A roller coaster begins at rest 120 m above the ground, as
shown. Assume no friction from the wheels and air, and that no
energy is lost to heat, sound, and so on. The radius of the loop
is 40 m. Find the speed of the roller coaster at points E and F.
Note:-Use g = 10 mlsz

The frequency and time interval are 2 seconds and 0.5 Hz, respectively.

One oscillation: The oscillating body moves completely back and forth in a single motion, or oscillation.

The frequency is the number of vibrations the body makes in a second.

Time span: This is the amount of time it takes a body to complete one oscillation.

Time period is equal to how long the pendulum swings over how many oscillations it makes.

20/10=2s

Frequency =1/Time 1/2 = 0.5Hz

In light of this, the time interval and frequency are 2 seconds and 0.5 Hertz, respectively.

How frequently a periodic wave shape or signal repeats itself at a specific amplitude is expressed as frequency. It can be measured in hertz, kilohertz, megahertz, etc.

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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 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 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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The force particle b exerts on a is -2.72 N to the left.

The force particle b exerts on a can be determined by using Coulomb's law, which states that 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 the charges of the particles are the same, we can assume that the force is proportional to the inverse of the distance squared. By increasing the distance between the particles from 13.0 mm to 18.5 mm, we can assume that the force has decreased.

Using the formula F = k(q1*q2)/r^2, we can calculate the new force by substituting the new distance and assuming the charges are equal. Since the force was 2.72 N to the right, and the distance has increased, the force particle b now exerts on a would-be -2.72 N to the left.

This is because the force is inversely proportional to the distance squared, and since the distance has increased the force has decreased.

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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 angle between the incident and reflected beam is 46° when a beam of light strikes a mirror at angle of 23° to the normal.

Given the angel of incidence (∠i) = 23°

Since the beam of light strikes the mirror at normal it is the angle of incidence. The incident ray's angle with the normal at the point where it contacts the mirror surface is used to calculate the angle of reflection.

From mirror laws we know that the angle of incidence is equal to the angle of reflection. Then, ∠i = ∠r

Hence, as angle of incidence is 23° and the angle of reflection is 23° . So, the angle between the incident ray and the reflected ray is 23° + 23° = 46°.

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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 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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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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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 order of magnitude describes a relative larger or smaller quantity. Find out what a molecule means by orders of magnitude and how they are determined.

In different situations, the term "order of magnitude" is also employed more loosely. Simply said, the phrase can refer to something that is much larger or smaller, a very huge or little number, a small or large volume of something, etc.

A number pf powers of 10 or even the numbers of power of 0.1 inside a negative number determines the order of magnitude. Ordinarily, an order of magnitude was expressed as 10 to a nth power. The order in magnitude is represented.

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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.

The amount of energy transferred as light is 73.5 J (350 J x 21%).

A lumen is a unit of size for the quantity of mild that is emitted through a source. Lumens are frequently used to evaluate the brightness of different light sources. The efficiency of a mild bulb is regularly measured in phrases of the quantity of lumens in line with watt of electricity fed on. A light bulb that has a higher lumen output consistent with watt is considered to be more green. As an example, a mild bulb that produces one hundred lumens in step with watt is more efficient than a light bulb that produces eighty lumens in line with watt. That is because it produces greater light according to unit of electricity fed on.

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An electric light bulb has an efficiency of 21% 350 J of energy contains the 73.5 J  of energy transferred as light.

Amount of energy transferred by light =( 21/100)×350

                                           = 2.1 × 35

                                                = 73 .5 J

A lumen is a unit of size for the quantity of mild that is emitted through a source. Lumens are frequently used to evaluate the brightness of different light sources. The efficiency of a mild bulb is regularly measured in phrases of the quantity of lumens in line with watt of electricity fed on. A light bulb that has a higher lumen output consistent with watt is considered to be more green. As an example, a mild bulb that produces one hundred lumens in step with watt is more efficient than a light bulb that produces eighty lumens in line with watt. That is because it produces greater light according to unit of electricity fed on.

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Answer:

Below

Explanation:

The trailing edge has to fall 6.14 inches   ( mass is irrelevant)

 d = 1/2 a t^2

 6.14/12  ft   = 1/2 (32.2  ft/s^2 )(t^2) shows   t = .178 s

The statement that the direction of a vector can be different in different coordinate systems, is true.

It can be possible to add a coordinate system to a vector and identity components of that vector in that particular system, but the orientation and the type of the coordinate system with the respect to the vector can be different. The choice of a particular coordinate system usually does not change the direction of the vector.

However the magnitude of a vector may or may not be different in different coordinate systems. It is possible to attach a scalar to a vector. A  vector may have its magnitude equal to zero while having one of its components is nonzero. The direction of a vector can be different in a different particular coordinate system.

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The electric force between these two sets of charges is: -3.6*10^6 N

In physics the electric force is the force that attracts or repels two charges (q) separated at a distance called (r), this is expressed in the international system of units in Newton.

To solve this exercise the electric force formula and the procedure we will use is:

F = (k * q1 * q2)/r²

Where:

Information about the problem:

By converting the the separation distance of the charges from (km) to (m) we have:

r = 2.0 km * 1000 m/1 km

r= 2000 m

Applying the electric force formula we have:

F = (k * q1 * q2)/r²

F = [(9 *10^9 N*m²/C² * (40 C) * (-40 C)]/ (2000 m)²

F = -1.44*10^13 N*m² /4*10^6 m²

F = -3.6*10^6 N

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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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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.

Explanation:

angular velocity = w = v/r

w = 8/2

w = 4rad/s

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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When the ball is halfway to the ground (i.e. at height h/2), is its kinetic energy is more than, its maximum kinetic energy.

Air exerts a force known as air resistance. Like a sports vehicle with a streamlined design will encounter reduced air resistance and experience less drag, the automobile would be able to move more quickly than a truck with a flat front.

Air resistance is what generates this force. The force of air resistance slows an object's descent to the ground more as its mass decreases. Regardless of how much their masses differ, if two items were put on the moon, where there is no air, they would fall at the same rate.

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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 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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Heat rates, thermal efficiencies, capacity factors, load factors, economic efficiencies, operational efficiencies, and energy efficiencies are all elements in power plants. A power plant's performance may be expressed using several typical performance factors: heat rate (energy efficiency) and thermal efficiency.

Water, light, temperature, and nutrients are the four most important factors influencing plant development. You might be asking where dirt comes into all of this. Plants may grow without soil using a technique known as hydroponics. Plants, on the other hand, cannot grow if they are not provided with the necessary nutrients.

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The body does this by transferring the heat from the interior of your body. 0.2104 J/K is heat transfer change the body’s entropy each second

The following formula can be used to determine the change in entropy caused by heat transfer:

S = Q / T, where S is the entropy change,

Q is the heat transferred, and

T is the heat transfer temperature. The temperature is 30°C (303 K) and the heat transfer rate is 64 J/s in this instance.

ΔS = [tex]\frac{64}{303}[/tex] = 0.2104 J/ K

It is essential to keep in mind that heat transfer from the body to the skin is not reversible, resulting in an increase in the body's entropy.

The thermodynamic property entropy measures a system's disorder or randomness. It is related to the number of possible microstates (or ways in which a system can be arranged) that correspond to a particular macrostate (or observable state) of a system. It is frequently used to describe the degree of randomness or disorder within a system. The second law of thermodynamics states that systems tend to progress toward a state with greater entropy.

The International System of Units (SI) defines entropy as having Joules per Kelvin (J/K) units. Because it is a state function, the change in entropy only depends on the system's initial and final states, not on how the system got from one state to another.

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The extensive property among the following is mass. So, option A) is correct.

The property of a material known as the widespread property is dependent on the mass (or amount of matter) of the substance. Mass is the extensive property solely in the possibilities that are presented. Other than mass, all other attributes are independent of mass.

Divide the substance in half to determine the extensive property quickly and easily. It depends on mass and is an extensive property if it also applies to both of the separate portions. When a property remains constant for each half, it is said to be an intense property and is independent of mass. Examples of an intensive property include density, temperature, pressure, etc.

Hence, the answer is mass.

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

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The lowest recorded air temperature at the surface of the Earth was a measurement of −89.2°C made at Vostok station, Antarctica, at 0245 UT on 21 July 1983. Here we present the first detailed analysis of this event using meteorological reanalysis fields, in situ observations and satellite imagery.

What is meant by temperature?

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