define work done against friction
(helpp)​

Answer:

Electromagnetic waves do not require a medium to propagate means they  can travel through air and solid material and the vacuum of space too.

they move the fastest through gases mostly because particles in gases are spread out more than the particles in solids or in liquids so they move quickly through gases.

Explanation:

Answer:

The largest reservoir of phosphorous is sedimentary rock.

Major sources of phosphorous to aquatic ecosystems are fertilizer runoff, sewage leaks, and industrial wastes.

Eccess phosphorous can lead to eutrophication

Explanation:

Phosphorus come from different sources such as aquatic ecosystems and fertilizers used for plants. When these substances containing phosphorus and those from industrial wastes find their way into water bodies, they tend to cause eutrophication, which is the natural enrichment of water bodies.  

Also, it is known that a very small portion of phosphoric acid contribute to acid rain in the atmosphere.  

Answer:

The statements that are true are:

-The largest reservoir of phosphorous is sedimentary rock

- Major sources of phosphorous to aquatic ecosystems are fertilizer runoff, sewage leaks, and industrial wastes.

- Excess phosphorous can lead to eutrophication.

Explanation:

In nature, phosphorous is found in form of phosphate ions PO₄⁻³, which are forming part of sedimentary rocks. Upon the action of wind and rain, phosphorous is washed into the soil (it dissolves and its passes into the soil in form of phosphate compounds). So, the largest reservoir of phosphorous is sedimentary rock.

Phosporous in the soil is absorbed by animal and plants and it is transformed in biological components (like nucleic acids, phospholipids, etc), and when animal and plants die, phosphorous return to the soil. So, the most of the phosphorous cycle occurs in the Earth (soil, water, living beings). In fact, phosphorous does not circulate through atmosphere.

Human activities such as farming and industry impact in phosphorous cycle. Fertilizers, wastes from human activities and phosphorous-containing products are poured in oceans and they feed the cycle.

But the excess of phosphorous often leads to an overgrowth of algae, which causes a lack of oxygen in water and consequenty the death of aquatic organisms. This fenomena is called eutrophication.

Finally, the major acid found in acid rain is sulphuric acid (it is not phosphoric acid).

The characteristic that changes in each isotope of calcium is the number of neutrons in the nucleus. The atomic number remains the same for all the isotopes.

The characteristic that differs in each isotope of an element, in this case, Calcium (Ca), is D. the number of neutrons in the nucleus. An isotope is a variant of a particular chemical element, and what distinguishes one isotope from another is the number of neutrons. For instance, Ca-40, Ca-42, Ca-43, and Ca-44 hold 20, 22, 23, and 24 neutrons, respectively. The atomic number, which represents the number of protons in an atom, remains the same for all isotopes of an element. Therefore, the number of neutrons in the nucleus is the only characteristic that changes within isotopes of the same element.

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The correct answer is D. The only characteristic that varies among the listed calcium isotopes is the number of neutrons in the nucleus.

Since the atomic number of calcium (Ca) is 20, each isotope of calcium has 20 protons. The isotopes listed in the question, Ca-40, Ca-42, Ca-43, and Ca-44, have atomic masses of 40, 42, 43, and 44, respectively.

To find the number of neutrons in each isotope, we subtract the number of protons (which is constant for calcium) from the atomic mass:

- For Ca-40: 40 (atomic mass) - 20 (protons) = 20 neutrons

- For Ca-42: 42 (atomic mass) - 20 (protons) = 22 neutrons

- For Ca-43: 43 (atomic mass) - 20 (protons) = 23 neutrons

- For Ca-44: 44 (atomic mass) - 20 (protons) = 24 neutrons

As we can see, the number of neutrons varies in each isotope, which is the characteristic that is different for each isotope listed.

The other options provided in the question can be ruled out based on the following reasons:

 A. the position in the periodic table of the elements - All calcium isotopes have the same position in the periodic table because they all have 20 protons, which defines their atomic number and thus their position in the periodic table.

B. the net charge of the nucleus - The net charge of the nucleus is determined by the number of protons, which is the same (20) for all calcium isotopes. Therefore, the net charge of the nucleus does not vary among these isotopes.

C. the mass of the protons in the nucleus - The mass of a proton is constant and does not vary from one isotope to another. All calcium isotopes have the same number of protons, so the mass of the protons is not the characteristic that differs among these isotopes.

Answer:

You now this question state why a person standing at point Y hears an echo

Explanation:

Density is mass divided by volume.  For example, Block A:

ρ = m / V

ρ = 60 g / 125 cm³

ρ = 0.48 g/cm³

I assume each block is a cube, so the length of block underwater divided by the side length of the block is the percent underwater.

% = 1.8 / 3.9

% = 46%

Repeat for Blocks B through E.

Answer:

The velocity of the package before hitting the floor is 35.28 m/s.

Explanation:

Given:

The package is dropped, so initial velocity is, [tex]u=0\ m/s[/tex]

Time taken to reach the floor is, [tex]t=3.60\ s[/tex]

The motion is a complete free fall motion.

When the body is in free fall, the only acceleration acting on the body is due to gravity.

Therefore, the acceleration of the package is, [tex]a=g=9.8\ m/s^2[/tex]

Now, final velocity of the package is, [tex]v=?[/tex]

In order to find the final velocity, we need to use the Newton's equation of motion that relates initial velocity, final velocity, acceleration and time taken.

So, the equation of motion used is given as:

[tex]v=u+at[/tex]

Plug in the given values and solve for 'v'. This gives,

[tex]v=0+9.8\times 3.60\\v=35.28\ m/s[/tex]

Therefore, the velocity of the package before hitting the floor is 35.28 m/s.

Answer:

35.316 [tex]m/s[/tex]

Explanation:

Given: [tex]t=3.60\ sec[/tex]

In free fall velocity does not depend upon height of fall.

Now, we will use the relation between final velocity (v) and initial velocity (u) and time (t) under free fall.

That is [tex]v=u+gt[/tex]

Where 'g' is acceleration due to gravity which is [tex]9.81 m/s^2[/tex]

Here initial velocity (u) is zero as package was dropped from rest.

Plugging the values in the equation, we get.

[tex]v=u+gt\\\\v=0+9.81(t)\\\\v=9.81(3.60)\\\\v=35.316\ m/s[/tex]

Hence, the velocity with which the ball will hit the ground will be [tex]v=35.316\ m/s[/tex].

In an analogy between water and electric current, the flow of water would correspond to the electric current. Electric current is defined as the rate at which charge flows, and can be envisioned as similar to the flow of water moving past a given section in a pipe. The direction of the current is the direction the positive charge would flow, although it's driven by the movement of negatively charged electrons.

In an analogy between water and electric current, if water corresponds to charge, the flow of water would correspond to the electric current. This is because electric current is defined as the rate at which charge flows. Specifically, 1 Ampere (A) is equal to 1 Coulomb per second (1C/s), meaning it represents one coulomb of charge passing through a given area per second, similar to how we might measure the number of water molecules flowing past a specific point in a pipe per second.

Just as water flows from high to low elevation, electric current flows from high to low electrical potential. For example, in a battery, electrons (which carry the charge) will move from the low-potential terminal (negative end) through to the high-potential terminal (positive end). It should be noted that the direction of conventional current is defined as the direction positive charge would flow, even though, in reality, it is the negatively charged electrons that are moving.

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Answer:

4 kWh or 4 units

Explanation:

energy = power × time

            = 400 W×  10 h

            = 4000 Wh

           =( 4000/ 1000 )  kWh

            = 4 kWh

             = 4 commercial units

Answer:

The mass of the block is 0.025 kg

Explanation:

Mass-Spring Harmonic Motion

When a mass m is attached to a spring of constant k, they produce a simple harmonic motion which angular frequency is

[tex]\displaystyle w=\sqrt{\frac{k}{m}}[/tex]

We also know

[tex]w=2\pi f[/tex]

which means

[tex]\displaystyle \sqrt{\frac{k}{m}}=2\pi f[/tex]

Squaring

[tex]\displaystyle \frac{k}{m}=4\pi^2 f^2[/tex]

Solving for m

[tex]\displaystyle m=\frac{k}{4\pi^2 f^2}[/tex]

We have

[tex]k=10 N/m, f=10/\pi Hz[/tex]

[tex]\displaystyle m=\frac{10}{4\pi^2 \left (\frac{10}{\pi}\right )^2}[/tex]

Operating

[tex]\displaystyle m=\frac{10}{4\pi^2 \frac{100}{\pi^2}}[/tex]

Simplifying and computing

[tex]\displaystyle m=\frac{1}{40}=0.025\ kg[/tex]

The mass of the block is 0.025 kg

A 2 kg fluffy pillow has more volume, while a 3 kg small piece of iron has more mass due to their differences in density.

A 2 kg fluffy pillow has more volume, while a 3 kg small piece of iron has more mass.

The volume of an object is the amount of space it occupies. The fluffy pillow, being soft and compressible, takes up more space than its mass would suggest.

The mass of an object, on the other hand, is the amount of matter in it. The small piece of iron, though heavier, occupies less space and has a higher density than the fluffy pillow.

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A 3 kg piece of iron has more mass than a 2 kg pillow, but the pillow likely has a greater volume due to lower density. The difference in density affects the volume that the same mass of two different materials occupies.

The 3 kg small piece of iron has more mass than the 2 kg fluffy pillow because 3 kg is greater than 2 kg. However, the fluffy pillow likely has more volume because it is less dense than the iron. This difference occurs because density is defined as mass divided by volume. The iron has a higher density which means it has more mass in a given volume compared to the pillow's material. For instance, a kilogram of feathers has the same mass as a kilogram of iron, but the feathers occupy a much larger volume because they are less dense.

Let's consider the weight in Newtons as an example. The weight of an object on Earth can be calculated by multiplying its mass in kilograms by the acceleration due to gravity (9.8 m/s2). So, the weight of a 3 kg textbook is approximately 29.4 Newtons (3 kg × 9.8 m/s2).

Finally, comparing materials of the same weight, a pound of gold has the same mass as a pound of iron on Earth’s surface, but their volumes and thus their densitiess Will differ. The density is the critical factor determining volume for the same mass of two different substances.

Answer:A

Explanation:just took the test

The question is missing the graph. So, the graph is attached below.

Answer:

The value of [tex]F_{max}[/tex] is 7380 N.

Explanation:

Given:

Mass of the ball is, [tex]m=45\ g=0.045\ kg[/tex]

Initial velocity of the ball is, [tex]u=0\ m/s(Assuming)[/tex]

Final velocity of the ball is, [tex]v=41\ m/s[/tex]

From the graph,

Time interval for which the force acts, [tex]\Delta t=0.5\ ms=0.5\times 10^{-3}\ s[/tex]

Height of the triangle is equal to the maximum force acting on the ball = [tex]F_{max}[/tex]

Now, we know that, impulse acting on the ball is equal to the area under the curve of force and time graph.

So, impulse is equal to the area of the triangle and is given as:

Impulse = [tex]\frac{1}{2}\times base\times height[/tex]

Here, base is time interval [tex]\Delta t[/tex] and height is [tex]F_{max}[/tex].

Impulse = [tex]\frac{1}{2}\times (0.5\times 10^{-3})\times F_{max}[/tex]

Impulse = [tex]0.25\times 10^{-3}F_{max}[/tex]

Now, we also know that, impulse is equal to the change in momentum of a body.

Therefore, change in momentum (Δp) is given as:

[tex]\Delta p=m(v-u)\\\Delta p = 0.045(41-0)=1.845\ kgms^{-1}[/tex]

Now, change in momentum is equal to impulse acting on the ball. Thus,

[tex]0.25\times 10^{-3}F_{max}=1.845\\\\F_{max}=\frac{1.845}{0.25\times 10^{-3}}\\\\F_{max}=7380\ N[/tex]

Therefore, the value of [tex]F_{max}[/tex] is 7380 N.

Answer:

The arrow is pointing to the "nucleus."

Explanation:

A cell is the smallest unit in an organism. It mainly functions to provide structure to the human body, thus it is call "the building blocks of life."

There are 6 organelles in a cell and these are: Nucleus, Ribosomes, Endoplasmic Reticulum, Golgi Aparatus, Chloroplasts and Mitochondria.

The arrow is pointing to the cell's nucleus in the image above. This is an organelle that is enclosed in a membrane. It is where you can find the deoxyribonucleic acid or the DNA, which is essential for hereditary function. It also coordinates activities in the cell, such as metabolism, synthesis of proteins, cell division, etc.

Remember, not all cells have nucleus. Only eukaryotic cells have a nucleus. This cells are considered as more advanced.

the arrow is pointing to nucleus

the function of this organelle that it controls the activities of the cells

Answer:

A) Shape of Continental coastlines matching up together

Explanation:

It helped provide evidence for how the plates moved. Answer B could be right, but the moving of the plates helped provide evidence as to why we were finding similar fossils on different countries so it's almost opposite

An area where the water table is at, near, or above the land surface long enough during the year to support adapted plant growth is called a wetland.

Explanation:

Wetland is a private water body, which gets fed permanently or seasonally. Wetland is not purely a water body, because it allows some aquatic plants to grow which have adapted to its hydric soil.  They have their place in almost every continent. They have some types too, namely swamp, marsh, bog, etc.

Mangrove forests are also a type of wetlands because the roots of the mangrove trees store a huge amount of water, which can be used for different purposes. And also, the wetland is at sea-level, which means it is near to the water table also. Its spatial flow is identical to that of the flow of groundwater.

Answer:

D

Explanation:

All the options A, B, and C are true for a swinging pendulum. As it swings, potential energy is converted to kinetic energy and vice versa, and the lowest potential energy occurs at the lowest point of the swing.

During the swing of the pendulum, energy is continuously being transformed between kinetic and potential forms.

At the highest points of the swing, the pendulum has the most potential energy because it is the furthest away from the point of equilibrium, and as it starts falling, this potential energy is converted into kinetic energy. Conversely, as it swings upwards, the kinetic energy is transformed into potential energy.

At the lowest point of the swing, the pendulum has its maximum kinetic energy and minimum potential energy, thereby making all the provided statements true.

Answer:

C. The procedure scientist use to gain knowledge about the ohysical world

Explanation:

The correct answer is C. The procedure scientists use to gain knowledge about the physical universe.

Explanation:

The scientific method is a non-linear procedure used to answer questions about specific phenomena or understand the world. This method includes a set of steps that are used to create a hypothesis and then tested it successfully. Besides this, the scientific method is applied in most areas related to science because through this scientist can explain or understand the physical universe. According to this, the scientific method can be best described as "The procedure scientists use to gain knowledge about the physical universe".

Answer:

false

Explanation:

its a trick question. not all evidence should be collected from the crime scene due to not all the evidence be useful.

Answer:

The frequency should increase.

Explanation:

The wavelength of a wave varies inversely to frequency of the wave.

The relation between the frequency and wavelength of a wave is given as:

[tex]f\lambda=v[/tex]

Here, [tex]f\to frequency\\\lambda\to wavelength\\v\to velocity\ of\ wave[/tex]

Therefore, as the wavelength increases then the frequency will decrease.

Similarly, as the wavelength of the wave decreases, then the frequency will increase.

So, the frequency should increase if you decrease the wavelength of a wave.

Answer:

Potential energy converted = 4.2*10^7 [J]

Explanation:

This problem has to be analysed under the principle of energy conservation. For this case potential energy that is transformed into kinetic energy, but however not all potential energy is transformed into kinetic energy, as we are told that some of this energy dissipates in the form of heat. We must first find the potential energy.

Potential energy

[tex]E_{p} =m*g*h\\where:\\m = mass =3.5*10^4[kg]\\g = gravity = 9.81[m/s^2]\\h = elevation = 126.5 [m]\\therefore\\E_{k} = 3.5*10^4*9.81*126.5\\E_{k} = 43433775 [J][/tex]

Kinetic Energy

[tex]E_{k}=\frac{1}{2} * m*v^{2}\\ where:\\v = velocity = 10[m/s]\\therefore:\\E_{k}=\frac{1}{2} * 3.5*10^4*10^{2}\\\\E_{k}=1750000[J][/tex]

As we can see, not all potential energy has been transformed into kinetic energy. That is, part of this energy dissipates as thermal energy, so this difference of energies will be equal to the loss of energy represented as dissipated energy.

[tex]Thermal Energy\\T_{e} = 43433775-1750000\\T_{e} =41683775[J][/tex]

The previous value can be approximated to 4.2 * 10^7 [J]

Answer:

4.2 x 10^7

I hope this helps!

a) It means that the relative change of length of the copper, [tex]\Delta L/L[/tex], increases by 0.000017 for each increase in temperature of 1 degrees

b) The safety gap must be 0.33 mm

Explanation:

a)

The linear expansivity of a material is a measure of how much the length of a sample of that material expands per unit increase of temperature.

Mathematically, the linear expansivity can be written as

[tex]\alpha = \frac{\Delta L/L}{\Delta T}[/tex]

where

[tex]\Delta L[/tex] is the change in length of the sample

L is the original length of the sample

[tex]\Delta T[/tex] is the change in temperature of the sample

For instance, in this problem, we are told that the linear expansivity of copper is

[tex]\alpha = 0.000017/K[/tex]

Which means that the relative change of length of the copper, [tex]\Delta L/L[/tex], increases by 0.000017 for each increase in temperature of 1 degrees.

b)

We can re-write the formula written in part a as

[tex]\Delta L = \alpha L \Delta T[/tex]

where, applied to this problem, each variable means:

[tex]L[/tex] is the length of the steel bar

[tex]\alpha[/tex] is the linear expansivity of steel

[tex]\Delta L[/tex] is the change in length of the steel bar when the temperature increases by [tex]\Delta T[/tex]

In this problem, we have:

L = 3 m

[tex]\alpha = 1.0\cdot 10^{-5}/K[/tex]

[tex]\Delta T = 40^{\circ}C-29^{\circ}C=11^{\circ}C[/tex]

Therefore, the change in length of a steel bar is

[tex]\Delta L = (1.0\cdot 10^{-5})(3)(11)=0.00033 m = 0.33 mm[/tex]

Which means that the safety gap between two successive bars must be 0.33 mm.

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Answer:

B. A line angled upward

Explanation:

velocity is plotted along y- axis and time is plotted along x- axis so we get a line angled upward

a) The mechanical advantage is 4

b) The velocity ratio is 5

c) The efficiency is 80%

Explanation:

a)

The mechanical advantage of a lever (or any other machine) is given by

[tex]MA=\frac{Load}{Effort}[/tex]

Where

[tex]Eff[/tex] is the effort (the force applied in input)

[tex]Load[/tex] is the load (the force in output to the lever)

For the lever in this problem, we have:

[tex]Eff = 50 N[/tex]

[tex]Load = 200 N[/tex]

Substituting into the equation, we find the mechanical advantage of the lever:

[tex]MA=\frac{200}{50}=4[/tex]

b)

The velocity ratio of a lever (or any other machine) is given by the equation

[tex]vr=\frac{d_{res}}{d_{eff}}[/tex]

where

[tex]d_{res}[/tex] is the length of the resistance arm

[tex]d_{eff}[/tex] is the length of the effort arm

For the lever in this problem, we have

[tex]d_{res} = 20 cm[/tex]

[tex]d_{eff}=1 m = 100 cm[/tex]

Therefore, the velocity ratio is

[tex]vr=\frac{100}{20}=5[/tex]

The velocity ratio represents the ideal mechanical advantage of the machine, i.e. the mechanical advantage in absence of friction, or the maximum theoretical mechanical advantage.

c)

The efficiency of the lever is given by the following ratio:

[tex]\eta = \frac{MA}{vr}[/tex]

where

MA is the mechanical advantage

vr is the velocity ratio

For the lever in this problem, we have

MA = 4 (calculated in part a)

vr = 5 (calculated in part b)

Therefore, the efficiency of the lever is

[tex]\eta = \frac{4}{5}=0.80[/tex]

Which means an efficiency of 80%.

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Answer:the realization or fulfillment of one's talents and potentialities, especially considered as a drive or need present in everyone.

Explanation:

your welcome

Answer:

the realization or fulfillment of one's talents and potentialities, especially considered as a drive or need present in everyone.

Explanation:

In other words, for our purposes, self-actualization can be thought of as the full realization of one’s creative, intellectual, or social potential.

Answer:

18%

Explanation:

There are two equal and opposite forces on a floating object: weight and buoyancy.

W = B

The weight of an object is its mass times gravity: W = mg

Buoyancy is the weight of the displaced fluid: W = mf g

Plugging in:

mg = mf g

m = mf

Mass is density times volume:

ρV = ρf Vf

Solving for the ratio of Vf / V:

Vf / V = ρ / ρf

Given that ρ = 0.82 g/mL and ρf = 1.00 g/mL:

Vf / V = 0.82

That means 82% of the object's volume (and therefore, 82% of its mass, assuming uniform density) is submerged.  Which means that 18% is above the water line.

Answer:

The length of the runway to the nearest meter is 306 m.

Explanation:

Given:

Initial velocity of Christina is, [tex]u=0\ m/s(Rest)[/tex]

Time taken is, [tex]t=5\ s[/tex]

Acceleration experienced by Christina is, [tex]a=24.5\ m/s^2[/tex]

The length of the runway is, [tex]d=?[/tex]

Now, we use Newton's equation of motion that relates the distance, initial velocity, time and acceleration.

So, we have the following equation of motion:

[tex]d=ut+\frac{1}{2}at^2[/tex]

Plug in all the given values and solve for 'd'. This gives,

[tex]d=0+\frac{1}{2}\times 24.5\times 5^2\\\\d=\frac{1\times 24.5\times 25}{2}\\\\d=\frac{612.5}{2}\\\\d=306.25\approx 306\ m(\textrm{Rounding to nearest meter})[/tex]

Therefore, the length of the runway to the nearest meter is 306 m.

Answer:

1)  both velocity and acceleration at x =  λ /2 are 0

2)maximum velocity at x=λ /4 is -2Aω

  maximum acceleration at x=λ /4 is Aω²

3)maximum velocity at x=λ /8 is √2Aω

maximum acceleration at x=λ /8 is (-Aω²/√2)

Explanation:

When a string is tied at both ends and vibrated, we get standing waves.

The general form of standing wave is,

y(x,t) = 2A×sin(kx)×cos(ωt)   (displacement of string at x and at time t)

where, A = amplitude of wave

ω = 2πv , v = frequency of the wave

k = 2π/λ ;  λ = wavelength of wave

Speed V = ω/k.

Now, differentiating y(x,t) by once with t gives velocity

⇒V(x,t) = -2Aω×sin(kx)×sin(ωt)

And differentiating once again gives acceleration

a(x,t) = -Aω²×sin(kx)×cos(ωt)

1) x= λ/2

⇒V(x,t) = -2Aω×sin(k(λ /2))×sin(ωt)

            = -2Aω×sin(π)×sin(ωt)

            = 0

a(x,t) = -Aω²×sin(kx)×cos(ωt)

⇒ a(x,t) = -Aω²×sin(k(λ /2))×cos(ωt)

             = -Aω²×sin(π)×cos(ωt)

             = 0

2) x= λ /4

⇒V(x,t) = -2Aω×sin(kx)×sin(ωt)

            = -2Aω×sin(k(λ /4))×sin(ωt)

            = -2Aω×sin(π/2)×sin(ωt)

             = -2Aω sin(ωt)

⇒ maximum velocity at x=λ /4 is -2Aω (minimum sin value is -1)

a(x,t) = -Aω²×sin(kx)×cos(ωt)

        = -Aω²×cos(ωt)

⇒ maximum acceleration at x=λ /4 is Aω² (minimum cos value is -1)

3) x= λ /8

⇒V(x,t) = -2Aω×sin(kx)×sin(ωt)

             = -√2Aω×sin(ωt)

⇒ maximum velocity at x=λ /8 is √2Aω (minimum sin value is -1)

a(x,t) = -Aω²×sin(kx)×cos(ωt)

         = (-Aω²/√2) × cos(ωt)

⇒ maximum acceleration at x=λ /8 is (-Aω²/√2) (minimum cos value is -1)

The velocity perpendicular to the radius vector is called the transverse velocity. The transverse acceleration is the acceleration produced by an inertial force acting across the body. The expression for the maximum transverse velocity and acceleration has been obtained for given values of x.

A horizontal string tied at both ends is vibrating in its fundamental mode.

Velocity perpendicular to the radius vector is called the transverse velocity.

The formula for the maximum transverse velocity can be given as,

[tex]V_m=-2A\omega\sin(kx)\times \sin(\omega t)[/tex]

Transverse acceleration is the acceleration produced by an inertial force acting across the body.

[tex]a_m=-A\omega^2 \sin(kx)\times \cos(\omega t)[/tex]

[tex]V_m=-2A\omega\sin(k\dfrac{\lambda}{y} )\times \sin(\omega t)\\ V_m=-2A\omega\sin(\pi )\times \sin(\omega t)\\ V_m=0[/tex]

[tex]a_m=-A\omega^2 \sin(k\dfrac{\lambda}{2} )\times \cos(\omega t)\\ a_m=-A\omega^2 \sin(\pi )\times \cos(\omega t)\\ a_m=0[/tex]

[tex]V_m=-2A\omega\sin(k\dfrac{\lambda}{4} )\times \sin(\omega t)\\ V_m=-2A\omega\sin(\dfrac{\pi}{2} )\times \sin(\omega t)\\ V_m=-2A\omega \times \sin(\omega t)\\ [/tex]

[tex]a_m=-A\omega^2 \sin(k\dfrac{\lambda}{4} )\times \cos(\omega t)\\ a_m=-A\omega^2 \sin(\dfrac{\pi}{2} )\times \cos(\omega t)\\ a_m=-A\omega^2 \times \cos(\omega t)\\[/tex]

[tex]V_m=-2A\omega\sin(k\dfrac{\lambda}{8} )\times \sin(\omega t)\\ V_m=-{\sqrt{2} }{A\omega\times \sin(\omega t)} \\ [/tex]

[tex]a_m=-A\omega^2 \sin(k\dfrac{\lambda}{4} )\times \cos(\omega t)\\ a_m=\dfrac{-A\omega^2\times \cos(\omega t)}{\sqrt{2} } \\ [/tex]

Thus the maximum transverse velocity and maximum transverse acceleration at given points has been obtained.

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Answer:

11.85 kg m/s

Explanation:

impulse = mass ( change in velocity )

              = mass ( final velocity - initial velocity )

               = 0.150 ( 32.0 - (-47.0))

                = 0.150 ( 32.0 +47.0)

                = 0.150 (79)

                = 11.85 kg m/s

Answer:

11.85

Explanation:

its correct

Answer:

The kinetic energy will be 49000[J]

Explanation:

This problem is the common use of energy conservation when the body is at the top at the point where its elevation is the highest (usually the lowest point is taken as the reference level) at that point the body will have the highest potential energy, then as the body descends its potential energy decreases but its kinetic energy begins to increase. By the time the body reaches the lowest point or reference point, its potential energy will be zero, but its maximum kinetic energy, as all potential energy has become kinetic energy.

Therefore:

[tex]Ep=m*g*h\\where\\m =100 [kg]\\g= 9.81 [m/s^2] gravity\\h = 50 [m]\\\\Ep= 100*9.81*50\\Ep=49000 [J][/tex]

This energy will be transformed into kinetic energy at the bottom of the hill.

The kinetic energy of the roller coaster car at the bottom of the hill is 49,000 J, which equals the potential energy at the top of the hill assuming no energy loss to friction.

The motion of roller coasters relies on the conversion between potential and kinetic energy.

At the top of a hill, a roller coaster car has maximum gravitational potential energy, which is given by the equation:

where

Thus,

Assuming no energy loss due to friction, this potential energy is entirely converted to kinetic energy at the bottom of the hill.

Hence, the kinetic energy of the car at the bottom is: 49,000 J.

Answer:

True

Explanation:

Just as Isaac Newton says, "For every action, there is an equal and opposite reaction."

Answer:

70,000 N

Explanation:

Draw a free body diagram of the Jeep.  There are two tension forces, both pulling the Jeep towards the tree.

The net force is:

ΣF = 2T

ΣF = 2 (35,000 N)

ΣF = 70,000 N

The maximum force that can be exerted on the Jeep due to the cable arrangement is 70000N.

The net force, ΣF ; can be calculated thus :

ΣF = 2 × Tension

Net force = 2 × 35000

Net force = 70,000 N

Therefore, the net force that is exerted on the Jeep is 70,000N.

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