The ______ and _______ are used to calculate magnitude and direction of a resultant vector.

Answer:

[tex]W_{tot}=W_{1}+W_{2}=mgh_{2}=7.55[J][/tex]

Explanation:

The work done on an object is the scalar product between force and displacement. So we can write the work:

[tex]W=F\cdot d=Fd[/tex]

In our case F and d are parallels then we have a common product of their magnitudes.

Now, the total work will be the sum these two works:

Let's recall that the force in this problem is just the weight of the book. F=m*g

Finally, the total work will be the sum of W₁ and W₂.

[tex]W_{tot}=W_{1}+W_{2}=mgh_{2}=2.2*9.81*0.35=7.55[J][/tex]

I hope it helps you!

To calculate the work done on the book, the student librarian must use the formula W = mgh for each segment of lifting the book vertically. The total work done is the sum of the work for lifting the book to 1.25 m and then to 0.35 m. The horizontal distance carried does not contribute to work against gravity.

The work done on the book by the student librarian can be calculated by considering the work done against gravity to lift the book to different heights. The distance carried horizontally does not involve work against gravity under the assumption that there is no horizontal force like friction opposing the motion. The work done to lift the book from the floor to 1.25 m can be calculated using the formula W = mgh, where m is the mass of the book, g is the acceleration due to gravity (approximately 9.8 m/s2), and h is the height.

The initial lift is W = 2.2 kg × 9.8 m/s2 × 1.25 m. When placing the book from the carried position to a shelf at 0.35 m height, the work done is W = 2.2 kg × 9.8 m/s2 × 0.35 m since the vertical displacement is from 1.25 m to 0.35 m, not the full 1.25 m again.

The total work done on the book is the sum of these two amounts of work. Please note that the gravitational constant (g) could be given or assumed in this context. The exact value used may vary slightly depending on the context of the problem.

The force exerted by the chin-up bar on the person's body depends on the acceleration. At certain times, the force is 0 N, while at other times it can be calculated using the formula Force = Mass x Acceleration.

The force exerted by the chin-up bar on the person's body can be calculated using the equation:

Force = Mass x Acceleration

At t = 0s, the person's body is at rest, so the acceleration is 0. Therefore, the force exerted by the bar is 0 N.

At t = 0.5s, the person's body is moving upward with a constant speed. Since the velocity is constant, the acceleration is 0 and the force exerted by the bar is 0 N.

At t = 1.1s, the person's body is moving upward with an increasing speed. The acceleration can be calculated using the change in velocity over time, and then substituted into the force equation to find the force exerted by the bar.

At t = 1.6s, the person's body is moving upward with a decreasing speed. The acceleration can be calculated using the change in velocity over time, and then substituted into the force equation to find the force exerted by the bar.

Answer:

Columns

Explanation:

The groups are arranged in columns on the Periodic Table.

The efficiency of the machine is  54.76%.

The efficiency of a machine refers to the amount of useful work that is done by the machine. Efficiency is usually expressed as a percentage.

From the question;

Work output= 230 J

Work input=  420 J

We know that efficiency = Work output/work input × 100/1

efficiency =230 J/420 J × 100/1

efficiency = 54.76%

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Answer : Distance, d=6.98 × 10⁷ Km

Explanation :

Given that,

Mass of the sun, m₁ = 1.99 × 10³⁰ kg

Mass of Mercury, m₂ = 3.30 × 10²³ kg

Gravitational force between the sun and mercury, F = 8.99 × 10²¹ N

According to Universal law of gravitation,

[tex]F=G\dfrac{m_1m_2}{d^2}[/tex]

d is the distance of mercury from the sun

[tex]d=\sqrt{\dfrac{Gm_1m_2}{F}}[/tex]

[tex]d=\sqrt{\dfrac{6.67\times 10^{-11}\times 1.99\times {30}\times 3.30\times 10^{23}}{8.99\times 10^{21}}}[/tex]

[tex]d=\sqrt{4.87\times 10^{21}} m[/tex]

[tex]d=6.98\times 10^{10}\ m[/tex]

or

[tex]d=6.98\times 10^{7}\ Km[/tex]

So, mercury is [tex]6.98\times 10^{7}\ Km[/tex] far from the sun.

The forces that two charged particles exert on each other are equal in magnitude and opposite in direction, so F2 = -F1, where F2 is the force Q1 exerts on Q2, and F1 is the force Q2 exerts on Q1.

When two charged particles Q1 and Q2, with Q2 being 5 times the charge of Q1, are separated by a distance r, the force they exert on each other can be determined using Coulomb's law. According to Coulomb's law, the magnitude of the force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. Since Q2 is 5 times Q1, we have Q2 = 5Q1. However, the force that Q2 exerts on Q1 (F1) is equal in magnitude and opposite in direction to the force that Q1 exerts on Q2 (F2) due to Newton's third law of motion, which states that every action has an equal and opposite reaction.

Therefore, the correct answer to the question is F2 = -F1. This indicates that the forces are equal in magnitude but opposite in direction. The negative sign simply denotes the opposite direction of the force, not that the magnitude of the force is negative.

According to Coulomb's law and Newton's third law, two charged particles exert forces of equal magnitude but opposite directions on each other, so if Q2 = 5Q1, then F2 = -F1.

When considering two charged particles exerting forces on each other, it's important to apply Coulomb's law, which states that the force between two point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. Additionally, Newton's third law of motion tells us that for every action, there is an equal and opposite reaction. This means that if a charge Q2 exerts a force F1 on Q1, then Q1 must exert a force F2 of equal magnitude but in the opposite direction on Q2.

Given that Q2 = 5Q1 and they are a distance r apart, Coulomb's law would indicate that the magnitudes of the forces each charge exerts on the other (F1 and F2) would be equal. Thus, the correct answer is F2 = -F1, where the negative sign indicates the forces have opposite directions.

Answer:

[tex]v = 3.28 m/s[/tex]

Explanation:

At the top position of the arc if ball continue in its circular path then we can say that tension force must be zero at that position for the minimum value of the speed.

So we will have

[tex]T + mg = \frac{mv^2}{R}[/tex]

so if minimum speed is required to complete the circle T = 0

[tex]0 + mg = \frac{mv^2}{R}[/tex]

so we will have

[tex]v = \sqrt{Rg}[/tex]

again we will have

[tex]v = \sqrt{1.10\times 9.81}[/tex]

[tex]v = 3.28 m/s[/tex]

Answer: The answer to this question is Unbalanced force.

Explanation: There are two types of forces:

1. Balanced force: When two forces equal in their magnitude act opposite to each other are known as balanced force. The net force is equal to 0.

2. Unbalanced force: When two forces acting opposite to each other are not equal in magnitude results in the unbalanced force. The net force of this is not equal to 0. Direction of force is in the direction of net force.

Now, according to Newton's first law of motion, which says that force is the product of the object's mass and acceleration. The force should have some value and hence it cannot be equal to zero. therefore the force must be Unbalanced force.

According to Newton's second law of motion, a net external force causes a body to accelerate, with the acceleration being directly proportional to the force and inversely proportional to its mass.

According to Newton's second law of motion, a force is expected to cause a body to accelerate when it acts upon the body. This law can be summarized by the equation Fnet = ma, where Fnet denotes the net force acting on the body, m stands for mass, and a signifies acceleration. Therefore, the linear acceleration of a rigid body is directly proportional to the net force acting on it and inversely proportional to its mass. It is important to note that the acceleration occurs in the same direction as the net external force. In simple terms, if you apply a net external force to an object, it will accelerate, and the magnitude of this acceleration can be calculated by dividing the net force by the object’s mass.

The car was initially traveling at approximately 22.02 m/s.

To solve this problem, we can break it down into horizontal and vertical components. Let's call the initial velocity of the car 'v.'

The car's horizontal velocity after the collision is given by its initial velocity multiplied by the cosine of the angle, which is 28 m/s * cos(37°). The truck's horizontal velocity after the collision is 0 m/s since it was initially stationary.

Since no horizontal forces act on the system after the collision, the momentum in the horizontal direction is conserved. Thus, the sum of the initial flat rates of the car and the truck must equal the final horizontal velocity. Therefore, m * v = m * (28 m/s * cos(37°)), where 'm' represents the mass of the car and the truck.

If we divide both sides of the equation by 'm', we get v = 28 m/s * cos(37°). Evaluating this expression, we find v ≈ 22.02 m/s.

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Final answer:

The work done by a person who exerted a force of 500 Newtons to move a full wheelbarrow over a distance of 30 meters is 15000 Joules.

Explanation:

If a person exerted a force of 500 Newtons (F = 500 N) to move a full wheelbarrow over a distance of 30 meters (d = 30 m), the work done can be calculated using the formula:

Work (W) = Force (F) × Distance (d)

Plugging in the given values, we get:

W = (500 N) × (30 m) = 15000 Joules (J)

The work done is therefore 15000 Joules, which demonstrates the transfer of energy through force applied over a distance.

The correct balanced equation is N₂ + 3H₂ ⇒ 2NH3, which represents the chemical reaction where one mole of nitrogen reacts with three moles of hydrogen to produce two moles of ammonia. The coefficients reflect the simplest whole number ratio for the stoichiometry of the reaction.

The balanced chemical equation among the given options is N₂ (g) + 3H₂ (g) ⇒ 2NH3 (g). This reflects the stoichiometry of the reaction where each nitrogen molecule (N₂) reacts with three hydrogen molecules (3H₂) to form two molecules of ammonia (2NH3). The coefficients indicate the mole ratio needed for the reaction to occur, which is also demonstrated through models showing the combination of gas volumes following the reaction stoichiometry. Alternatively, the equation 3N2 + 9H2 → 6NH3 is not balanced at the simplest ratio. After dividing each coefficient by the greatest common factor (3), the previous balanced equation is obtained, which is the preferred simplified form. This balanced equation can be used to establish an equilibrium in a sealed container, showcasing the relationship between changes in the concentrations of the species involved, as determined by the stoichiometry.

Final answer:

The balanced chemical equation for the synthesis of ammonia from nitrogen and hydrogen is N₂ (g) + 3H₂ (g) → 2NH3 (g), which follows the stoichiometric ratio of 1:3:2.

Explanation:

The balanced equation for the reaction between nitrogen (N₂) and hydrogen (H₂) to form ammonia (NH₃) is N₂ (g) + 3H₂ (g) → 2NH3 (g). This equation satisfies the law of conservation of mass, meaning that the number of atoms for each element is the same on both the reactant and product sides of the equation. One mole of nitrogen gas reacts with three moles of hydrogen gas to yield two moles of ammonia gas, indicating a mole ratio of 1:3:2, respectively. The equation shows ammonia molecules are produced from nitrogen and hydrogen molecules in a 2:3 ratio, reflecting the stoichiometry of the reaction.

So,option A)Change in the fullback's momentum:779 kg·m/s,B)Change in the defensive tackle's momentum: -779 kg·m/s,C)Defensive tackle's original momentum:-779 kg·m/s (opposite direction),D)The original speed of the defensive tackle:6.09 m/s.

Understanding Momentum and Collision:

A) Change in the fullback's momentum: Momentum is the product of mass and velocity. For the fullback running at 8.2 m/s with a mass of 95 kg, his initial momentum was 95 kg × 8.2 m/s = 779 kg·m/s. After the collision, since they stop, the fullback's speed is 0 m/s, giving a final momentum of 0 kg·m/s. Therefore, the change in momentum is 779 kg·m/s - 0 kg·m/s = 779 kg·m/s.

B) Change in the defensive tackle's momentum: The defensive tackle has mass 128 kg and final speed 0 m/s. Since we are not given the initial velocity, we cannot calculate the change directly; however, by conservation of momentum, the change will be equal and opposite to the fullback's, which is -779 kg·m/s.

C) Defensive tackle's original momentum: As mentioned above, the change in momentum is the negative of the fullback's, so if the fullback's momentum decreased by 779 kg·m/s, the tackle's momentum increased by this amount, meaning it was -779 kg·m/s (opposite direction).

D) The original speed of the defensive tackle: To find the original speed, we take the original momentum (from C) and divide by the tackle's mass. This gives us -779 kg·m/s ÷ 128 kg = -6.09 m/s. The negative indicates that he was moving in the opposite direction to the fullback.

Note that 'negative' here is used to indicate direction in one-dimensional motion, and the actual speed is just the absolute value, 6.09 m/s.

Answer:

s = - 4 cos 4t + 2t + 6.

Explanation:

a = dv/dt = 16 cos 4t ,

dv = 16 cos 4t dt

integrating on both sides

v = 16 x sin 4t /4 + c

    = 4 sin 4t + c

when t = 0 , v = 2

2 = 0 + c

c = 2

v = 4 sin 4t + 2

ds/dt = 4 sin 4t + 2

ds = ( 4 sin 4t + 2) dt

integrating on both sides

s = - 4 cos 4t/4 + 2t + k

    = - cos 4t + 2t + k

when t = 0 s = 5

5 =  -1 + 0 + k

k = 6

s = - 4 cos 4t + 2t + 6.

Ans.

Answer:

The answer is: B. boiling.

Explanation:

The value of the melting and boiling points are affected by the value of the atmospheric pressure.

The Celsius degree is the unit corresponding to the melting and boiling temperatures of water at 1 atm pressure. Celsius: Melting 0 ℃, Boil 100 ℃.

When a food is frozen at normal atmospheric pressure, its temperature drops to 0 ° C, at which time the water begins to turn into ice.

Normally, the atmospheric pressure that exists at sea level is taken as a reference. There it takes a value of 1 atmosphere.

Therefore, although the pressure is 1 atmosphere for all processes, the one that needs more temperature is the Boiling, which is 100 ° C.

The answer is: B. boiling.

Answer: The correct answer is 0.11 Hz.

Explanation:

The relation between frequency of the wave and time period is as follows;

[tex]f=\frac{1}{T}[/tex]

Here, f is the frequency of the wave and T is the time period.

Here, the frequency is inversely proportional to the time period.

It is given in the problem that a wave has a wavelength of 45 meters and a period of 9.0 seconds.

Calculate the frequency of the wave.

[tex]f=\frac{1}{T}[/tex]

Put T= 9 s.

[tex]f=\frac{1}{9}[/tex]

f=0.11 Hz

Therefore, the frequency of the wave is 0.11 Hz.

Answer:

2. B. energy

3. D.kinetic energy

4. C. chemical

5. A.68.1 percent

6. A.chemical energy into thermal energy

7. D.mechanical energy

Explanation:

2. Energy is  the ability of matter to produce work in the form of movement, light, heat, etc.

3.  The kinetic energy of a body is that energy it possesses due to its movement.

4 .Chemical energy is the energy stored in the bonds of chemical compounds (atoms and molecules).

5. Efficiency can be calculated as (128J/188J)*100= 68%

6. Chemical energy is defined in item 4 and thermal energy is a type of energy that bodies possess when exposed to the effect of heat. It is precisely what produces that the atoms that make up the molecules are in constant motion either moving or vibrating.

7. Mechanical energy is the energy that bodies present because of their movement (kinetic energy), and their situation with respect to another body, usually the earth.

All your selected answers are correct. The ability to do work is energy, a person jogging has kinetic energy, energy in food is chemical, the rake has 68.1 percent efficiency, natural gas heating water is a chemical to thermal energy transformation process, and motion and position of an object relate to mechanical energy.

Yes, you are correct with your answers. The ability to do work or cause change is indeed called B.energy. A person jogging demonstrates D.kinetic energy as they are in motion. The type of energy available in food is C.chemical energy which is stored and can be transformed into other energy forms our body needs. With the work done raking leaves, if Dan does 188.0 J of work and the rake itself does 128.0 J of work then the efficiency of the rake would be (128.0 / 188.0) * 100 = 68.1 percent, hence, it is A.68.1 percent. The transformation of energy taking place when natural gas is used to heat water is A. Chemical energy into thermal energy. Finally, the energy associated with the motion and position of an object falls under D. mechanical energy, although if considering only the motion aspect, it is indeed A. Kinetic energy.

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Answer:

it is cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc

Explanation:

becai=use i know

Answer:

-1.176 m/s²

Explanation:

Given:

weight of aluminium block is w = 20.0 N

frictional force, f = 2.4 N

final velocity, v = 0

distance covered, d = 10 m

From Newton's second equation of motion,

F = ma

where, m is the mass and a is the acceleration.

mass of the block, m g = 20.0 N

m = 2.04 kg

The block is brought to rest by friction force:

f =- m a

⇒ 2.4 N = -(2.04 kg)(a)

⇒a = -1.176 m/s²

Answer:

C.the moon at apogee coming between Earth and the sun along a straight line

Explanation:

As we know that Earth rotate about the sun in elliptical orbit as one of the planet.

While moon rotate about the Earth similarly as one of the satellite around it

now when moon, Sun and Earth all lie in the same line such that position of moon is between the positions of Sun and Earth then in this case the light coming from sun is totally bounded by the position of moon

This situation of moon is known as Solar Eclipse

so here during the motion if the moon at apogee coming between Earth and the sun along a straight line then it is the most likely cause of annular solar eclipse.

Answer:

Explanation:

The work is defined as the force needed to move an object a certain distance, if there's no change of position, there's no work.

In this case, the work is defined:

[tex]W=Fd[/tex]

Where [tex]F[/tex] is the weight defined with the following equation

[tex]F=W=mg[/tex]

Now, we'll replace all given values and solve for [tex]m[/tex]:

[tex]W=mgy\\178=m(9.8)(0.5)\\m=\frac{178}{4.9}=36.33 kg[/tex]

Therefore, the mass is 36.33 kilograms.

Fleming's right-hand rule (for generators) shows the direction of induced current when a conductor moves in a magnetic field. It can be used to determine the direction of current in a generator's windings.

When a conductor such as a wire attached to a circuit moves through a magnetic field, an electric current is induced in the wire due to Faraday's law of induction. The current in the wire can have two possible directions. Fleming's right-hand rule gives which direction the current flows

The right hand is held with the thumb, first finger and second finger mutually perpendicular to each other (at right angles.