of a moving body, is the straightforward definition of momentum. By multiplying the mass with the velocity, the amount of motion is calculated. Momentum is defined as the result of multiplying mass and velocity.

According to a mathematical formula, an object's momentum is determined by multiplying its mass by its speed. Mass multiplied by velocity equals momentum. Momentum is represented by the lower case letter p in physics. As a result, p = m • v may be used to rewrite the previous equation.

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ODE solver ode15s does non-stiff problems more slowly than ode45, but it performs stiff problems more quickly. almost always The solver you should use initially is ode45. If there are rough tolerances or moderate stiffness present, ode23 may perform better than ode45.

The ODE solvers' preferred function is often ODE45. In order to calculate step size and estimate error, it compares approaches of orders four and five. Because ODE45 is so precise, using its interpolant to produce results at intermediate points is its default practice.

In cases of tight tolerances or when evaluating the ODE function is very costly, ode113 might be more effective than ode45. ODE 113 is a multistep solver; in order to calculate the current solution, it typically needs the solutions at several earlier time points.

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The order of a differential equation is the order of the highest derivative appearing in it.

The degree of a differential equation is the power of the highest derivative occurring in it, after the Equation has been expressed in a form free from radicals as far as the derivatives are concerned.

What is a differential equation?

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