Describe the motion of the object in the graph for the entire time. Explain how the motion changes, including direction and whether or not it is speeding up, slowing down or moving at a constant velocity.

The angular momentum of the ballet dancer is 14.98 kgm²/s.

The angular momentum of the ballet dancer is calculated by applying the following formula as show below.

L = Iω

where;

The moment of inertia of the dancer, I = MR²

I = 62 kg  x  (0.16 m )²

I = 1.59 kgm²

The angular momentum of the ballet dancer is calculated as;

L = 1.59 x 9.42

L = 14.98 kgm²/s

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The emf of the battery is 7.2 volts when the internal resistance of a battery is 2 ohms. when a resistance of 10 ohms is connected to the battery, it draws a 0.6 amp current.

Given,

Internal resistance, r = 2 ohms

Resistance connected, R = 10 ohms

Current, i = 0.6 amp

let emf = V

Using ohm's law in the circuit

V = i(r+R)

or V = 0.6(2+10) = 0.6 x 12

V = 7.2 volts

Therefore, the emf of the battery is 7.2 volts when the internal resistance of a battery is 2 ohms. when a resistance of 10 ohms is connected to the battery, it draws a 0.6 amp current.

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Explanation:

angular velocity = w = v/r

w = 8/2

w = 4rad/s

Yes, by bringing the positively-charged object near the object to be charged, then discharging the far side.

Positively-charged particles, or ions, are atoms or molecules that are missing one or more electrons, giving them a surplus of positive charge. This imbalance between the number of protons and electrons causes the particle to be attracted to objects with a negative charge, such as other ions.

The positively-charged object will cause electrons to be transferred to the object to be charged, thus resulting in a negative charge on the object.
Yes, by rubbing the two objects together. By rubbing the two objects together, electrons can be transferred from one object to the other, thus resulting in negative charge on one object and positive charge on the other.

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The length of the truck that is 75 percent longer than the car is 315 inches.

The length of the truck that is 75 percent longer than the car is determined from the percentage increment of the truck from the car.

The length of the car is given as 180 inches, then the length of the truck that is 75 percent longer than the car is calculated as follows;

Lt = ( 75 %  + 100 % ) x Lc

where;

Lt = ( 175% ) x Lc

Lt = ( 1.75 ) x 180 inches

Lt = 315 inches

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The projectile's top height is indicated by the number h. Max equals u squared x divided by 2 g. In this case, the initial horizontal velocity is maximized by u square at a rate of 6 meters per second square.

The projectile's top height is indicated by the number h. Max equals u squared x divided by 2 g. In this case, the initial horizontal velocity is maximized by u square at a rate of 6 meters per second square.

This rate is then multiplied by two to get 9.8 meters per second square, which equals 1.84 meters.

The projectile can only fly as high as this, then. Here, we already know that the projector is located at a distance of h from the ground, which is the height the projectile has reached from ground level. Please excuse the distance, the cannon is h feet above the ground.          

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The amount of charge that will flow from the battery is 77000pC

A capacitor is a device that stores electrical charge. The amount of charge stored in a capacitor is proportional to the voltage applied across it, according to the equation Q = C*V.

where Q is the charge in coulombs, C is the capacitance in farads, and V is the voltage in volts.

In this case, the capacitance of the air-gap capacitor is 3500pF (pico-farads) and the voltage is 22V, so the charge stored in the capacitor is:

Q = 3500pF * 22V = 77000pC (pico-coulombs)

When a piece of mica is placed between the plates, it reduces the space between the plates, which will increase the capacitance of the capacitor. The increase in capacitance will result in an increase in the amount of charge stored in the capacitor.

It's worth noting that the charge that flows from the battery is equal to the initial charge stored in the capacitor. Since the initial charge stored in the capacitor is 77000pC, this is the amount of charge that will flow from the battery.

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The gravitational acceleration of this new planet is [tex]24.3 * 10^{9} G m/s^{2}[/tex].

                                        g = GM/R^2

Here,

G = the universal gravitational constant (G = gravitational constant of planet)

M = Mass of planet = [tex]3.5*10^{31} kg[/tex]

R = Radius = 1.2*10^11 m

Putting these values in above equation we get: g=  [tex]24.3 * 10^{9} G m/s^{2}[/tex].

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If an object is traveling in a circular orbit where its speed is doubled, then its centripetal acceleration will be quadrupled.

Centripetal acceleration is the acceleration of an object traversing a circular path. Because velocity is a vector quantity, i.e., it has both a magnitude ( the speed and a direction), so when the object travels on a circular path, its direction changes constantly and thus as a result of this its velocity changes, producing acceleration,

For instance, when an object in a circular orbit is moved with double doubled, then it has quadrupled centripetal acceleration.

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The correct option: (e) There is a negative charge on the surface of the cavity, and a positive charge on the outer surface of the conductor.

Any extra charge on the a conductor will be located on its surface, according to Gauss' Law.

Thus, on the cavity's surface there is a negative charge, while the conductor's outer surface has a positive charge.

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The complete question is-

A positive point charge is placed in a cavity inside a neutral conductor without transferring charge to the conductor. What is the sign of the charge on the surface of the cavity and the outer surface of the conductor?

(a) There is no charge on the surface of the cavity or the outer surface of the conductor.

(b) There is a positive charge on the surface of the cavity, but no charge on the outer surface of the conductor.

(c) There is a negative charge on the surface of the cavity, but no charge on the outer surface of the conductor.

(d) There is no charge on the surface of the cavity, but a positive charge on the outer surface of the conductor.

(e) There is a negative charge on the surface of the cavity, and a positive charge on the outer surface of the conductor.

when 300 waves pass a point in one minute, the frequency is 5 Hz.

Frequency can be defined as, the no.of waves that pass in a unit of time through a fixed point. frequency is measured hertz (Hz)

Wave: The propagation of disturbances that have place in a medium  is referred to as a wave.

There are two types of waves.

1.Longitudinal waves

2.Transverse waves

Wavelength(λ): The distance between two peaks or two troughs can be used to define a wavelength. It is measured in meters (m), centimeters (cm) or millimeters (mm).

Wavelength Formula: λ=ν/f,

where ν is velocity, f is frequency .

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A frequency of 5 Hz is achieved when 300 waves pass a place in one minute.

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The instantaneous speed at the instant you turn around to move in the opposite direction is (b) always zero.

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Where θ 1 is the angle of the first line, and θ 2 is the angle of the second line.

Angle is the measure of a turn or displacement between two intersecting lines. Angles are typically measured in degrees, with 360 degrees in a full circle. acute angles are smaller than 90 degrees, while obtuse angles are larger than 90 degrees. Straight angles are exactly 180 degrees, while reflex angles are greater than 180 degrees.

The equation for the diffraction grating for the sodium is:
nλ = d sinθ
Where n is the order of the spectrum, λ is the wavelength of the light, d is the distance of the spectrum, and θ is the angle of the light.
For the first order, the initial angular position is:
nλ = d sinθ
θ = sin-1 (λ/d)
For the first order, the final angular position is:
nλ = d sinθ
θ = sin-1 (λ/d)
The angular separation of the two closely spaced yellow lines of sodium is:
Δθ = θ 1 - θ 2
Where θ 1 is the angle of the first line, and θ 2 is the angle of the second line.

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The momentum of the object afterwards will be 80 Kgms-1.

Given the following data as per the question:

Mass of the object is given as 6 Kg

Force is given as 10 N in the question

Time is given as the following 8 sec

The value of the Momentum is same as impulse.

So, the formula of impulse is given as:

I = Ft

Where

I is the impulse

F is the force

and t is the time

From the given information,

F = 10 N

t = 8 secs

Therefore,

I = 10 × 8

I = 80 Ns.

Momentum is 80 Kgms-1.

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The angular velocity of the rider is 2.9 rad/s. The result is obtained by using the formulas in circular motion.

Circular motion is a motion of an object along a circular path. When an object moves with an acceleration, it has a centripetal acceleration calculated by

ac = v²/r

Where

In circular motion, an object moves with linear and angular velocity. The relationship between both velocities is

v = ωr

Where

A rider moves in a circular motion with

Find the angular velocity! (ω = ?)

We find the centripetal acceleration in m/s².

ac = 10.5g

ac = 10.5 × 9.8 m/s²

ac = 102.9 m/s²

The linear velocity is

ac = v²/r

102.9 = v²/12.5

v² = 102.9 × 12.5

v² = 1,286.25

v ≈ 35.9 m/s

Use the equation of relationship between linear and angular velocity!

v = ωr

35.9 = ω (12.5)

ω ≈ 2.9 rad/s

Hence, the rider has the angular velocity of 2.9 rad/s.

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The initial speed of the bullet before striking the basket of mass 1 kg is 1.98 m/s. Speed of each bullet is given below

To determine the mass of the ball and basket of the ballistic pendulum using a balance, you can simply weigh the pendulum and record its mass.

To calculate the initial speed of the pendulum after the ball has collided with the pendulum basket, you can use the conservation of energy. The initial kinetic energy (KE) of the ball is equal to the final kinetic energy of the pendulum (ball and basket combined), and the initial gravitational potential energy (GPE) of the ball is equal to the final GPE of the pendulum. The equation for KE is KE = 1/2mv^2, where m is the mass of the ball and v is its velocity. The equation for GPE is GPE = mgh, where m is the mass of the ball, g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the pendulum at its maximum displacement.

Using the values for mass, height, and velocity, you can set up the conservation of energy equation as follows:

1/2mv^2 + mgh = 1/2(m + M)v_f^2 + (m + M)gh_f

where m is the mass of the ball, M is the mass of the pendulum basket, v is the initial velocity of the ball, v_f is the final velocity of the pendulum, h is the height of the pendulum at its maximum displacement, and h_f is the height of the pendulum at its maximum displacement after the collision.

Solving for v, we get:

v = sqrt(2gh)

Next, you can use the conservation of momentum to determine the initial speed of the ball before it collided with the pendulum basket. The conservation of momentum states that the total initial momentum of an isolated system is equal to the total final momentum of the system. The equation for momentum is p = mv, where m is the mass of the ball and v is its velocity.

Before the collision, the momentum of the ball is simply equal to its mass times its velocity:

p_i = mv

After the collision, the momentum of the pendulum is equal to the mass of the ball plus the mass of the pendulum basket times the final velocity of the pendulum:

p_f = (m + M)v_f

Setting the initial and final momenta equal to each other and solving for v, we get:

mv = (m + M)v_f

v = (m + M)v_f / m

So, by measuring the mass of the ball and basket, the maximum height of the pendulum, and the final velocity of the pendulum, you can use the conservation of energy and conservation of momentum to determine the initial velocity of the ball and the pendulum.

Speed of each bullet depending on the mass are:-

          m (kg)    v (m / s)

            0.05      41.58

            0.10       21.78

            0.15       15.18

            0.20      11.88

            0.25       9.90

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Question - Using a balance, determine the mass of the ball and basket of the ballistic pendulum. Fire the ballistic pendulum and measure the maximum height the pendulum reaches. Use the conservation of energy (initial KE + initial GPE = final KE + final GPE; KE = ½mv2; GPE = mgh) to calculate the initial speed of the pendulum after the ball has collided with the pendulum basket. Next, use the conservation of momentum (total initial p = total final p; p = mv) to determine the initial speed of the ball before it collided with the pendulum basket.

A ball launch horizontally from the top of a 70.6-m building lands 188 m from the building's base. The ball will fly for 3.79 seconds.

A displacement is a vector whose length is the shortest distance between a moving point's initial and final positions.

The beginning velocity in the problem is described as horizontal, which implies that the initial vertical velocity(u) is zero. In order to solve for the time of flight using the formula, we also have the height of the building, which is a downward displacement.

We know,

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

Here, Y = height of the building =  70.6m, u = 0, a = g = 9.81m/[tex]s^{2}[/tex]. We have to find the time of flight t.

⇒ [tex]70.6 = 0*t + \frac{1}{2} (9.81)t^{2}[/tex]

⇒ [tex]t^{2} = 14.3934[/tex]

⇒ [tex]t = 3.79 s[/tex]

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The speed of the car traveling when it went over the cliff is 38.12 m/s.

The equation of motion for calculating the displacement of a moving object is given as

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

u = initial velocity

t = time taken

a = acceleration of the object

S = displacement of the object

The above equation can be used to find out the speed of the car.

        Therefore, the above equation can be written as

                                               [tex]h = \frac{1}{2} gt^{2}\\t = \sqrt[]{\frac{2h}{g} } \\t = \sqrt[]{\frac{2(57)}{9.8} } \\\\t = 3.41 s[/tex]

Therefore, the time of flight = 3.41 s.

If the point of impact from the base of the cliff is 130 m and the time of flight is 3.41 s.

Then, the velocity of the car traveling over the cliff is calculated as

                                            [tex]v = \frac{point of impact}{t} \\\\v = \frac{130}{3.41} \\\\v = 38.12 m/s[/tex]

The velocity of the car traveling when it went over the cliff is 38.12 m/s.

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The final velocity of the composite object after collision is 1.8002 m/s in the direction of the first object.

Initial velocity of the first object, v₁ = 5.001 m/s

Mass of the first object, m₁ = 3.0 kg

Initial velocity of the second object, v₂ = -3.001 m/s (In opposite direction)

Mass of the second object, m₂ = 2.0 kg

Let the final velocity of the composite object, = V

Mass of the composite object, = (3.0 + 2.0) = 5.0 kg

By the law of conservation of momentum,

m₁v₁ + m₂v₂ = (m₁ + m₂) × V

V = (m₁v₁ + m₂v₂)/(m₁ + m₂)

V = (3 × 5.001 + 2 × (-3.001))/(2 + 3)

V = 9.001/5

V = +1.8006 m/s

Positive sign indicates that the direction of the velocity will be the same as that of the first object.

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When the stretch distances are at half of their maximum displacement, the acceleration will be half of its maximum value by Hooke's Law.

F= -kx

In accordance with Hooke's law, a principle of elasticity, for relatively minor deformations of an object, the displacement or size of the deformation is directly proportional to the deforming force or load The elasticity of an object is likewise governed by Hooke's law; for example, a metal spring can only be stretched so far before being broken by too much effort. A mass that we already have is then expanded out by x. Displacement and acceleration are inversely related. When the stretch distances are at half of their maximum displacement, the acceleration will be half of its maximum value.

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The average speed of a helium atom at a certain temperature is 1100 m/s expressed in miles per hour is: 2460.63 mi/h

It is the transformation of a value expressed in one unit of measurement into an equivalent value expressed in another unit of measurement of the same nature.

To solve this problem the we have to convert the units with the given information.

Information about the problem:

By converting the speed units from (m/s) to (mi/h) we have:

v= 1100 m/s * 1 mi/1609.34 m * 3600 s/1 h

v= 2460.63 mi/h

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The component of robot which helps detect the change in environment is a sensor. The correct option is A.

Robotics is the study area devoted to creating robots and automation, while a robot is a programmable machine that can execute a task. Different robots have varying degrees of autonomy. These levels range from totally autonomous bots that operate independently to bots that are controlled by humans and accomplish tasks.

Robots consist of some sort of mechanical construction. The mechanical part of a robot helps it perform tasks in the environment for which it was designed.

Robots have some degree of computer programming. If a robot didn't have a set of instructions telling it what to perform, it would just be another piece of simple hardware. Programming a robot can teach it when and how to perform a task.

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According to the problem the voltage across the capacitor is 1.73 V.

A capacitor is an electrical component that stores energy in the form of an electrostatic field. It is composed of two conducting plates separated by an insulating material called a dielectric. When a voltage is applied to the plates, the dielectric stores an electrical charge. Capacitors are used in a variety of electronic devices and are essential for the operation of many electrical and electronic systems.

The voltage across a capacitor is given by V = Q/C, where Q is the charge on the capacitor, and C is the capacitance.
In this case, the charge on the capacitor is 16.5 x 10-8 C, and the capacitance is 9500 pF = 9.5 x 10-8 F.
Therefore, the voltage across the capacitor is V = 16.5 x 10-8 C / 9.5 x 10-8 F = 1.73 V.

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The work that has been done by the Korbel is  4.41kJ.

We have to note that we define work in physics as the product of the force and the distance. In the case of the chair in the question, we have been told that Korbel pushes a 15 kg chair for a distance of 30 meters.

The force in this case would be the weight of the chair that we have and we can write that;

W = mgh

m = mass

g = acceleration due to gravity

h = height

Thus

W = 15 * 9.8 * 30

W = 4.41kJ

Thus a work of about  4.41kJ is done.

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Only about 40 percent of the thermal energy in coal is converted to electricity, so the electricity generated per ton of coal is 0.4 x 6,150 kWh or 2,460 kWh/ .

Define  natural gas?

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The final velocity of the two-vehicle mass is 2.42m/s.

Momentum is defined as the product of mass and velocity of an object which is a vector quantity, which has a magnitude and a direction. If m is the mass of an object and v is its velocity, then p is the momentum of the object: [tex]\mathbf{p} = m \mathbf{v}.[/tex]

For above given information,

[tex]m_1= 1400kg\\m_2= 6400kg\\v_1_i=-13.5 m/s\\v_2_i= 0m/s[/tex]

Formula for this is:

[tex]m_1.v_1_i+m_2.v_2_i= (m_1+m_2)v_f[/tex]

(1400.-13.5)+ (6400.0) = (1400+6400).[tex]v_f[/tex]

-18900=7800.[tex]v_f[/tex]

-18900/7800=[tex]v_f[/tex]

[tex]v_f= 2.42m/s[/tex]

Thus, the final velocity of the two-vehicle mass is 2.42m/s.

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The level of the sound can be decreased by gradually draining the air from a plastic bottle. The sound about an alarm clock cannot be heard at all since sound cannot travel through a vacuum.

A ringing alarm clock will gradually grow quieter when air is gently drawn out of the area around it and placed beneath a glass jar. Because sound is indeed a mechanical wave that moves across a medium, this is the case.

We can hear the sound because the air molecules in the jar shake as sound waves pass through them. The amount of air particles available to vibrate and convey sound waves declines when air is eliminated, which lessens the sound's strength.  There will be so little remaining air to vibrate due to the almost full removal of the air that the sound will be almost undetectable.

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The point where the potential is zero is located at [tex]x = 5 cm * k * Q1/(Q1 + Q2)[/tex]

The potential at a point in space due to a point charge is given by the equation:

V = k * Q/r

where V is the potential, k is the Coulomb constant  [tex](8.99 x 10^9 N * m^2/C^2)[/tex], Q is the charge, and r is the distance from the point charge to the point where the potential is being calculated.

In this problem, we have two point charges placed 5 cm apart on the x-axis. How about we call the charges Q1 and Q2, and we should assume that Q1 is located at the origin (x = 0) and Q2 is located at x = 5 cm.

The potential at a point along the x-axis is the amount of the potentials due to each of the point charges.

V = k * Q1/r1 + k * Q2/r2

where r1 is the distance from the point to Q1 and r2 is the distance from the point to Q2.

In the event that the potential at a point is zero, the amount of the potential due to each of the point charges is zero.

So, k * Q1/r1 + k * Q2/r2 = 0

To find the points along the x-axis where the potential is zero, we can set the equation above equal to zero and address for x.

r1 = x and r2 = |x - 5 cm|

k * Q1/x + k * Q2/|x - 5 cm| = 0

x = k * Q1/Q2 * |x - 5 cm|

x = k * Q1 * (5 cm - x)/Q2

x = 5 cm * k * Q1/(Q1 + Q2)

In this way, the point where the potential is zero is located at

x = 5 cm * k * Q1/(Q1 + Q2)

This is valid for any point in the x-axis, and these points are called equipotential points.

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The final speed of the UFO after experiencing a constant acceleration for 63 seconds is 351.3 m/s.

Acceleration is the rate at which an object increases its speed, velocity or rate of change. It is the rate of change of velocity over time, or the rate of change of the position of an object. Acceleration can be either positive, when the speed of an object is increasing, or negative, when the speed of an object is decreasing.

The final speed of the UFO can be determined by using the equation, v = u + at, where u is the initial velocity, a is the acceleration, and t is the time. So, in this case, v = 64 + (21,892.5/63) = 351.3 m/s. Therefore, the final speed of the UFO after experiencing a constant acceleration for 63 seconds is 351.3 m/s.

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The magnitude of the acceleration is |8.1 * 10^5| m/s^2 = 8.1 * 10^5 m/s^2

In mechanics, rate of change of velocity of an object with respect to the time is called as acceleration.

As it is known, F = k * (q1 * q2)/r^2

where F is force, k is Coulomb's constant (9 x 10^9 N * m^2/C^2), q1 and q2 are charges of the two spheres, and r is distance between the two spheres.

As we know that , F = m * a

a = F/m

a = (k * (q1 * q2))/r^2) / m

a = (9 * 10^9 N * m^2/C^2 * (-23 * 10^-9 C)^2) / (10^-2 m)^2

Acceleration of the upper sphere is a = -8.1 * 10^5 m/s^2. The negative sign indicates that acceleration is in opposite direction to the force, as expected, since the force is repulsive.

The magnitude of the acceleration is |8.1 * 10^5| m/s^2 = 8.1 * 10^5 m/s^2

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