Two blocks with mass M and 3M on a horizontal frictionless surface are pushed together and compress a spring of negligible mass that is squeezed between them. The spring remains in place because the compression leads to a sufficient amount of friction with the sides of the blocks. It is important to understand that the spring is NOT attached to the blocks, in other words, that it will fall down as soon as the distance between the blocks exceeds the natural length of the spring. After the blocks are pushed together, a horizontal rope then secures the blocks in place.Later the rope is cut with scissors and the heavier block is launched with a speed of 2 m/s in the positive x-direction.

Define very precisely the system, the interaction(s) and the interaction time(s) of interest, and justify very precisely the principle(s) you apply to calculate the launching speed of the lighter block.

The result of the ratio of the displacement module of the second body at the point of meeting is 0.5.

To determine the ratio of the displacement of the first body to the displacement of the second body at the moment of their meeting, use the equation of motion:

d = vt + 1/2at²

where d is the displacement, v is the initial velocity, t is the time, and a is the acceleration.

Since the bodies are moving simultaneously towards each other, then assume that their initial velocities are zero. Also, at the moment of their meeting, their displacement will be the same, d₁ = d₂.

Assume that the time at which they meet is t, then:

d₁ = 1/2 * 2.4t²

And the equation for the displacement of the second body:

d₂ = 1/2 * 4.8t²

If d₁ = d₂

then, 1/2 * 2.4t² = 1/2 * 4.8t²

Solving this equation for t and substituting it into the equation for d₁ or d₂, the ratio of the displacement of the first body to the displacement of the second body: d₁/d₂ = 2.4/4.8 = 0.5 or 1/2

So, at the moment of their meeting, the displacement of the first body is half of the displacement of the second body.

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The kinetic energy of the flywheel after 1 minute of rotation, given that it has a mass of 50 and radius of 40 cm is 32.4 KJ (Option D)

We'll begin by obtaining the velocity of the flywheel. This is shown below:

v = at

v = 0.6 × 60

v = 36 m/s

Finally, we shall determine the kinetic energy of the flywheel. Details below:

KE = ½mv²

KE = ½ × 50 × 36²

KE = 25 × 1296

KE = 32400 J

Divide by 1000 to express in KJ

KE = 32400 / 1000

KE = 32.4 KJ

Thus, the kinetic energy is 32.4 KJ (Option D)

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Answer:

1. ELE to KE = Electrical energy conversion to kinetic energy.

2. KE to ELE = kinetic energy conversion to electrical energy.

3. CE to ELE = chemical energy conversion to electrical energy.

Explanation:

The Law of Conservation of Energy states that energy cannot be destroyed but can only be transformed or converted from one form to another.

Some examples of energy are chemical energy, electrical energy, kinetic energy, sound energy, potential energy, light energy, etc.

The transformation of energy from one form to another are described below;

1. A hair dryer plugged into the wall: it involves the conversion of electrical energy to kinetic energy. The energy type present in the wall socket is electrical energy which powers the hair dryer to have kinetic energy i.e the energy possessed due to motion of hair dryer.

2. A hand crank generator emergency radio: it illustrates the conversion of kinetic energy to electrical energy. The hand crank generator possess kinetic energy as it is being wounded before it is then converted into electrical energy which powers the radio.

3. A battery operated fan: it illustrates the conversion of chemical energy to electrical energy. The cells present in battery possess chemical energy that is being converted into electrical energy to power the fan.

(a) Velocity with which the mug leaves the counter is approximately 5.02 m/s.

(b) The direction of velocity of mug just before it hits the floor is downwards, since mug is falling under influence of gravity.

Velocity is a quantity that designates how fast and also in what direction a certain point is moving.

(a) As we know, PE = m g h

\(\mathrm{PE = mgh }\)

\(\mathrm{= (m)(9.81 m/s^2)(1.36 m) }\)

= 13.4mJ

\(\mathrm{KE =\frac{1}{2} mv^2}\)

PE = KE

\(\mathrm{mgh = \frac{1}{2}mv^2}\)

\(\mathrm{v = \sqrt{2gh}}\)

\(\mathrm{v = \sqrt{2 \times 9.81 \times 1.36 m}}\)

v = 5.02 m/s

Therefore, the velocity with which the mug leaves the counter is approximately 5.02 m/s.

(b) The direction of the velocity of mug just before it hits the floor is downwards, since mug is falling under the influence of gravity. Velocity vector has a vertical component that points downwards and horizontal component that is parallel to counter.

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Answer:

Whenever one body exerts a force on a second body, the first body experiences a force that is equal in magnitude and opposite in direction to the force that it exerts

Explanation:

Answer: According to Khan Academy "Newton's third law: If an object A exerts a force on object B, then object B must exert a force of equal magnitude and opposite direction back on object A.

Explanation: This law represents a certain symmetry in nature: forces always occur in pairs, and one body cannot exert a force on another without experiencing a force itself. We sometimes refer to this law loosely as action-reaction, where the force exerted is the action and the force experienced as a consequence is the reaction.

We can readily see Newton’s third law at work by taking a look at how people move about. Consider a swimmer pushing off from the side of a pool, as illustrated below.

A swimmer pushes on the wall with her feet, which causes the wall to push back on her feet due to Newton's third law."

Hope this helps ^_^ and have a great day

The volume of the tire at the given diameter and thickness of tube is determined as  1,128.2 cubic inch.

Volume is a scalar quantity expressing the amount of three-dimensional space enclosed by a closed surface.

The volume of the tire is the measure of the product of area and thickness of the tire.

The volume of the tire is calculated as follows;

Radius of the tire = 0.5 x 26" = 13"

Volume of the tire = Area x thickness

Volume of the tire = πr² x h

where;

Volume of the tire = π(13)² x (2.125)

Volume of the tire =  1,128.2 cubic inch

Thus, the volume of the tire at the given diameter and thickness of tube is determined as  1,128.2 cubic inch.

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The net force acting on the car is equal to -12000 Newton.

Given the following data:

To determine the net force acting on the car:

Mathematically, the net force acting on the car is given by Newton's Second Law of Motion:

\(F = \frac{m(v\;-\;u)}{t}\)

Where:

Substituting the given parameters into the formula, we have;

\(F = \frac{1200 \times (0\;-\;30)}{3}\\\\F = \frac{1200 \times (-30)}{3}\\\\F = \frac{-36000 }{3}\)

Net force = -12000 Newton.

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The example of a crime against a person is Injuring a stranger.

Injury is any physical damage or harm caused to the body, including cuts, scrapes, bruises, broken bones, and burns. It can be caused by an accident, medical negligence, or intentional harm. Injuries can range from mild to severe and can be temporary or permanent. Treatment for an injury often involves rest, medications, physical therapy, and sometimes surgery. In more severe cases, an injury can cause lasting disability or even death. Prevention of injuries is important, and can be achieved through education, wearing protective gear, and avoiding risky activities.

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Answer:

animals and wildlife (c)

Explanation:

Ecotourism is essentially tourism of nature--which highly incorporates animals/wildlife

> it usually has a goal of conservation of nature

poaching is illegally hunting wild animals, which is focused on an aspect of nature protection (which is why it is ecotourism)

the only option listed here that is about ecotourism is animals and wildlife (c), meaning that this is the correct fill-in

hope this helps! have a lovely day :)

The speed of the cylindrical container will increase as you increase the temperature of the fluid.

The speed of an object moving down an inclined plane is determined by applying Newton's second law of motion.

F(net) = ma

where;

The net force on the object is determined by subtracting force of friction from the applied force and it is given as;

F(net) = F - Ff

F(net) = F - μmg

where;

When the temperature of the fluid inside the sealed cylindrical container increases, the container becomes more light because the fluid will acquire more kinetic energy and kinetic frictional force resisting the motion of the container reduces and consequently the speed of the cylindrical container will increase.

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Answer:

r =\(\frac{ 1 \pm \sqrt{ \frac{m}{M} } }{1 - \frac{m}{M} }\)

Explanation:

Let's apply the universal gravitation law to the body (c), we use the indications 1 for the planet and 2 for the moon

          ∑ F = 0

           -F_{1c} + F_{2c} = 0

             F_{1c} = F_{2c}

let's write the force equations

             \(G \frac{m_c M}{r^2} = G \frac{m_c m}{(d-r)^2}\)

where d is the distance between the planet and the moon.

              \(\frac{M}{r^2} = \frac{m}{(d-r)^2}\)

             (d-r)² = \(\frac{m}{M} \ \ r^2\)  

              d² - 2rd + r² = \frac{m}{M} \ \ r^2

              d² - 2rd + r² (1 - \(\frac{m}{M}\)) = 0

              (1 - \(\frac{m}{M}\))  r² - 2d r + d² = 0

we solve the second degree equation

              r = [2d ± \(\sqrt{ 4d^2 - 4 ( 1 - \frac{m}{M} ) }\) ] / 2 (1- \(\frac{m}{M}\))

              r = [2d ±  2d \(\sqrt{ \frac{m}{M} }\)] / 2d (1- \(\frac{m}{M}\))

              r =\(\frac{ 1 \pm \sqrt{ \frac{m}{M} } }{1 - \frac{m}{M} }\)

there are two points for which the gravitational force is zero

The distance between object from planet will be "\(\frac{R}{[1+\sqrt{\frac{m}{M} } ]}\)".

According to the question,

Let,

As we know,

→ \(Prerequisites-Gravitational \ force = \frac{GMm}{r^2}\)

Now,

→ \(\frac{GMm_1}{x^2} = \frac{Gmm_1}{(R-x)^2}\)

→ \(\frac{(R-x)^2}{x^2} = \frac{m}{M}\)

→     \(\frac{R-x}{x} =\sqrt{\frac{m}{M} }\)

→          \(x = \frac{R}{[1+ \sqrt{\frac{m}{M} } ]}\)

Thus the answer above is appropriate.          

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Answer:

Hello your question lacks some information and that is the distance

At r = 0.150 m (outside the cable)  note :  (μ 0 = 4π × 10-7 T · m/A)

answer: 4.7 * 10^-6 T

Explanation:

R1 = 0.03 m

R2 = 0.07 m

R3 = 0.1 m

Inner conductor carries current = 4.5A in one direction

outer conductor carries current = 8A in opposite direction

Determine the value of magnetic field at r = 0.150 m

net current = 8 - 4.5 = 3.5 A

∴ β ( value of  magnetic field )

= ( 4π * 10^-7 * 3.5 ) / ( 2π * 0.150 )

= 4.4*10^-6 / 0.94

= 4.7 * 10^-6 T

Answer:

True

Explanation:

Answer: Depends

Explanation:

It completely depends on your religion and beliefs. This is not a question you can truly answer since it's opiniative.

To determine the angle through which the wheel rotates in 1.00 second, we can start by finding the angle covered in 0.0710 seconds and then scale it up to 1.00 second.

In 0.0710 seconds, the wheel completes 3.10 revolutions. One revolution corresponds to an angle of 360 degrees or 2π radians. Therefore, in 0.0710 seconds, the wheel rotates through an angle of:

Angle = 3.10 revolutions * 2π radians/revolution = 6.20π radians

To find the angle in 1.00 second, we can use proportional reasoning. Since the time increases by a factor of 1.00/0.0710, the angle covered will also increase by the same factor:

Angle in 1.00 second = 6.20π radians * (1.00/0.0710) = 87.32π radians

Approximately, the angle through which the wheel rotates in 1.00 second is 274.39 radians.

Therefore, the wheel rotates through an angle of approximately 274.39 radians in 1.00 second.

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The worker must apply 600N of force to lift the sound system. The mechanical advantage of 2.5 means that the worker only needs to apply 600N of force to lift the sound system.

We can employ pulley systems to provide ourselves a mechanical advantage by multiplying our input effort to apply more force to a load.

They can be used to apply tension within a system, such as in a Tensioned Line or Tyrolean, in addition to their traditional uses of hauling and lifting loads. The basic operating principles of pulley systems are explained on this page; for details on how to use them for hauling, check the topic on hauling systems.

The dynamic unit of Newtons is commonly used to express force, which is an impact that has both magnitude and direction (N). On this page, kilograms have been utilized for the sake of clarity.

Therefore, The worker must apply 600N of force to lift the sound system. The mechanical advantage of 2.5 means that the worker only needs to apply 600N of force to lift the sound system.

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Answer:

when we get images from the telescope, we're not seeing those object like they are right now. we're seeing them like they looked when that light left those distant objects...... the animation cuts to a visualization of distant galaxies imaged by Hubble.

The half-life of hypothetical element  technetium-99 is 210,936 years.

Half-life of the hypothetical element From the graph provided in the question, the half-life of the hypothetical element can be obtained by finding the time taken for the element to reduce to half its original quantity. Here, it can be seen from the graph that the quantity of the element reduces from 40 to 20 on day 4. Therefore, the half-life of the hypothetical element is 4 days.2. Time taken for a sample to decay from 100 grams to 25 gramsIf the half-life of a given substance is 65 days, then the quantity of the substance reduces to half every 65 days. From 100 grams to 50 grams, it takes one half-life cycle. From 50 grams to 25 grams, it will take another half-life cycle.

Therefore, it will take two half-life cycles, which is 2 × 65 = 130 days, for a 100-gram sample of the substance to decay until there is only 25 grams of the radioactive material remaining.3. Half-life of a sample that decays from 200 grams to 50 grams in 60 minutesIt is given that the sample of radioactive isotopes takes 60 minutes to decay from 200 grams to 50 grams. To find the half-life, we need to determine how many times the sample has lost half of its mass, which tells you how many half-life cycles have occurred.At 30 minutes, the sample reduces to half its original quantity, which is 100 grams. At 45 minutes, it reduces to 50 grams, which is half of 100 grams. Therefore, it takes two half-life cycles to reduce from 200 grams to 50 grams in 60 minutes. Hence, the half-life of the isotope is 15 minutes.4. Half-life of technetium-99 that decays from 500.0 g to 62.5 g in 639,000 yearsIt is given that a 500.0 g sample of technetium-99 decays to 62.5 g of technetium-99 remaining in 639,000 years. We can use the half-life formula to find the half-life of technetium-99.t1/2 = (t × log2) / log(N0 / Nt) Where,t1/2 = half-life of the substanceN0 = initial quantity of the substance Nt = quantity of the substance left after time t (in years)t = time (in years)From the given data,t1/2 = (639000 × log2) / log(500.0 / 62.5)t1/2 = 210,936 years.

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Power= current x potential difference

To find total resistors in ohms, in parallel circuit, do 1/given ohms for all resistors first; then, add them together:

1/3 ohms + 1/2 ohms = 5/6 ohms

V= IR

xR

VR = I

I=VR

= 9 x 5/6

= 7.5 amps

P = I x V

= 7.5 x 9

= 67.5

Hope this helps!

The energy transferred in Joules by the radio when it has been switched on for 2 minutes would be 6000 Joules.

Power is defined as the rate of energy transfer or the rate at which work is done, and is given by the equation:

Power = Energy transferred / Time

Rearranging the equation to solve for energy transferred, we get:

Energy transferred = Power x Time

We are given:

Power = 50 W

Time = 2 minutes = 120 seconds

Therefore, the energy transferred by the radio when it has been switched on for 2 minutes is:

Energy transferred = Power x Time = 50 W x 120 s = 6000 J

In other words, the energy transferred by the radio is 6000 Joules.

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Answer:

\(F=3.61\times 10^{-47}\ N\)

Explanation:

Mass of a proton, \(m_p=1.67\times 10^{-27}\ kg\)

Mass of an electron, \(m_e=9.11\times 10^{-31}\ kg\)

The distance between the electron and the proton is, \(r=5.3\times 10^{-11}\ m\)

We need to find the mutual attractive gravitational force between the electron and proton. The gravitational force is given by :

\(F=G\dfrac{m_em_p}{r^2}\)

Where G is the universal Gravitational constant

\(F=6.67\times 10^{-11}\times \dfrac{9.11\times 10^{-31}\times 1.67\times 10^{-27}}{(5.3\times 10^{-11})^2}\\\\F=3.61\times 10^{-47}\ N\)

So, the force between the electron and proton is \(3.61\times 10^{-47}\ N\).

250 BC by Aristarchus is the answer ot the question

Data supporting the theory of a round earth was collected as early as _____.

1570 AD by Galileo

1500 AD by Copernicus

250 BC by Aristarchus

1640 AD by Kepler

A to B : not moving

B to C : negative acceleration

C to D : constant velocity

D to E : not moving

E to F : positive acceleration

The boat's final velocity can be determined using the work-energy principle. Since the boat starts at rest, the work done on it will be equal to its change in kinetic energy.

Using the equation:

Work = Change in Kinetic Energy

300 J = (1/2) * m * v^2

where m is the mass of the boat and v is the final velocity, we can solve for v.

Plugging in the values:

300 J = (1/2) * 4.5 kg * v^2

Simplifying the equation:

v^2 = (2 * 300 J) / 4.5 kg

v^2 = 200 J / 4.5 kg

v^2 = 44.44 m^2/s^2

Taking the square root of both sides:

v = √(44.44 m^2/s^2)

v ≈ 6.66 m/s

Therefore, the boat's final velocity is approximately 6.66 m/s.

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The reactants in the given chemical equation are methane (CH₄) and oxygen (O₂), while the products are carbon dioxide (CO₂) and water (H₂O).

During a chemical reaction, the atoms of the reactants reorganize to form new compounds in the products. A chemical change is this atomic rearrangement.

A chemical change is the transformation of one or more substances into new ones with distinct chemical and physical properties. New substances are created when the original substances' atoms are rearranged and new chemical bonds are formed during a chemical change.

Typically, a transfer of energy in the form of heat, light, or sound occurs in conjunction with this kind of change. Reactions like combustion, oxidation, decomposition, and synthesis are all examples of chemical changes. Physical changes, on the other hand, involve alterations in a substance's physical properties without altering its chemical composition.

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The efficiency of the ramp is 80% and the mechanical advantage is 2.

To solve this problem, we can use the formulas for efficiency and mechanical advantage:

Efficiency = (output work / input work) x 100%

Mechanical Advantage = output force / input force

First, we need to find the output force and output work of the ramp.

The output force is the weight of the box, which is 1200 N.

The output work is the force applied by the output force over the distance it moves. Since the box moves a distance of 1.0 m up the ramp,

the output work is:

Output work = output force x output distance

Output work = 1200 N x 1.0 m

Output work = 1200 J

Next, we need to find the input force and input work of the ramp.

The input force is the force applied by the man, which is 600 N.

The input work is the force applied by the input force over the distance it moves. Since the man moves a distance of 2.5 m along the ramp,

the input work is:

Input work = input force x input distance

Input work = 600 N x 2.5 m

Input work = 1500 J

Now we can calculate the efficiency and mechanical advantage:

Efficiency = (output work / input work) x 100%

Efficiency = (1200 J / 1500 J) x 100%

Efficiency = 80%

Mechanical Advantage = output force / input force

Mechanical Advantage = 1200 N / 600 N

Mechanical Advantage = 2

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Answer:

v = (1500/10) = 150 [miles/h]

Explanation:

The velocity can be easily calculated using the following kinematics expression:

v = x/t

where:

v = velocity [miles/h]

t = time = 10 [hr]

x = distance = 1500 [miles]

v = (1500/10) = 150 [miles/h]

Answer: Pressure of gases.

Explanation:

In a heat engine, the air-fuel mixture is ignited, which causes an increase in pressure of the gases inside the cylinder. This pressure pushes the piston, which is connected to a crankshaft, causing it to rotate and do work. Therefore, pressure is an essential property of gases for the ability of a heat engine to do work.