an object moves in an xy - plane and has the following coordinates

27m./s speed do a bicycle and its rider, with a combined mass of 120 kg , have the same momentum as a 1800 kg car traveling at 5.4 m/s.

Speed can be defined as the distance travelled by the object per unit time. Momentum can be defined as the product of the mass and the speed of the object.

The equation for the momentum is     p = mv

Here, m is the mass of the object and v is the speed of the object. The equation for the impulse is,                 I = mΔ v

Here, m is the mass and is the change in momentum. The equation for the change in speed is                      

Here,   ΔV = [tex]V_{f} -V_{i}[/tex]

is the initial speed [tex]v_{i}[/tex]

is the final speed.[tex]v_{f}[/tex]

Step: 1

The equation for the momentum of the bike and rider is, P (B+R)= M [tex](B+R)^{V}[/tex]…… (1)

Here, M (B+R) is the mass of the bike and rider, and v is the speed of the bike and rider.

The equation for the momentum of the car is [tex]P_{car} = m_{car} V_{car}[/tex]…… (2)

Here,

[tex]m_{car }[/tex]is the mass of the car and

[tex]V_{car}[/tex]is the speed of the car.

According to the question, the momentum of the bike and rider is the same as that of the momentum of the car, that is,

Substitute the equations (1) and (2) in above equation.

[tex]M_({B+R^{v} )}[/tex]= [tex]M_{car}V_{car}[/tex]

Rearrange the above equation for v.  v = [tex]M_{car}V_{car}[/tex]/[tex]M_({B+R^{} )}[/tex]

Substitute  1800 kg for[tex]M_{car}[/tex] , and for 5.4m/s in above equation.

v = ( [tex]\frac{(1800) (5.4)}{120}[/tex] = 27m./s

Here, the momentum of the bike and rider is depending on the combined mass of the bike and rider and the speed of the bike and raider.

Measurement is the most important concept in science. There are many measurable quantities that are measured in basic or fundamental physical  units. Speed ​​is one such measurable quantity that measures the ratio of the distance travelled by an object to the time it takes to travel. Acceleration is defined as the rate of change of velocity with respect to time. Acceleration is a vector quantity because it has both magnitude and direction. It is also the second derivative of position with respect to time or  the first derivative of velocity with respect to time.

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An object has an acceleration of 8.0 m/s/s. If the net force experienced by the object is decreased by a factor of 3.7 and if the mass of the object is decreased by a factor of 2.6, then the new acceleration would be 5.62 [tex]m/s^{2}[/tex]

force 1 = mass1 * acceleration 1

force 1 = mass1 * 8  

f1 = m1 * 8

force 2 = mass 2 * acceleration 2

force1 / 3.7  = (mass 1 / 2.6) * acceleration 2

f1 / 3.7 = (m1 / 2.6) * a2  

( m1 * 8 ) / 3.7 = (m1 / 2.6) * a2

a2 = 5.62 [tex]m/s^{2}[/tex]

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The electrons are transferred from hair to balloon when a balloon is being rubbed on a girl’s hair and attains a negative charge.

Rubbing the balloon against the hair leads to the transfer of electrons from the hair to the balloon because electrons are negatively charged, the balloon attains a negative charge, while on the other hand, the hair with the loss of negative charges gets a net positive charge. Static electricity occurs due to an imbalance between negative charges and positive charges in a body. These charges can build up on the surface of a body until they find a path to be released or discharged. Static electricity is produced when positive and negative charges are not in a balanced situation. Protons and neutrons don't move around but electrons jump from one place to another place. When an object has more electrons than protons, it has a negative charge.

So we can conclude that when a balloon is being rubbed on a girl’s hair, the electrons are transferred from hair to balloon.

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The rms voltage will be 82.7 v

"RMS" stands for Root Mean Square and is a way of describing the amount of AC voltage or current in terms that are functionally equivalent to DC. For example, 10 Volts AC RMS is the amount of voltage that will produce the same amount of heat dissipation in a given value resistor as a 10 Volts DC power supply.

The root mean square (rms) voltage of a sinusoidal source of emf (Vrms) is used to characterize the source. It is the square root of the square of the time-averaged voltage. The value of Vrms is v₀/√2 or equivalently 0.707 v₀

For the given question:

At the same time interval same heat is produced. Therefore, power in both DC and AC will also be same.

So the rms voltage will be:

= 117.0/√2

= 117.0 × 0.7071

= 82.7 v

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The temperature at which the bar will fit exactly into a hole of constant width 10.005 cm if coefficient of linear expansion of steel is 11x10-6 C-1 is 95.5 °C

Δ L = L - Lo

Δ T = T - To

Δ L = Change in length

L = Initial length

Lo = Final length

α = Co-efficient of linear expansion

Δ T = Change in temperature

T = Initial temperature

To = Final temperature

L = 10 cm

Lo = 10.005 cm

T = 50 °C

Δ L = - 0.005 cm

α = 11 * [tex]10^{-6}[/tex] / °C

Δ L / L = α Δ T

Δ L / α L + T = To

To = ( - 0.005 ) / 11 * [tex]10^{-6}[/tex] * 10 + 50

To = 45.5 + 50

To = 95.5 °C

Therefore, the temperature at which the bar will fit exactly into a hole is 95.5 °C

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Answer:

The steel bar will fit exactly into the hole at a temperature of 95.45°C.

Explanation:

To find at what temperature the steel bar will fit exactly into a hole of a constant width, use the Linear Expansion equation.

[tex]\boxed{L_1-L_0=L_0 \cdot \alpha \cdot (T_1-T_0)}[/tex]

where:

As we want to find the final temperature, rearrange the equation to isolate T₁:

[tex]T_1=\dfrac{L_1-L_0}{L_0 \cdot \alpha}+T_0[/tex]

Given values:

Substitute the values into the equation:

[tex]\implies T_1=\dfrac{10.005-10}{10 \cdot 11 \times 10^{-6}}+50[/tex]

[tex]\implies T_1=\dfrac{0.005}{0.00011}+50[/tex]

[tex]\implies T_1=95.45^{\circ}\text{C}\; \sf (2\;d.p.)[/tex]

Therefore, the steel bar will fit exactly into the hole of  constant width 10.005 cm at a temperature of 95.45°C (to two decimal places).

Note: The answer is not one of the options provided.

Taking into account the definition of density, the density of the liquid is 0.8 g/cm³.

Density is defined as the property of matter, whether solid, liquid, or gas, that allows the amount of mass in a given volume of a substance to be measured.

The expression for the calculation of density is the quotient between the mass of a body and the volume it occupies:

density= mass÷ volume

It can be deduced that density is inversely proportional to volume: the smaller the volume occupied by a given mass, the higher the density.

In this case, you know that:

Replacing in the definition of density:

density= 40 g÷ 50 cm³

Solving:

density= 0.8 g/cm³

In summary, the density in this case is 0.8 g/cm³.

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An example of an anomaly that led to a theory being overturned is: The discovery that materials, when burned, release phlogiston.

A theory can be defined as an integrated set of principles and rules that can be used by a scientist to explain and predict observed events.

According to Thomas Kuhn, the process of any scientific discovery usually starts with the awareness of an anomaly and ends with making an adjustment to scientific theory in order to make a previously anomalous to become expected.

The phlogiston theory can be defined as a superseded scientific theory which stated that a fire-like materials (elements) referred to as phlogiston, are found within combustible bodies and they are released when burned or during combustion.

However, the phlogiston theory is an anomaly that was later overturned by a scientists known as Antoine Lavoisier in 1772, who proved that combustion and burning of any chemical substance or materials (elements) requires a gas that has mass.

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If it starts at rest, the angular velocity after 0.750 is 5.1. The symbol for angular velocity in SI units is s1.

When an object rotates or circles around an axis, its angular velocity is the rate at which the angle between the two bodies changes. The angle that is made by a line on one body and a line on the other in the illustration represents this displacement.

Examples of angular velocity include a roulette ball on a wheel, a race car travelling in a circle, and a Ferris wheel. In addition, the object's angular displacement with respect to time is represented by the angular velocity of the object.

Since the radian is a dimensionless quantity and the SI unit of angular velocity is radians per second.

Angular acceleration

a = a /r

 = 1.7/0.250

a =6.8

Angular velocity

omega = a*t

            = 6.8 *0.75

           =5.1

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The ratio of turns in the primary and secondary coils of her transformer is 1.916

Primary voltage = 230v

secondary voltage = 120v

The ratio of turns in primary and secondary coils of transformer is given by,

Np/Ns = 230/120

           = 1.916

Transformer: a piece of equipment used to increase or decrease voltage while transferring electrical energy from one alternating-current circuit to another or several circuits. Transformers are used for a wide range of tasks, including lowering the voltage of traditional power circuits to operate low-voltage appliances like doorbells and toy electric trains and raising the voltage of electric generators to enable long-distance transmission of electrical power.

Transformers alter voltage using electromagnetic induction, which means that current is induced in a second coil known as the secondary as the magnetic lines of force (flux lines) build up and collapse with changes in current travelling through the primary coil. To determine the secondary voltage, multiply the primary voltage by the number-to-number ratio. Transformers are devices that convert electrical energy from a single alternating-current turn in the secondary coil to the number of turns in the main coil, a measurement known as the turns ratio.

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To incubate the eggs, we need to use a low-efficiency light bulb because it will produce more heat.

The working light bulb in the incubator is when it turned on the machine the bulb lit up and the box got hot. When the temperature reaches 38 degrees Celsius, the sensor triggers the temperature controller to turn off the bulb. Therefore, the temperature of the box was kept up to a certain limit. Humidity in the box was maintained by a jar filled with water. Water was added daily to keep the humidity between 60% and 90%. Eggs were rotated twice daily to ensure that all sides of the eggs were hatched. This buildup was monitored for up to 22 days.

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Since the kinetic energy equation squares velocity, velocity increases have exponential effects: while doubling an object's mass doubles its kinetic energy, doubling its velocity quadruples it!

The energy of motion, or kinetic energy, is manifested in the motion of a particle, an object, or a group of particles. Kinetic energy is used by any moving thing, including people moving, baseballs being thrown, table crumbs falling, and charged particles in electric fields.

Kinetic energy is divided into three subtypes: vibrational, rotational, or translational. Unsurprisingly, items that vibrate produce vibrational kinetic energy. Moving objects generate rotational kinetic energy, whereas object collisions generate translational kinetic energy.

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The minimum number of steps visible on the escalator at any given time is 150.

Let's assume that the escalator is moving upward at a constant rate, so that the distance traveled by al in one unit of time is equal to three times the distance traveled by bob in one unit of time, which means that al will take three times as many steps as bob does.

Let's say that al walks down 50 steps per unit time, and bob walks up 25 steps per unit time. We know from our earlier assumption about constant speed that al will take three times as many steps as bob does, so if al walks down 50 steps per unit time, then bob walks up 75 steps per unit time—but we also know that there are 150 total visible steps on the escalator at any given point in time.

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The story that fits the graph is; he elevator moves up, is stationary for a while, then moves down at a slower rate.

The term position time graph shows us how the position of the object is changing with time. The position in this case has to do with the exact point in space where the object can be found. We have here an elevator that could be found at various points.

We now have to turn to the graph and see how the graph can be able to give a description of the motion of the elevator. If we look at the position time graph, it tends to move up and then remain at a point for some time before it moves down.

Based on the analysis that we have made above, we can now look out for any of the stories that fits the description that we have just made here.

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A proton will accelerate at 1.27 109 m/s2. The rate of a change in velocity is called acceleration.

It is the kind of field that produces magnetic force. use a magnetic field to assist. The field that is sensed around a moving electric charge is how the magnetic force is measured.

The information provided in the issue is;

What is a proton's acceleration equal to?

The speed is 8.0 m/s, therefore v.

B = 1.8 T is the magnetic field.

The centripetal force and the megnetic force are equivalent;

qvB =m v/r

ac = 1.6 * 10 -18* 9.5* 1.8/1.67810-27

=1.27*10m/s

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The image screen is 10.5 cm from the lens.

The focal length of the lens is 10.0 cm, so once the lens focuses, it will be 10.0 cm from the object. In order to find how many centimeters away from the lens the image screen is, we need to use trigonometry and Pythagorean theorem.

Where x is the distance between our object and our projector in meters, and y is the distance between our projector and our image screen in meters. We know that y = 10.5 cm, or 0.105 m; we also know that x = 0 meters because our object is placed directly on top of our projector (therefore it's at 0 m).

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The equivalent resistance of the circuit is 14.28 ohms.

Resistance- 25 ohms and 30 ohms in parallel

so, the equivalent resistance

1/R =1/R1+1/R2

1/R =1/25+1/30

1/R =0.07

R =  14.28 ohms

If two or more components are connected in parallel, they have the same difference of potential (voltage) across their ends. The potential differences across the components are the same in magnitude, and they also have identical polarities. The same voltage is applied to all circuit components connected in parallel. The total current is the sum of the currents through the individual components, in accordance with Kirchhoff's current law.

A parallel circuit's total resistance is always lower than any of its branch resistances. The total resistance in the circuit decreases when more parallel resistances are added to the lines.

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the maximum velocity of movement of any particle of the wire is 3.87 m/s

AND)

and)

L = wire length = 25 m

m = weight of wire = 100 g = 0.1 kg

The linear mass density of the wire is given as

μ = m/L = 0.1/25 = 0.004 kg/m

T = tensile force in the wire = 10 N

the speed of the wave along the wire is given as

v =√(T/μ)

v = √ (10/0.004)

v = 50 m/s

(ii)

A = amplitude = 15 mm = 0.015 m

f = frequency = 25 Hz

the maximum lateral velocity is given as

Vmax = 2πfA

Vmax = 2(3.14)(25)(0.015)

Vmax = 2.4 m/s

b)

F = force acting on each edge = 2.5 N

L = length of each edge = 0.75 m

m = weight of each edge = 125 g = 0.125 kg

the speed of the waves on the sheet is given as

v = √(FL/m) = √(2.5 x 0.75/0.125) = 3.87 m/s

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Since the toy car is halting, the acceleration is -36 m/s2, which equals the toy's deceleration.

A moving object can occasionally alter its velocity by the same amount every second. The data table above depicts an item altering its velocity by 10 m/s every second, as was described in the paragraph above. Since the velocity is changing by a fixed amount every second, this is known as a constant acceleration.

The object's force is calculated by multiplying its mass by the speed at which it is traveling. The product is the vector. Kg-m/s2 or Newton is the SI symbol for force (N). The force's equation is as follows:

F = ma

where,

Force is F

m is mass

a is acceleration

The specified values for force are f = 9.0N and m = 0.25kg.

∴ F = ma

9.0 = 0.25 × a

a = 36 m/s²

Therefore, the magnitude is -36m/s2 and the negative sign denotes the toy car's deceleration.

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There is 20% probability that the seal catches a mackerel.

How likely something is to occur is known as its probability.

To determine probability, divide the total number of possible outcomes by the number of possible ways an event could occur. There are differences between probability and odds. Odds are calculated by dividing a situation's likelihood of occurring by its likelihood of not occurring.

Given,

mackerel 15

herring 23

harbor pollock 37

probability = possible event/ no. of event

probability = 15/ 15+23+37

probability = 15/ 75

probability = 0.2

∴ probability is 20%

For numbers less than 1 out of 1,000 (such as 0.20 out of 1,000), it is clearer to recast them as “200 out of 10,000” (“2 out of 10,000,” for instance).

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Kinetic energy, which can be seen in the movement of an object, particle, or group of particles, is the energy of motion.

energy KE = units

mass m =  15

velocity v =  30

KE = 6750 J

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The force between the two charges will be 25k N m.

This can be determined by using Coulomb's Law, which is a formula relating the forces between two charges (q 1 and q 2 ) at a distance r apart. The formula states that their force is equal to kq1q2/r2, where k is a constant (9 × 109 N m2/C2). If we plug in the values of 100 newtons for each charge and 4 meters for their distance, we get:

F = 100k/(4 × 109) = 25k N m

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200 g mass is placed on meter stick 20 cm from fulcrum. a 170 g mass is used to balance the system and placed the meter stick at 23.52cm.

A dynamic or static equilibrium between opposing forces or actions, such as when forces are acting on a body and the resultant is zero (as in a reversible chemical reaction when rates of reaction in both the directions are equal)

The word "equilibrium" derives from the Latin word "libra," which means "weight" or "balance." As a constellation, astrological sign, and representation of the zodiac, Libra is sometimes shown as a set of balance scales, frequently held by the blindfolded goddess of justice, which stands for justice, fairness, and equality. Biology, chemistry, physics, and economics all have different definitions of equilibrium, yet they all refer to the harmony of opposing forces.

F₁d₁ = F₂d₂

m₁gd₁ = m₂gd₂

m₁d₁ = m₂d₂

here,

m₁ is mass of known object = 200 g

m₂ is mass of unknown object = 170 g

d₁ is distance from fulcrum of known object = 20 cm

d₂ is distance from fulcrum of unknown object = ?

∴ 200 × 20 = 170 × d₂

4000 = 170 × d₂

4000/170 = d₂

d₂ = 23.52 cm

170 g mass is placed at the distance of 23.52 cm.

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In both the cases gravitational potential energy is same.

Gravitational potential energy is energy an object possesses because of its position in a gravitational field. The most common use of gravitational potential energy is for an object near the surface of the Earth where the gravitational acceleration can be assumed to be constant at about 9.8 m/s².

Given two cases height of the top is 3 ft so the potential energy is same as potential energy is dependent on height of the ball.

In both the cases gravitational potential energy is same.

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The total work done by the gas during this cycle is A −40J.

For process 2→3 (volume constant)

Q=−40 J

W=0 (As V is constant)

ΔU=Q=−40

U3−U2=−40 (i)

For process 1→2 (temperature constant)

T1=T2

U1=U2 (ii)

From (i) & (ii)

U3−U1=−40

ΔU3→1=40 J

For process 3→1 (Adiabatic process)

W=−ΔU

W=−40J

A thermodynamic cycle comprises of a connected grouping of thermodynamic forms that include the exchange of warm and work into and out of the framework.

Whereas changing weight, temperature, and other state factors inside the framework, inevitably returns the framework to its introductory state.

The thermodynamic cycles are exceptionally fundamental for the control-creating frameworks (such as petrol motors, diesel motors, gas turbines, etc.).

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The gravitational force exerted on the satellite of mass 1000 kg moving in a circular orbit with a centripetal acceleration of 5 m/s² by the planet is 5000 N (option C). The, the force acting on the satellite is: Therefore, the gravitational force exerted on the satellite by the planet is 5000 N (option C).

f

An influence that can alter an object's motion is called a force. A mass-containing object's velocity can change, or accelerate, as a result of a force. Intuitively, a push or a pull can also be used to describe force. Being a vector quantity, a force has both magnitude and direction. The rate at which an object's velocity with respect to time changes is called its acceleration. Vector quantities include accelerations. The direction of the net force acting on an object provides information about its acceleration.

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The tension must a rope withstand is 1296.42N

Given- Mass m=1054 kg

acceleration= 1.23 m/s²

To find Tension generated .

Principle -Tension is the reaction of the action applied that means due to application of mass along with acceleration there is a urge towards earth and to substantiate it or to form a couple the reaction occurred is tension that equalises the role of force,

Mathematically , Force = ma ⇒Tension

F=T

T=ma

Calculations & Answer - T= 1054 x 1.23

= 1296.42N

Since T=F so unit of force and tension will  be same.

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The electric field is radially outwards from positive charge and radially in towards negative point charge.

Any sort of charge causes an electric field to be associated to a location in space. The strength and direction of the electric field are expressed by the value of E, also referred to as the electric field strength, electric field intensity, or simply the electric field. The SI unit for the electrical field is volts per meter (V/m). This unit is equivalent to the Newtons per coulomb. Both Newton, which represents for force, and Coulomb, which stands for charge, are the ancestors of these units. These two are sometimes referred to as the sources of the field since they produce the magnetic field with moving charges (currents) and the electric field with stationary charges, respectively.

AV = EAX = (2.4*10N.X0.018) V/M

off = 432

N2V jk N.mm

1/2=12

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The voltage and current are related is to resistive circuit.

What is resistive circuit?

In a fully resistive circuit, current and voltage are in phase, and the power factor is 1. In a circuit where the current lags the voltage by 90 degrees, the power factor is zero trailing. The current leads the voltage in a completely capacitive circuit by 90 degrees, and the power factor is zero.

What is the relationship between the phases of voltage and current?

Current and voltage in a pure resistive circuit are in phase with one another. Thus, the peak values of both the current and the voltage will occur simultaneously.

Therefore, the phase angle between the voltage and the current is, capacitive circuit by 90 degrees, and the power factor is zero.

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A prize wheel is spinning in a vertical circle when an acceleration of 2.0 rad/s2 is applied to the edge of the wheel for 3.0 s. if the final velocity of the wheel was measured to be 9.0 rad/s, the initial velocity of the wheel will be  ω0 = 3 rad/s

time = 3 seconds

acceleration = 2 [tex]rad/s^{2}[/tex]

final velocity = 9.0 rad/s

initial velocity = ?

using

ω = ω0 + αt

9 = ω0  + 2 * 3

ω0 = 3 rad/s

The initial velocity of the wheel will be ω0 = 3 rad/s

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The kinetic energy will start dropping that is slows down , she keeps slowing down while the kinetic energy keeps decreasing with potential energy rising.

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