Lance is working in a library using a trolley to carry books. As he stacks books from the trolley on shelves, it gets easier to push or pull the trolley. Which part of Newton’s laws of motion explains the increased ease of moving the trolley?

The center of mass of the rigid body in the world space will be given below.

[tex]\rm x_{cm} = \dfrac{m_1x_1 + m_2x_2 + ... }{m_1 + m_2 + ... }\\\\\\\rm y_{cm} = \dfrac{m_1y_1 + m_2y_2 + ... }{m_1 + m_2 + ...}\\\\\\\rm z_{cm} = \dfrac{m_1z_1 + m_2z_2 + ... }{m_1 + m_2 + ... }[/tex]

The unique location where the graded relation of the scattered mass adds to zero is known as the center of mass in physics. Here is where a load may indeed be exerted to produce a moving object without also producing an angular acceleration.

The center of mass is given as,

[tex]\rm x_{cm} = \dfrac{m_1x_1 + m_2x_2 + ...... + m_nx_n}{m_1 + m_2 + .... + m_n}\\\\\\\rm y_{cm} = \dfrac{m_1y_1 + m_2y_2 + ...... + m_ny_n}{m_1 + m_2 + .... + m_n}\\\\\\\rm z_{cm} = \dfrac{m_1z_1 + m_2z_2 + ...... + m_nz_n}{m_1 + m_2 + .... + m_n}[/tex]

For a rigid body with particles, let the particle positions in the world space be 1, 2, … and the masses of the particles be 1, 2, ….

Then the center of mass will be

[tex]\rm x_{cm} = \dfrac{m_1x_1 + m_2x_2 + ... }{m_1 + m_2 + ... }\\\\\\\rm y_{cm} = \dfrac{m_1y_1 + m_2y_2 + ... }{m_1 + m_2 + ...}\\\\\\\rm z_{cm} = \dfrac{m_1z_1 + m_2z_2 + ... }{m_1 + m_2 + ... }[/tex]

More about the center of a mass link is given below.

https://brainly.com/question/8662931

#SPJ4

Answer:

Statement of the given problem,

A ball is thrown vertically upwards at 19.6 m/s. For its complete trip (up and back down to the starting position), what is its average speed?

Let H & T denote the maximum height (in m) of the given ball & the time (in s) required for it to reach there.

Hence from above data we get following kinematic relations,

T = [19.6 m/s - 0 m/s)]/(9.8 m/s^2) [9.8 m/s^2 = gravitational acceleration (assumed)]

or T = 2 (s)

H = (19.6 m/s)*(2 s) - (1/2)*(9.8 m/s^2)*(2 s)^2

or H = 19.6 (m)

Therefore,

assuming vertically upward & downward motions are identical with respect to time & distance covered by the given ball,

the required average speed of the ball during its travel up and back down to the starting position

= (total travel-distance)/(total travel-time)

= 2*(19.6 m)/[2*(2 s)]

= 9.8 m/s [Ans]

An absolute value inequality to describe this situation will be

| 2.5 ≤ W ≤ 11.5 |

An absolute value can be a value of any variable which will always be non - negative value.

Given that an average birth weight of a new born baby is 7 pounds. However, this weight can vary as much as 4.5 pounds. This means the weight can be

7 + 4.5 = 11.5

or

7 - 4.5 = 2.5

If W = average birth weight of a new born baby which is 7 pounds

Therefore, an absolute value inequality to describe this situation will be

| 2.5 ≤ W ≤ 11.5 |

Learn more about Absolute Value here: https://brainly.com/question/729268

#SPJ1

The correct answer is Einstein proposed that light must be made up of packets to explain the photoelectric effect (particles). The frequency of a light packet affects how much energy it contains. Whether or not a single photon has enough energy to knock an electron loose determines whether or not a metal will emit electrons.

The kinetic energy of the electrons is precisely proportional to intensity because, according to wave theory, the energy of electromagnetic waves is uniformly distributed over the wavefront and solely depends on the intensity of the input light beam. However, it was discovered through experimentation that the kinetic energy is unrelated to the brightness of the incident light.

To learn more about photoelectric effect refer the link:

https://brainly.com/question/726233

#SPJ4

That identical spaceship takes around a year to get to mars.

The Earth's axial wobble is stabilized by the Moon, the biggest and brightest object in our night sky, leading to a typically stable climate. As a result, Earth is a more hospitable planet. Moreover, it produces tides, which result in a rhythm that has guided mankind for a very long time. The following calculation must be performed to determine how long it will take the same spacecraft to reach Mars given that Mars is 140 times further away from Earth than the Moon and that a spacecraft can traverse the 386,400 kilometers between the Earth and the Moon in 3 days:

140 x 3 = 420 days

This spaceship will travel from Earth to Mars in just about one year and two months, assuming a year has 365 days.

Learn more about Earth here-

https://brainly.com/question/14042561

#SPJ4

Her average speed is 8.0 km/h, and her average velocity is 0 km/h. The

average velocity of the jogger is zero since net displacement is zero.

Velocity is the directional speed of a thing moving as an indication of its speed of progress prepared as seen from a particular edge of reference and as assessed by a particular standard of time (for instance 60 km/h toward the north). Speed is a urgent thought in kinematics, the piece of dated mechanics that portrays the development of bodies. Velocity is a genuine vector sum; both significance and heading are supposed to describe it. The scalar through and through worth (degree) of speed is called speed, being a perceptive decided unit whose sum is assessed in the SI (decimal norm) as meters each second (m/s or m⋅s−1). If there is a change of speed, heading or both, the thing should go through a speed increment.

To learn more about velocity ,visit:

https://brainly.com/question/18084516

#SPJ4

polar liquid is most likely true about the unknown liquid.

Polar Molecule Examples

To learn more about polar liquids refer to

https://brainly.com/question/26117248

#SPJ4

The relative velocity of object 1 with respect to object 2 will be → +5 mph along the positive y - axis.

We have two objects moving in north direction.

We have to determine the relative velocity of object 1 relative to object 2.

The velocity of an object A relative to another object B is the velocity that object A would appear to have to an observer moving with B.

According to the question, we have -

The velocity of Object 1 = v(1) = [tex]10\;a_{y}[/tex] mph

The velocity of Object 2 = v(2) = [tex]5\;a_{y}[/tex] mph

Since the two objects 1 and 2 are moving in the same direction, therefore the velocity of object 1 relative to object 2 will be -

v(1)' = v(1) - v(2) =  [tex]10\;a_{y}[/tex]  -  [tex]5\;a_{y}[/tex] =  [tex]5\;a_{y}[/tex] mph

Hence, the relative velocity of object 1 with respect to object 2 will be → +5 mph along the positive y - axis.

To solve more questions on Relative velocity, visit the link below-

https://brainly.com/question/22236244

#SPJ4

Answer:

v = a t = 4 m/s^2 * 5 s = 20 m/s

It can increase its speed by 20 m/s

Using V = V0 + a t

V0 (initial speed) had to be 12 m/s

[tex]{\color{Blue} N=3.47\ billions}[/tex]

The electric flux through green spherical surface is[tex]\rightarrow \Phi=62.8\ N\ m^{2}\ C^{-1}[/tex]

Permittivity of free space is [tex]\rightarrow \epsilon_{0}=8.85\times10^{-12}\ F\ m^{-1}[/tex]

Fundamental unit charge value is [tex]\rightarrow q=1.602\times10^{-19}\ C[/tex]

According to Gauss's law, electric flux is directly proportional to the enclosed charge [tex]Q_{enc}[/tex] inside spherical surface, which is given as:

[tex]\therefore \Phi=\frac{Q_{enc}}{\epsilon_{0}}[/tex]

[tex]\therefore Q_{enc}=\Phi \epsilon_{0}[/tex]

[tex]\therefore Q_{enc}=62.8 \times8.85\times10^{-12}[/tex]

[tex]\therefore Q_{enc}=555.75\times10^{-12}\ C[/tex]

therefore, total enclosed charge inside spherical surface is [tex]Q_{enc}=555.75\times10^{-12}\ C.[/tex]

Since charge is quantized, number of fundamental charges N is given as:

[tex]Nq=Q_{enc}[/tex]

[tex]\therefore N=\frac{Q_{enc}}{q}[/tex]

[tex]\therefore N=\frac{555.76\times10^{-12}}{1.602\times10^{-19}}[/tex]

[tex]{\color{Blue} \therefore N=3.47\times10^{9}}[/tex]

[tex]{\color{Blue} \therefore N=3.47\ billions}[/tex]

Therefore, [tex]{\color{Blue} N=3.47\ billions}[/tex] fundamental charges make up the value of the enclosed charge.

To know more about   Gauss's law   visit : https://brainly.com/question/14767569

#SPJ4

The frequency of electromagnetic waves is 10⁶ Hz or 1 MHz.

We need to know about electromagnetic waves to solve this problem. Electromagnetic waves can propagate without media. The speed of electromagnetic in vacuum media is equal to the speed of light. Hence, the wavelength and frequency can be determined as

c = λ . f

where c is the speed of light (3 x 10⁸ m/s), λ is wavelength and f is frequency.

From the question above, we know that

λ = 300 m

By substituting the given parameter, we can calculate the frequency of radiowaves

c = λ . f

f = c / λ

f = 3 x 10⁸ / 300

f = 10⁶ Hz

f = 1 MHz

Hence, the frequency of radiowaves is 10⁶ Hz or 1 MHz.

Find more on electromagnetic waves at: https://brainly.com/question/25847009

#SPJ4

The rate of change of displacement is known as velocity. The rate at which velocity changes is called acceleration. Due to the fact that it includes both magnitude and direction, velocity is a vector quantity. Acceleration is likewise a vector quantity as it is only the rate of change of velocity.

Speed serves as the baseline for both velocities and acceleration measurements. Speed is a scalar quantity that measures the amount of distance traveled over a period of time. Acceleration and velocity are both vector quantities, which means they both employ magnitudes and a designated direction. The rate of motion of an object is measured by both speed and velocity. The fact that speed is a scalar quantity, nevertheless, means that it can be quantified.

Learn more about acceleration here-

https://brainly.com/question/12550364

#SPJ9

1. The horizontal component of the velocity is 70.6 m/s

2. The vertical component of the velocity is 23.2 m/s

From the question given, the following data were obtained:

Horizontal component = u × Cosθ

Horizontal component = 74.3 × Cos18.2

Horizontal component = 70.6 m/s

Vertical component = u × Sineθ

Vertical component = 74.3 × Sine18.2

Vertical component = 23.2 m/s

Learn more about projectile motion:

https://brainly.com/question/20326485

#SPJ1

Speed is the time rate at which an object is moving along a path

Velocity is the rate of motion, speed, or action.

While Trial B and Trial D do not have the same average velocity, the only difference is the direction! The magnitudes are the same. Neither one is 'larger' than the other, and it is only because of how we chose our axes that Trial B has a positive average velocity while Trial D has a negative average velocity. In Trial C the object does not move, so it has an average velocity of zero. During Trial A the object has a positive average velocity but its magnitude is less than that in Trial B and Trial D.

For more information on average velocity click on the link below:

https://brainly.com/question/24739297

#SPJ4

The correct answer is rate of acceleration will be reduced by 3.

Newton's law states that the force acting on an object is inversely proportional to its rate of acceleration. This means that if an object's mass remains constant, its acceleration will fluctuate in accordance with its applied force, and vice versa.

A vector number called acceleration can be used to describe how quickly an object changes its velocity. If an object is constantly altering its velocity, it is still accelerating.

By Newton's law.

F=ma

The force is F.

m is the object's mass.

A represents acceleration.

The mass will triple if

a'=1/3×F/m

a'=a/3

To learn more about rate of acceleration refer the link:

https://brainly.com/question/2136991

#SPJ4

Answer: It is B

Explanation:

1. x + 14 = -6
2. x + 14 -14 = -6 -14
3. x = -20
4. So, x = -20

When the following solutions are brought into touch with one another on various sides of a semipermeable membrane, the net direction that water would diffuse (via osmosis) is that Water travels through osmosis from low solute concentration areas to high solute concentration areas.

Osmosis is the naturally occurring diffusion or passage of water or other solvents over a semipermeable membrane (one that prevents the passage of solutes, or dissolved compounds).

German plant physiologist Wilhelm Pfeffer began a systematic study of the crucial biological process in 1877.

Both the pressure gradient and the concentration gradient affect the net direction and rate of osmosis.

Hypertonic, isotonic, and hypotonic are the three osmotic states.

To know more about osmosis visit:

https://brainly.com/question/1799974

#SPJ4

The magnetic field within the solenoid is 0.013T

An electromagnet known as a solenoid creates a regulated magnetic field using a helical coil of wire whose length is significantly higher than its diameter. When an electric current is sent through the coil, it may create a consistent magnetic field inside a defined region of space.

A solenoid operates by creating an electromagnetic field surrounding an armature, which is a moving core. The electromagnetic field causes the armature to move, and when it does, it opens and closes valves or switches, converting electrical energy into mechanical motion and force.

The magnetic field within the solenoid can be calculated by the expression given below.

Write the expression for magnetic field within the solenoid.

B = u₀nI

B = 4π * 10⁻⁷ * 2000 * 5.2

= 0.013 T

to learn more about solenoid go to -

https://brainly.com/question/1873362

#SPJ4

As the projectile moves down, its vertical velocity is positive.

As the projectile moves down, its acceleration remains constant.

As the projectile moves up, its vertical velocity decreases.

As the projectile moves down, its vertical velocity increases.

As the projectile moves up, its acceleration remains constant.

As the projectile moves up, its vertical velocity is negative.

As the projectile moves down, its horizontal velocity remains constant.

As the projectile moves up, its horizontal velocity remains constant.

A projectile is any object thrown into space upon which the only acting force is gravity. The primary force acting on a projectile is gravity.

In a projectile motion, acceleration is always constant and acts vertically downward. Also velocity changes during a projectile motion.

The true statements about projectile motion in the given options include;

Learn more about projectile motion here: https://brainly.com/question/24216590

#SPJ1

The best explains why mars' and venus' surface temperatures vary, despite both planets having atmospheres that contain mostly carbon dioxide because

Venus has a dense atmosphere that prevents heat from the surface from escaping. Mars's thin atmosphere is unable to hold a lot of heat. Red sand and rocks on Mars' surface reflect heat.

High mountains cover Venus' surface, absorbing heat.

Find out more information about carbon dioxide.

https://brainly.com/question/3049557?referrer=searchResults

#SPJ4

By using one as a frame of reference, we will see that 6 seconds elapse before the two cars meet.

The correct option is B.

A frame of reference is a clearly defined coordinate system that is used to represent a body's motion or state of rest. Reference frames can be divided into two categories: inertial or non-accelerating frames and non-inertial or accelerating frames.

This moves at 30 m/s, then we will see that car A does not move, while car B moves with a speed of:

S = 20m/s + 30m/s = 50m/s

The two cars are moving in opposing directions, therefore the velocities are summed (So car A sees that car B comes faster than it actually does).

We just need to determine how long it will take automobile B to drive 300 metres at 50 m/s now that we are in this frame of reference.

Distance/speed = time

distance = 300m

speed = 50m/s.

(300m)/( 50 m/s) = 6s

This means that 6 seconds elapse before the two cars meet.

To know  more about frame or reference visit:

https://brainly.com/question/9820962

#SPJ9

The complete question is -

Two cars, A and B start out 300 meters apart. Car A travels due east toward car B at 30 meters per second. Car B travels due west toward car B at 20 meters per second. How long does it take before the two cars meet?

A- 15s

B- 6s

C- 10s

D- 5s

When we increase the intensity of incident light, the number of electrons ejected from the metal surface has increased energy. Thus, correct option is D.

Electrons are emitted from the metal surface when it is exposed to light. This is called the photoelectric effect. Each metal has a certain threshold frequency of light at which an electron is emitted. Above this frequency, the electron is emitted and the extra energy is transferred to the electron.

On increasing the intensity of incident light, the kinetic energy of electrons increases several folds. This is because, energy of an electron is directly proportional to the intensity of incident light. Thus, D is the correct option.

Learn more about Photons here:

https://brainly.com/question/2393994

#SPJ1

Your question is incomplete, probably the complete question/missing part is:

You shoot a beam of 4. 5 ev light at a metal surface and notice that electrons are being released from the metal. What will happen if you then increase the intensity of the 4. 5 ev light?

A. The metal will bend and warp.

B. Nothing, the energy of the light is the same.

C. More electrons would be released.

D. Photons would come off at higher speeds.

The speed of the plane with respect to the ground will be 117.89 meters per second.

In this question, we need to determine the plane's relative speed to the ground because that will move east at 130 meters per second. The wind is blowing roughly in this direction at 30 meters per second and is at an angle of 30 degrees west of north.

Therefore, we need to identify the x and y components of the wind in order to compare these. We know that x will be equal to 30 times the cosine of our angle. Y will equal 30 times the sine of 60 degrees and we obtain a cosine of 60 degrees.  Therefore, in this instance, 30 cosine of 60 will result in 15 and 30 sin of 60 will result in 15 square roots of 3 points.

Therefore, if we want to determine the magnitude of the plane with respect to the graph, we must combine our similar forces. To do this, we will need the square root of 130 for the plane, the minus sign because the wind is blowing in the opposite direction in this case, the x minus 15 square, the n plus our y component,  15 square root of 3 square, and the plane itself.

We now know that 3600 seconds equal 1 hour when translated to seconds. Therefore, we are aware that distance equals velocity multiplied by time. We should arrive at 24804 meters if we multiply our speed, which is 117.89 meters per second, by 3600 seconds.

To learn more about time and speed refer: brainly.com/question/13233744

#SPJ1

let east is the positive x direction

north is the positive y direction

for the net displacement

d = 4 * (- cos(45) i - j * sin(45)) + 5 i + 6 * (cos(60) i + j * sin(60))

d = 5.17 i + 2.37 j

for the return vector

d = - 5.17 i - 2.37 j

d = sqrt(5.17^2 + 2.37^2) at arctan(2.37/5.17) degree south of west

d =  5.69 m at 24.6 degree south of west  

the return vector is 5.69 m at 24.6 degree south of west  

To know more about  vector   visit : https://brainly.com/question/13322477

#SPJ4

The temperature can be converted by using the conversion relationship.

It is defined as the conversion from one quantity unit to another quantity unit followed by the process of division, and multiplication by a conversion factor.

It is given that:

Air temperature rises from a morning low of 42'f to an afternoon high of 70f.

The temperature of 42°F can be converted as:

Converting from F to C:

= (5/9)(42 - 32)

= 5.55°C

Converting from F to R:

= (42 + 459.670)

= 501.67°R

Converting from F to K:

= [5/9](42 - 32) + 273.70

= 278.705°K

The temperature of 70°F can be converted as:

Converting from F to C:

= (5/9)(70 - 32)

= 21.11°C

Converting from F to R:

= (70 + 459.670)

= 529.67°R

Converting from F to K:

= [5/9](70 - 32) + 273.70

= 294.261°K

Thus, the temperature can be converted by using the conversion relationship.

Learn more about the unit conversion here:

https://brainly.com/question/11543684

#SPJ4

The magnitude of the displacement vector of the bee will be 2 km. Because the distance between the endpoints is 2km.

A displacement is a vector in engineering and mechanics that has a length equal to the smallest distance between a point P's initial and final positions. It is a vector quantity. The SI unit of the displacement is the meter.

A honeybee leaves the hive and travels a total distance of 2 km before returning to the hive.

The bee's displacement vector will be 2 kilometers in length. Mostly due to the 2 kilometers between the terminals.

More about the displacement link is given below.

https://brainly.com/question/11934397

#SPJ4

By conservation of energy, the height of the playground slide should be 108.241 meters.

We need to know about the conservation of energy to solve this problem. The energy can not be created or destroyed, the only way is to change to another form. It can be written as

Ei = Ef

where Ei is initial energy and Ef is the final energy

From the question above, we know that

m = 35 kg

v = 4.7 m/s

The playground slide is converting the potential energy from height to kinetic energy. Hence,

Ei = Ef

PE = KE

m . g . h = 1/2 . m . v²

h = 1/2 . g . v²

h = 1/2 . 9.8 . 4.7²

h = 108.241 meters

Hence, the height of playground slide should be 108.241 meters to reach 4.7 m/s of velocity at bottom.

Find more on conservation of energy at: https://brainly.com/question/166559

#SPJ4

The time taken for the box of supplies to crash into the ground below is 3.75 s

From the question given above, the following data were obtained:

The time taken for the box of supplies to fall to the ground can be obtained as follow:

h = ½gt²

138 = ½ × 9.8 × t²

138 = 4.9 × t²

Divide both side by 4.9

t² = 138 / 4.9

Take the square root of both side

t = √(138 / 4.9)

t = 3.75 s

Thus, it will take the box of supplies 3.75 s to crash into the ground.

Learn more about motion under gravity:

https://brainly.com/question/20385439

#SPJ1

The electric force on the top charge is -9.1158 x [tex]10^{5}[/tex]N.

The electric force is given by

F=[tex]k_{e}[/tex][tex]\frac{q_{1}q_{2} }{(r_{12})^2 }[/tex] = (8.99 x [tex]10^{9}[/tex] N.[tex]m^{2}/C^{2}[/tex]) [tex]\frac{(+39C)(-39C)}{(1500m)^2}[/tex]

=-9.1158 x [tex]10^{5}[/tex]N

= 9.1158 x  [tex]10^{5}[/tex]N downward

The Coulomb’s inverse-square law, that is sometimes known as Coulomb’s law, is a kind of experimental physical principle that measures the force exerted between two electrically charged particles that are considered stationary.

The electric force between two charged objects at rest include electrostatic force and Coulomb force.

Coulomb listed the following characteristics of the electric force for charges in a resting state: Unlike charges attract each other whereas like charges repel one another.

As a result, a positive charge pulls a negative charge toward it whereas two negative charges repel one another. The line between the two charges is where the attraction or repulsion occurs.

To know more about Coulombs law, visit:

https://brainly.com/question/506926

#SPJ4

Answer: 0.20075

Explanation: