In a popular classroom demonstration, a cotton ball is placed in the bottom of a strong test tube. A plunger fits inside the tube and it makes an air-tight seal. It is then pushed down very rapidly, and the cotton flashes and burns. This happens because ______.

Answer:

The turbine is rotated and rotates the generator to produce electricity.

Explanation:

Within a turbine enters the superheated steam which is at high pressure and high temperature, this steam is previously formed in the boiler when the steam enters the turbine hits each one of the blades of the turbine making it rotate at a given speed, the turbine shaft is coupled to the shaft of an electric generator and thus generates electricity.

It is also important to say that when the steam comes out of the turbine comes out at low pressure, this way the internal operating process is carried out within the turbine.

Answer:

A. fuel mileage and longevity          

Explanation:

           For a person purchasing a car, car longevity is one of the main concern. They are also interested in many things such as maximum mileage and service life.

           By properly monitoring and assessing few measures one can maintain the efficiency and longevity of the car. One such thing is by monitoring the liquid levels of the car. Certain liquids like the coolant or radiator water level should be well maintain in proper level in order to run the car economically.

Thus by doing this, one can optimize the car's longevity and the fuel mileage.

Hence the correct option is (A).

Final answer:

Monitoring fluid levels can optimize a car's fuel mileage and longevity. Hybrid cars are noted for their fuel efficiency, while vehicle weight and aerodynamic design also play roles in gas mileage. Efficient driving habits and vehicle technology contribute to both cost savings and environmental responsibility.

Explanation:

Assessing and monitoring your fluid levels is important for maintaining your vehicle and optimizing its fuel mileage and longevity. Proper fluid levels ensure that your car operates efficiently, which can lead to improved fuel efficiency, thus making the vehicle more cost-efficient and environmentally responsible. Option A

For instance, maintaining the correct level of engine oil can reduce friction in the engine, which can prevent excessive fuel consumption. Furthermore, ensuring proper coolant levels can help manage the vehicle's temperature, preventing overheating that might otherwise lead to engine damage and reduce fuel efficiency.

In addition to regular maintenance, driving behaviors such as adhering to speed limits and accelerating smoothly also contribute to fuel economy, as indicated by the feedback from eco-driving aids like the one in the Ford Fusion that displays a plant with leaves when driving efficiently.

Studies have shown that hybrid cars are not only reliable but also have a significant advantage in terms of fuel efficiency over conventional cars. A Toyota Prius, for example, gets notable gas mileage, boasting 48 miles per gallon on the highway and 51 mpg in the city, while a Ford Fusion hybrid gets 47 mpg in both city and country conditions. These hybrid vehicles incorporate technology that enhances their overall fuel efficiency, providing cost savings over the long term and contributing positively to environmental sustainability.

It's also worth noting that the weight of a vehicle affects its fuel economy. Heavier vehicles typically consume more fuel. Therefore, car manufacturers aim to reduce the weight of cars to improve their miles per gallon. Such considerations also extend to the design of the cars. Aerodynamic shaping can reduce drag force, further enhancing a car's gas mileage. Lastly, road wear and tear incurred by heavy vehicles suggests a deeper relationship between weight distribution, axle weight, and the environmental impact of driving.

Answer:

1. The period doubles

2. The mechanical energy is unchanged

3. The speed is halved

4. The period is unchanged

5. The energy is quadrupled

6. The maximum is speed doubled

Explanation:

1.  From Hooke's law we have [tex]T\propto\sqrt{\frac{m}{k} }[/tex]

where T is period, m is mass and k is the spring constant

So If the mass is increased by a factor of 4 then period doubles while k constant

2 According to law of conservation of energy, the energy remains unchanged so therefore the total mechanical energy remain unchanged.

3. From the  [tex]w = \sqrt{\frac{k}{m} }[/tex]

where m is  mass and w is speed

so we see that mass and speed is inversely proportional therefore if we increase mass speed decreases.

4. The period is independent of amplitude

5. [tex]E=A^{2} [/tex]

where E is energy and A is amplitude

So if the amplitude is doubled the energy is quadrupled.

6.  we have the relation

[tex]v_{max}=A [/tex]

where [tex]v_{max}[/tex] is maximum speed and A is amplitude  

From the formular we can see they are directly proportional, so if we double amplitude then [tex]v_{max}[/tex] doubles also.

The period would double when the mass of the spring is increased by a factor of four (4).

Since all springs obey Hooke’s law, the period is given by this formula:

[tex]T\alpha \sqrt{\frac{m}{k}}\\\\T = 2\pi \sqrt{\frac{m}{k} }[/tex]

Where:

We can deduce that, the period is directly proportional to mass of the spring. Thus, the period would double when the mass of the spring is increased by a factor of four (4).

In accordance with the law of conservation of energy, the total mechanical energy of the spring would remain the same because energy can neither be created nor destroyed.

The speed of a spring in simple harmonic motion is an angular speed and it is given by this formula:

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

We can deduce that, the angular speed is inversely proportional to mass of the spring. Thus, the angular speed would decrease when the mass of the spring is increased by a factor of four (4).

In simple harmonic motion, the period of a spring is independent of its amplitude.

Mathematically, the the total mechanical energy of a spring is given by this formula:

[tex]E=A^2[/tex]

We can deduce that, the total mechanical energy is directly proportional to the square of amplitude of the spring. Thus, the total mechanical energy would quadruple when the amplitude of the spring is doubled.

Also, the maximum speed is directly proportional to the amplitude of the spring. Thus, the maximum speed would also double when the amplitude of the spring is doubled.

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Explanation:

Mass of ball, m = 2 kg

Acceleration due to gravity, g = 9.81 m/s²

Height of ball from ground = 3 - 1 = 2 m

Potential energy, PE = mgh

Potential energy of ball, PE = 2 x 9.81 x 2 = 39.24 J

a) Potential energy of ball at ceiling = 2 x 9.81 x 3 = 58.86 J

Potential energy of ball relative to ceiling = 58.86 - 39.24 = 19.62 J

b) Potential energy of ball at floor = 2 x 9.81 x 0 = 0 J

Potential energy of ball relative to floor = 39.24 - 0 = 39.24 J

c) Potential energy of ball at same elevation = 2 x 9.81 x 2 = 39.24 J

Potential energy of ball relative to same elevation = 39.24 - 39.24 = 0 J

The gravitational potential energy of the ball relative to the ceiling and a point at the same elevation as the ball is 0 Joules because they are at the same height. The gravitational potential energy of the ball relative to the floor is 39.24 Joules.

The gravitational potential energy of an object, in this case, the 2.00 kg ball, can be calculated using the formula: PE = mgh, where m is the mass of the object in kg, g is acceleration due to gravity (on Earth, it's about 9.81 m/s²), and h is the height in meters.

(a) the ceiling: The distance from the ceiling to the center of the ball is 1.00m, thus the potential energy relative to the ceiling is PE = 2.00 kg * 9.81 m/s² * 0 m = 0 J, since the ball is at the same level as the ceiling.

(b) the floor: The height of the ball from the floor can be calculated as the height of the room minus the distance from the ceiling to the center of the ball, which is 3.00 m - 1.00 m = 2.00 m. Thus, the potential energy relative to the floor is PE = 2.00 kg * 9.81 m/s² * 2.00 m = 39.24 J.

(c) a point at the same elevation as the ball: Since the point is at the same elevation as the ball, therefore, the potential energy would be PE = 2.00 kg * 9.81 m/s² * 0 m = 0 J.

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Answer:

Adding gallium, boron, or indium to pure silicon or germanium will create a material with an excess of holes which is called a p-type material.

Explanation:

gallium, boron or indium are elements with three valency electron, and they are called Acceptor impurities. When acceptor impurities are added to pure silicon, it is called dopping

dopping: This is the process by which impurities is added to semi conductors in order to alter its electrical conductivity. The impurities is called dopants.

Adding gallium, boron, or indium to pure silicon or germanium will create a material with an excess of holes which is called a p-type material.

Answer: the excess material created is called "Hole".

Explanation: When the semiconductor such as silicon or germanium with four electrons in the outermost shell known as valence electron is added to either of electrons from indium,gallium or boron which has three valency electrons, a hole is created.

A hole which has positive charge is caused as a result of the movement of valence electrons from an atom to another atom.

A hole brings about conduction in semiconductor materials, (i.e when the free electrons with negative charge and holes with positive charge move in opposite direction in the semiconductor, conduction takes place).

Answer:

The recoil velocity of the cannon is 7.61 m/s in the opposite direction of the cannonball

Explanation:

Linear Momentum

The principle of conservation of the linear momentum establishes that the sum of the linear momentums of every object in an isolated system (no external forces) is constant, regardless of the interactions between them.

Let's think we have two objects with masses [tex]m_1[/tex] and [tex]m_2[/tex], moving at speeds [tex]v_1[/tex] and [tex]v_2[/tex]. If they collide and change their speeds to [tex]v_1'[/tex] and [tex]v_2'[/tex], then

[tex]m_1v_1+m_2v_2=m_1v_1'+m_2v_2'[/tex]

In our problem, the 880 kg cannon is initially at rest and has the cannonball of 12.4 Kg inside of it. As the initial speed of both joined objects is zero, the initial total momentum is zero. After the ball is fired, the ball moves at v_2=540 m/s. We need to find the recoil velocity of the cannon [tex]v_1'[/tex]

[tex]m_1v_1'+m_2v_2'=0[/tex]

[tex]\displaystyle m_1v_1'=-m_2v_2'[/tex]

[tex]\displaystyle v_1'=-\frac{m_2v_2'}{m_1}[/tex]

[tex]\displaystyle v_1'=-\frac{12.4(540)}{880}=-7.61\ m/s[/tex]

The recoil velocity of the cannon is 7.61 m/s in the opposite direction of the cannonball

Answer:

a. Law of Constant Composition, Law of Multiple Proportions, Law of Conservation of Mass Alpha particles are scattered at a variety of angles (over 90 degrees) when bombarded at gold foil.

Explanation:

Which of the following supports the claim that the atom is like a solid positive cookie with negative electrons embedded within it? (This model is known as the Plum Pudding Model of the atom, and is illustrated to the right).

a. Law of Constant Composition, Law of Multiple Proportions, Law of Conservation of Mass Alpha particles are scattered at a variety of angles (over 90 degrees) when bombarded at gold foil.

b. When light from hydrogen emissions passes through a diffracting grating, there are distinct bands of color.

c. The Cathode Ray Tube experiment, in which the ray was attracted to the south pole of the magnet.

the plumbudding model of the atom was postulated by  JJ Thompson and plum pudding model. . ... Thomson had discovered that atoms are composite objects, made of pieces with positive and negative charge, and that the negatively charged electrons within the atom were very small compared to the entire atom.

so a. correctly typifies the thompson model of the atom

Final answer:

Option c, the Cathode Ray Tube experiment, supports the claim that the atom is like a solid positive cookie with negative electrons embedded within it.

Explanation:

The correct option that supports the claim that the atom is like a solid positive cookie with negative electrons embedded within it is option c. The Cathode Ray Tube experiment, in which the ray was attracted to the south pole of the magnet, is consistent with the Plum Pudding Model of the atom. This model describes atoms as having a diffuse positive charge with embedded electrons.

Answer:

μ= 0.3

Explanation:

Given that

F= 33 N

m = 11 kg

Given that crate is moving with constant velocity is means that acceleration of the crate is zero.If acceleration of the system is zero then the total force on the system will be balance.

Therefore

F= Friction force

F= μ m g

μ=Coefficient of friction

33 = μ x 10 x 11                       ( take g= 10 m/s²)    

3 = 10 μ

μ= 0.3

Therefore coefficient of friction will be 0.3 .

Explanation:

We have velocity

             v(t)= -32t + 83

Integrating

              s(t) = -16t²+83t+C

At t = 0 displacement is 46 feet

              46 = -16 x 0²+83 x 0+C

                 C = 46 feet

So displacement is

              s(t) = -16t²+83t+46

a) Initial velocity is

                 v(0)= -32 x 0 + 83 = 83 ft/s

       Initial velocity = 83 ft/s

b) Maximum velocity is when the object reaches ground, that is s(t) = 0 ft

Substituting

             0 = -16t²+83t+46

             t = 5.70 seconds

Substituting in velocity equation

           v(t)= -32 x 5.70 + 83 = -99.4 ft/s

           Object's maximum speed = 99.4 ft/s

c) Maximum displacement is when the velocity is zero

   That is

                 -32t + 83 = 0

                       t = 2.59 s

Substituting in displacement equation

                s(2.59) = -16 x 2.59²+83 x 2.59+46 = 153.64 ft

Object's maximum displacement = 153.64 ft

d) Maximum displacement occur at t = 2.59 seconds.

e) Refer part b

   The displacement is zero when t = 5.70 seconds

f) Same as option d

   Object's maximum height = 153.64 ft

Answer:

The initial velocity is 83 ft/s.

The maximum velocity of object is -82.76 ft/s.

The maximum displacement is 107.64 ft.

Time for maximum displacement is 2.59 s.

The object's displacement is zero at 5.18 s.

The maximum height of object is, 107.64 ft.

Explanation:

Given data:

Equation for the velocity is, [tex]v(t)=-32t+83[/tex].

Height is, [tex]H'=46\;\rm feet[/tex].

(a)

At initial, the time function is zero. Which means, t = 0.

Then, initial velocity is:

[tex]v(t=0)=-32(0)+83\\v(t=0)= 83\;\rm ft/s[/tex]

Thus, the initial velocity is 83 ft/s.

(b)

The maximum velocity of object is at ground. Then, equation for maximum distance covered is obtained as,

[tex]v(t)=\frac{dH}{dt} \\dH=\int\limits^H_0 {v(t)} \, dt \\dH=\int\limits^H_0 {(-32t+83)} \, dt[/tex]

Integrating as,

[tex]H =-16t^2+83t[/tex]

Maximum velocity is at ground, hence H=0. Solving as,

[tex]0 =-16t^2+83t\\16t=83\\t=5.18 \;\rm s[/tex]

Now, maximum velocity is,

[tex]v(t=5.18)=-32(5.18)+83\\v(t=5.18)=-82.76 \;\rm ft/s[/tex]

Thus, maximum velocity of object is -82.76 ft/s.

(c)

The maximum displacement will be at corresponding to zero velocity. Then,

[tex]v(t)=-32t+83\\0=-32t+83\\t=2.59 \;\rm s[/tex]

Then, maximum displacement is,

[tex]H =-16(2.59^2)+83(2.59)\\H = 107.64\;\rm ft[/tex]

Thus, maximum displacement is 107.64 ft.

(d)

The maximum displacement occurs at zero velocity. And, time is,

[tex]v(t)=-32t+83\\0=-32t+83\\t=2.59 \;\rm s[/tex]

Thus, time for maximum displacement is 2.59 s.

(e)

The object displacement is zero when it reaches back to the ground. At ground, H=0. Which means time is,

[tex]0 =-16t^2+83t\\\\16t=83\\t=5.18 \;\rm s[/tex]

Thus, object's displacement is zero at 5.18 s.

(f)

The maximum height of object is equal to maximum displacement. Thus, maximum height of object is, 107.64 ft.

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The truck coasting up the hill with its engine turned off is obeying the principle of conservation of mechanical energy because the kinetic energy is converted into gravitational potential energy without external work, while the sports car with the running engine is not conserving mechanical energy since it is adding energy to the system.

The principle of conservation of mechanical energy states that the total mechanical energy in a system remains constant if only conservative forces are doing work. When friction and air resistance are ignored, as requested, the truck that coasts up the hill with the engine turned off obeys this principle because its initial kinetic energy is converted into gravitational potential energy without any external work being done on or by the system. On the other hand, the sports car with its engine running is continually adding energy to the system to maintain a constant speed up the hill, which means it is not conserving mechanical energy as in the first case.

Answer:

a) F = 680 N, b)  W = 215 .4 J , c)  F = 1278.4 N

Explanation:

a) Hooke's law is

              F = k x

To find the displacement (x) let's use the elastic energy equation

            [tex]K_{e}[/tex] = ½ k x²

             k = 2 [tex]K_{e}[/tex]  / x²

             k = 2 85.0 / 0.250²

             k = 2720 N / m

We replace and look for elastic force

            F = 2720  0.250

            F = 680 N

b) The definition of work is

          W = ΔEm

          W = [tex]K_{ef}[/tex] - [tex]K_{eo}[/tex]

          W = ½ k ( [tex]x_{f}[/tex]² - x₀²)

The final distance

         [tex]x_{f}[/tex] = 0.250 +0.220

        [tex]x_{f}[/tex] = 0.4750 m

We calculate the work

          W = ½ 2720 (0.47² - 0.25²)

          W = 215 .4 J

We calculate the strength

          F = k [tex]x_{f}[/tex]

          F = 2720 0.470

          F = 1278.4 N

Answer:

E=6.75×10¹⁰J

Explanation:

Given data

Mass (m)=7.50×10⁻⁷kg

To find

Energy (E) = ?

Solution

From Albert Einstein’s theory of special relativity

E = mc²........eq(1)  

Where

E is energy

m is mass

c is speed of light which 3.0×10⁸m/s

put values in eq(1) we get

E=(7.50×10⁻⁷kg)×( 3.0×10⁸m/s)²

E=6.75×10¹⁰J

Answer:

0.39

Explanation:

distance from the center (r) = 32 cm = 0.32 m

speed of the coin (v) = 110 cm/s = 1.1 m/s

acceleration due to gravity (g) = 980 m/s^{2} = 9.8 m/s^{2}

find the coefficient of static friction (k) between the coin and the turn table

frictional force = kmg

before the table begins to move, the frictional force balances the centripetal force ([tex]\frac{mv^{2} }{r}[/tex])

therefore

frictional force = centripetal force

kmg = [tex]\frac{mv^{2} }{r}[/tex]

kg = [tex]\frac{v^{2} }{r}[/tex]

k = [tex]\frac{v^{2} }{r}[/tex] ÷ g

k = [tex]\frac{1.1^{2} }{0.32}[/tex] ÷ 9.8 = 0.39

Answer:

Gas at room temperature: Oxygen

Liquid metal: Mercury

Solid non-metal: Sulphur, Copper

Chemical compound: Water

Explanation:

                    It is highly reactive non-metal and third most abundant element   in the universe after hydrogen and helium. Diatomic oxygen(O₂) constitutes 20.8% of earth atmosphere that used in respiration in living organisms.

                    It is shiny, silvery and only metal which is found in liquid state at normal room temperature. Most common use of mercury is in thermometer, barometer, sphygmomanometer etc.

                    It is bright yellow crystalline solid non-metal at room temperature in elemental form. Combined sulphur exists in sulphates and sulphides i.e. CaSO₄.2H₂o, MgSO₄.7H₂O, PbS, ZnS etc. Abundance in earth crust is only 0.03-0.1%.

                   It is pinkish-orange, malleable and ductile metal found in solid state at room temperature. It is commonly used in making wire, alloy etc.

                   Water covers 71% of earth surface. A molecule contains one oxygen and two hydrogen atoms connected by covalent bonds. It is crucial for all forms of life.

Answer:

C. A decrease in the neural control to the gluteus medius and gluteus maximus muscles      

Explanation:

                 An ankle sprain is an injury that is caused by the twisting, rolling or turning the ankle in awkward manner. It can tear the ligaments of the bone muscles that helps to hold together the ankle bones.

                When we get an ankle sprain, the neural control of the gluteus medius as well as the gluteus maximus muscles decreases. Thereby limiting the control of the lower extremities during any functional activities.

Hence the correct option is (C).

Final answer:

The magnitude of the linear acceleration of the hanging masses in an Atwood machine can be calculated using the formula: a = (m2 - m1)g / (m1 + m2). The given masses are 1.33 kg on the right and 1.78 kg on the left. Plugging in these values, the magnitude of the acceleration is 1.3816 m/s^2.

Explanation:

In an Atwood machine, the magnitude of the linear acceleration of the hanging masses can be calculated using the formula:

a = (m2 - m1)g / (m1 + m2)

Where:

a is the magnitude of the linear acceleration

m1 is the mass on the left (1.78 kg)

m2 is the mass on the right (1.33 kg)

g is the acceleration due to gravity (9.8 m/s^2)

Plugging in the given values, we get:

a = (1.33 kg - 1.78 kg) * 9.8 m/s^2 / (1.78 kg + 1.33 kg)

a = -0.44 kg * 9.8 m/s^2 / 3.11 kg

a = -1.3816 m/s^2

Since the question asks for the magnitude of the acceleration, we take the absolute value:

a = 1.3816 m/s^2

Answer:

K= 1000 N-m

Explanation:

It is assumed that we asked to find the spring constant k of the spring

We know that under equilibrium condition

weight of the object = force applied by the spring

given m =10 Kg

x= extension in the spring = 9.8 cm

mg=kx

[tex]10\times9.8=k\times9.8\times10^(-2)[/tex]

K= 1000 N-m

The spring constant, k of the vertically suspended spring measured in Newton meter is 1000 N/m

Given the Parameters :

Using the Relation :

The expression can be written thus :

mg = ke

Converting, extension to meters = (9.8/100) = 0.098 m

(10 × 9.8) = 0.098k

98 = 0.098k

k = 98/0.098

k = 1000 N/m

Therefore, the spring constant is 1000 N/m

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scientists can prove the answer of the chemical reaction and in every case

Answer:

4) Scientists know that reactions at chemical equilibrium will shift to regain equilibrium when affected by external factors, so scientists can use external factors to manipulate these chemical reactions into producing specific results.

Explanation:

Le Châtelier's principle states that changes in the temperature, pressure, volume, or concentration of a system will result in predictable and opposing changes in the system in order to achieve a new equilibrium state. Le Châtelier's principle doesn't say anything about reaction rates.

The idea of an industrial process is to obtain an specific product. So, you can apply changes into a system in equilibrium to produce more desirable product. A simple example is to decrease the concentration of products by removing them or increasing the concentration of reactants by adding them, so that, more product is produced and more reactant is used, and the equilibrium is reached again.

Answer:

Northern Lights ( Aurora Borealis)

Explanation:

When the electricaly charged sunspot gases (they are named a solar wind) escape the sun's chromosphere and penetrates from the earth magnetic sheild which is called earth's magnetosphere then upon there interaction with atoms and molecules of our atmosphere there are little bursts of photons in the form of light which made up these northern lights.

The geologic time scale originally ordered Earth’s rocks by relative age.

Explanation:

Geologic time scale is the measure of events occurred in year wise from the starting of universe. Mostly dating of rocks and fossil fuels are doing the trends still now. In order to measure the age of rocks, geological time scale have preferred relative age mode.

In this system, the age of rocks are measured and compared layer by layer. So the lowest layer of rock will be having the maximum age. As we don’t know the starting time of universe, so this method of comparison between the layers to order the rocks is best. So, depending upon the position of the rocks, the age can be determined.

Answer:

Option B

10.36 m/s

Explanation:

Using the first given equation, then velocity=distance/time

Since distance is provided as 200 m and time, t is 19.3 seconds then substituting these figures yields

v=200/19.3=10.3626943

Rounding off to 2 decimal places, then

v=10.36 m/s

Answer:

600 rad/s²

450 rad/s

21 m/s²

Explanation:

r = Radius

[tex]\omega_f[/tex] = Final angular velocity

[tex]\omega_i[/tex] = Initial angular velocity

[tex]\alpha[/tex] = Angular acceleration

t = Time taken

Linear acceleration is given by

[tex]a=r\alpha\\\Rightarrow \alpha=\dfrac{a}{r}\\\Rightarrow \alpha=\dfrac{1.5}{0.25\times 10^{-2}}\\\Rightarrow \alpha=600\ rad/s^2[/tex]

Angular acceleration of the yo-yo is 600 rad/s²

[tex]\omega_f=\omega_i+\alpha t\\\Rightarrow \omega_f=0+600\times 0.75\\\Rightarrow \omega_f=450\ rad/s[/tex]

angular velocity of the yo-yo is 450 rad/s

[tex]a=r\alpha\\\Rightarrow a=3.5\times 10^{-2}\times 600\\\Rightarrow a=21\ m/s^2[/tex]

Tangential acceleration of a point on its edge is 21 m/s²

The angular acceleration, angular velocity and tangential acceleration are;

A) 600 rad/s²

B) 450 rad/s,

C) 21 m/s²

A) We are given;

Radius; r = 0.25 cm = 0.0025 m

Linear acceleration; a = 1.5 m/s²

Formula for Angular Acceleration is;

α = a/r

Thus; α = 1.5/0.0025

α = 600 rad/s²

B) We are given;

time; t = 0.75 s

final angular velocity is gotten from;

ω_f = ω_i + αt

ω_f = 0 + (600 * 0.75)

ω_f = 450 rad/s

C) We are given;

Radius; r = 3.5 cm = 0.035 m

Formula for tangential acceleration is;

α_t = rα

α = 0.035 * 600

α = 21 m/s²

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SHM in a mass-spring system involves a restoring force proportional to displacement, with power being maximal at extreme positions.

Simple Harmonic Motion (SHM) is a type of periodic motion defined by a restoring force proportional to displacement. In the context of a mass attached to a spring, the period of SHM can be calculated using the mass and force constant of the spring.

The power delivered to the mass by the spring is first a maximum when the restoring force is at its maximum, which occurs when the mass achieves its greatest displacement. This typically happens when the mass is at the equilibrium point after being displaced.

The time at which the power delivered by the spring is first a maximum aligns with the moments when the mass reaches its extreme positions during the oscillatory motion, typically when it's at the maximum displacement from equilibrium.

When a mass is attached to an ideal spring and set into simple harmonic motion (SHM) with an initial velocity from its natural length, the power delivered by the spring to the mass is first maximized when the mass passes through the equilibrium position at maximum speed. Since the period T is the time it takes for one complete cycle of the motion, the mass reaches its maximum velocity at equilibrium position at one quarter of the period. Therefore, the power delivered to the mass by the spring is first a maximum at t = T/4, where T is the period of the simple harmonic motion

Answer:

True

Explanation:

It is true that professionals in exercises and sport science need to provide quality specialized settings to prove that a higher degree of competence is needed to fulfill the responsibility of the careers.

Answer:

The density of the mixture is 0.55kg/m^3

Explanation:

P = 1bar = 100kN/m^2, T = 0°C = 273K, n = 0.4+0.6 = 1mole

PV = nRT

V = nRT/P = 1×8.314×273/100 = 22.70m^3

Mass of N2 = 0.4×28 = 11.2kg

Mass of H2 = 0.6×2 = 1.2kg

Mass of mixture = 11.2 + 1.2 = 12.4kg

Density of mixture = mass/volume = 12.4/22.7 = 0.55kg/m^3

Answer:

The work done against friction is 372 joules

Explanation:

It is given that,

Mass of block, m = 24 kg

Radius of the track, r = 15 m

Acceleration due to gravity, [tex]a=9.8\ m/s^2[/tex]

If the kinetic energy of the block at the  bottom of the track is, 3900 J

Let P is the work done against friction. It is given by :

[tex]P=mgh[/tex]

Here, h = r

[tex]P=24\ kg\times 9.8\ m/s^2\times 15\ m[/tex]

P = 3528 J

Since it ends up with 3900 J, the work done is given by or the lost in energy will be :

W = 3900 - 3528

W = 372 joules

So, the work done against friction is 372 joules. Hence, this is the required solution.

Answer:

The ball stops instantaneously at the topmost point of the motion.

Explanation:

Assume we have thrown a ball up in the air. For that we have given a force on the ball and it acquires an initial velocity in the upward direction.

The forces that resist the motion of the ball in the upward direction are the force of gravity and air resistance. The ball will instantaneously come to rest when the velocity of the ball reduces to zero.

The two forces acting in the downward direction reduces its speed continuously and it becomes zero at the topmost point.

Final answer:

The highest point of a ball's upward trajectory is when its velocity is zero, and it momentarily stops before falling back to Earth under the influence of gravity. This is the point where the ball has its maximum potential energy and is the peak of the trajectory.

Explanation:

When you throw a ball up in the air, it travels upwards and slows down under the influence of gravity. At the highest point of its trajectory, the ball's velocity momentarily becomes zero before it reverses direction and falls back to the ground. This moment is known as the peak or the apex of the ball's trajectory. The ball's vertical velocity increases in the downward direction as it descends due to the acceleration caused by gravity. At the peak, not only does the velocity become zero, but this is also the point where the ball has its maximum potential energy.

When calculating the time it takes for the ball to reach its highest point or how high it goes, you can use the initial velocity and the acceleration due to gravity. For example, if a ball is thrown upwards with a velocity of 10 m/s, you can calculate the maximum height using the formula for the displacement under constant acceleration, considering that the final velocity at the highest point is zero and the acceleration due to gravity is -9.8 m/s² (negative as it is in the opposite direction to the ball's initial motion).

Answer:

(D) It is equal to the original velocity of the skater.

Explanation:

The velocity of the center of mass of a system is

[tex]\vec{v}_{cm} = \frac{m1\vec{v}_1 + m_2\vec{v}_2}{m_1 + m_2}[/tex]

The velocity of the center of mass is constant if there is no external force, because the total momentum of the whole system is conserved.

So, before the snowball is thrown, the velocity of the center of mass is equal to that of the skater. This velocity will always be equal to the velocity of the center of mass of the system.

Immediately after the snowball is thrown, the velocity of the center of mass is equal to that of the skater. Option D is correct.

Velocity of the center of mass:

It is defined as the ratio of the sum of the momentum of the masses and total mass.

The velocity of the center of mass of a system given as

[tex]\bold {V_c_m = \dfrac {p_1 + p_2 } {m_1+m_2}}[/tex]

Where,

p1 - momentum of the first mass

p2 - momentum of the second mass

m1 + m1 - total mass of the system

If there is no external force, the velocity of the center of mass is constant because the total momentum of the whole system is conserved.

Therefore, immediately after the snowball is thrown, the velocity of the center of mass is equal to that of the skater.

To know more about  center of mass,

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Answer:

The mass of 10 cm³ of water, is 10 grams

Explanation:

Density of water = 1 g/cm³

Density = Mass / volume

Volume of water = 10 cm³

1 g/cm³ = Mass of water / 10 cm³

10 g = mass of water

The mass of 10.0 cm3 of water, given the density is 1.0 g/cm3, is found by multiplying the volume by the density, which gives us 10.0 g.

The question is asking for the mass of a certain volume of water. Given that the density of water is 1.0 g/cm3, and you have 10.0 cm3 of water, the mass can be found by multiplying the volume by the density. So, it's simply 1.0 g/cm3 * 10.0 cm3 = 10.0 g. Therefore, the mass of 10.0 cm3 of water is 10.0 g.

Learn more about Mass Calculation here:

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Answer:

The correct option is A)

Displacement: 6.71 m, Direction: 63.4 degrees north of east

Explanation:

Given that Dante is leading a parade across the main street in front of city hall.

Let, Initial location of parade is 0i+0j

One block of city is one units on the XY- graph

Statement 1: Parade marches the parade 4 blocks east, then 3 blocks south

New location of parade is 4i-3j

Statement 2: The parade marches 1 block west and 9 blocks north and finally stops.

Final location of parade is (4i-3j)+(-1i+9j)=3i+6j

Displacement is given by

Displacement = (Final destination)-(Initial destination)

Displacement = (3i+6j)-(0i+0j)=3i+6j

Thus,

Magnitude of displacement = [tex]\sqrt{3^{2}+6^{2}}[/tex]

                                              = 6.71 m

Direction of displacement =  [tex]tan^{-1}(\frac{Y}{X} )[/tex]

                                           =  [tex]tan^{-1}(\frac{6}{3} )[/tex]

                                           = 63.43 NE

Therefore, the correct option is A) Displacement: 6.71 m, Direction: 63.4 degrees north of east