Which object has the greatest kinetic energy?

A. a truck with a mass of 3,500 kg moving at 30 m/s
B. a fast pitched baseball with a mass of .5 kg moving at 46.9 m/s
C. a locomotive engine with a mass of 205,000 kg moving 5 m/s
D. a person with a mass of 73 kg running 6 m/s

Answer:

Approximately [tex]2.05 \times 10^{8}\; {\rm m\cdot s^{-1}}[/tex].

Explanation:

The refractive index [tex]n[/tex] of a material is the ratio between the speed of light in vacuum [tex]c[/tex] and the speed of light [tex]v[/tex] in that material. In other words:

[tex]\begin{aligned}n &= \frac{c}{v}\end{aligned}[/tex].

The speed of light in vacuum is [tex]c \approx 3.00 \times 10^{8}\; {\rm m\cdot s^{-1}}[/tex].

It is given that the refractive index is [tex]n = 1.46[/tex]. Rearrange this equation to find [tex]v[/tex], the speed of light in this material:

[tex]\begin{aligned}v &= \frac{c}{n} \\ &\approx \frac{3.00 \times 10^{8}\; {\rm m\cdot s^{-1}}}{1.46} \approx 2.05 \times 10^{8}\; {\rm m\cdot s^{-1}}\end{aligned}[/tex].

Answer: 9.8 J

Explanation:

Since the gravitational potential energy of the object is mgh or mass*acceleration due to gravity*initial height, its [tex]U_{g}[/tex] is 9.8 J. Due to the Law of Conservation of Energy, its kinetic energy will also be 9.8 J. This can be seen in the equation [tex]KE_{i}+ PE_{i}= KE_{f} + PE_{f}[/tex]. Since there is no initial kinetic energy and no final potential energy, its initial potential energy is equal to its final kinetic energy.

The velocity of projection of a stone following projectile motion which is projected vertically upwards from the foot of a vertical cliff 28.8n high so as to just reach the top is 23.75 m/s

When something (a projectile) is launched towards the surface of the Earth and moves along a curved path only under the influence of gravity, it experiences projectile motion (in particular, the effects of air resistance are passive and assumed to be negligible). Galileo showed that although this curved path can also be a straight line when thrown immediately above, it is a parabola in this case.

Gravity is the sole force acting on the item that is mathematically relevant; it acts downward and accelerates the thing towards the mass of the Earth. Due to the object's inertia, the horizontal velocity component of its motion does not require any external force.

According to the equation,

H = [tex]\frac{u^{2} }{2g}[/tex]

where,

H is the maximum height,

u is the velocity of projection and,

g is the acceleration due to gravity.

substituting the values and solving for u,

velocity of projection = 23.75 m/s

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Answer:

Explanation:

The formula for kinetic energy is K = 1/2mv^2, where K is kinetic energy, m is mass, and v is velocity.

Substituting the given values:

K = 1/2(2.50 kg)(2.00 m/s)^2

K = 1/2(2.50 kg)(4.00 m^2/s^2)

K = 5.00 J

Therefore, the 2.50kg ball traveling at 2.00m/s has 5.00 J of kinetic energy.

The skater's linear momentum has a value of 640 kg/m/s. Kinetic energy of the skater is 5120 J. The skater needs to be subjected to a steady net horizontal force of 160 N in order to come to rest in 4.00 seconds.

The sum of the mass and the instantaneous speed determines the size of the momentum.

The following equations can be used to calculate the skater's linear momentum:

p = mv

p = (40.0 kg)(16.0 m/s) = 640 kg·m/s

As a result, the skater's linear momentum is 640 kg/m/s in magnitude.

B) The skater's kinetic energy is given by:

K = (1/2)mv^2

Substituting the given values, we get:

K = (1/2)(40.0 kg)(16.0 m/s)^2

= 5120 J

Therefore, the skater's kinetic energy is 5120 J.

C) We need to provide a steady net horizontal force that is opposite in direction and of similar size to the skater's starting momentum in order to bring the skater to rest in 4.00 seconds. Applying the average force equation:

F = Δp/Δt

F = (-640 kg·m/s)/(4.00 s) = -160 N

In order to bring the skater to rest in 4.00 seconds, a steady net horizontal force of 160 N must be delivered to her in the opposite direction of her beginning motion.

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Answer:

5000 km

Explanation:

Sure, to calculate the diameter of Vesta, we can use the fact that Vesta's diameter is equal to the diameter of Mercury, which is 5000 km.

Therefore, the diameter of Vesta is also 5000 km.

We can show the working by using the following formula:

Diameter of Vesta = Diameter of Mercury

Diameter of Vesta = 5000 km

If the object starts at position 12 on a horizontal line with a reference point of 0, then its initial position relative to the reference point is:

Initial position = Reference point + Object's position = 0 + 12 = 12

If the object then moves 14 units to the left, its new position relative to the reference point is:

New position = Initial position - Distance moved to the left = 12 - 14 = -2

Therefore, the position of the object is -2 units from the reference point, which means that it has moved 2 units to the left of the reference point.

A drawing of the electric field lines around a positive charge, then make a second drawing of the electric field lines around a negative charge is mentioned below.

What is electric field ?

According to mathematics, the electric field is described as a vector field that may be connected to each point in space and represents the force per unit charge that is applied to a positive test charge that is at rest at that location. Either the electric charge or time-varying magnetic fields can produce an electric field.

What is electric charge ?

The physical quality of matter—its electric charge—is what causes it to feel a force when exposed to an electromagnetic field. Protons and electrons, the two types of charge carriers, typically carry positive and negative electric charges. Charges moving through a system produce energy.

Therefore, A drawing of the electric field lines around a positive charge, then make a second drawing of the electric field lines around a negative charge is mentioned above.

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Answer:

B. 1/2mv^2 + 1/2Iw^2

Explanation:

1) The total resistance is 2 ohms

The current is 4 A

In a parallel circuit, the total resistance (R_total) of the circuit is less than the resistance of any individual resistor in the circuit. This is because in a parallel circuit, each resistor provides a separate path for current to flow from the power source to the load, and the overall resistance of the circuit is reduced due to the increased number of paths.

For the resistors in parallel;

1/RT = 1/3 + 1/6

Rt = 2 ohms

In the 3 ohm resistor;

Current = 12 V/3 Ohm

= 4 A

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When current flows through a coil of wire, it generates a magnetic field. The direction of the magnetic field can be determined using the right-hand rule. If you point your right thumb in the direction of the current flow, your fingers will curl in the direction of the magnetic field.

In this case, the current is flowing in an anticlockwise sense when viewed from above. Using the right-hand rule, the direction of the magnetic field inside the coil can be determined to be perpendicular to the plane of the coil, and in a clockwise direction when viewed from above.

The diagram below shows the coil of wire lying flat on a horizontal surface with the direction of the magnetic field labelled:

        +-----+-----+-----+-----+-----+

        |                                 |

        |                                 |

        |                                 |

        +    X                    X    +

        |                                 |

        |                                 |

        |                                 |

        +-----+-----+-----+-----+-----+

Therefore, In this diagram, the X's represent the direction of the magnetic field lines inside the coil. As you can see, the magnetic field lines are oriented perpendicular to the plane of the coil and in a clockwise direction when viewed from above.

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0.16*10^-3m is the distance between two charges according to Coulomb's Law

How does Coulomb's law work?

Coulomb listed the following characteristics of the electric field for charges in a resting state: Unlike charges draw each other while like charges repel one another. As a result, a positive charge pulls a negative charge toward it while two negative charges resist one another.

We can determine the electric force produced between two electrical charges using Coulomb's Law. In particular, it enables the determination of the direction and strength of electric energy. Coulomb's law states that the force of attraction or repulsion between two charged bodies is inversely proportional to the cube of the distance between them and directly proportional to the product of their charges. It operates on the segment connecting the two charges regarded as point charges.

F = kq1q2/r^2

460 = 9*10^9 *2.8*10^-5 *3.1*10^-7 / r^2

r = sqrt ( 9*10^9 *2.8*10^-5 *3.1*10^-7 / 460)

r = 0.16*10^-3m

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California has an abundance of gold due to tectonic plate movement. Global factors acting over tens of millions of years led to the concentration of gold in California, United States.

Although there are numerous places in California where gold may be discovered, the eastern and central parts of Sierra Nevada include the most fruitful zones. The major deposits, which are linked to the intrusion of a Sierra Nevada batholith, typically consist of gem veins in metamorphic rocks.

Earth's core was created as molten steel sank to the planet's center during its creation. The great bulk of the earth's natural precious metals, including gold and platinum, were carried away by this. In truth, there are sufficient.

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The surface area of the 8 new cubes would be 96 cm².

Surface area is the total area of the exposed surface of a three-dimensional object, such as a cube, cylinder, or sphere. It is measured in square units, such as square inches, square feet, or square meters. Surface area is an important concept in geometry, trigonometry, and calculus. It is used in many areas of science, such as chemistry, physics, and engineering. Surface area is also important in everyday life, from home construction and remodeling to sports and recreation. For example, it is used to calculate the size of an area needed to paint a room, the amount of material needed to cover a swimming pool, or the dimensions of a soccer field.


This is because the surface area of a cube is equal to 6 times the length of one side of the cube squared. In this example, the length of one side of the 8 cubes is equal to 4 cm divided by 2 (since the cube was broken down into 8 cubes), which is equal to 2 cm. Therefore, the surface area of each of the 8 cubes would be 6 times 2 cm squared, which is equal to 12 cm².and the total surface area of the 8 cubes would be 12 cm^2 multiplied by 8, which is equal to 96 cm².

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Answer:

Explanation:

a) transverse

b)longitudinal waves

The real cubic expansivity of the liquid is 1.98 x 10^-4 K^-1.

To find the real cubic expansivity of the liquid, we need to use the formula:

β = (1/V) (dV/dT)

where β is the real cubic expansivity, V is the volume of the liquid, and dV/dT is the rate of change of the volume with respect to temperature. We can use the fact that the two samples have the same volume to eliminate V from the equation.

The change in mass of the liquid between 0°C and 50°C is:

Δm = 44.25 g - 42.02 g = 2.23 g

To convert the change in mass to a change in volume, we need to divide by the density of the liquid:

ρ = m/V

V = m/ρ

We can use the density of the liquid at 0°C to calculate the volume:

V = 2.23 g / (density of liquid at 0°C)

Next, we can use the volume and temperature data to find the rate of change of the volume with respect to temperature:

dV/dT = (V2 - V1) / (T2 - T1)

dV/dT = (V(50°C) - V(0°C)) / (50°C - 0°C)

Finally, we can substitute these values into the formula for β:

β = (1/V) (dV/dT)

β = (1/[(2.23 g) / (density of liquid at 0°C)]) [(V(50°C) - V(0°C)) / (50°C - 0°C)]

Simplifying this expression gives:

β = (density of liquid at 0°C) [(V(50°C) - V(0°C)) / (50°C - 0°C)] / 2.23 g

We can estimate the density of the liquid at 0°C using the mass and volume data:

density of liquid at 0°C = 44.25 g / V(0°C)

Substituting this into the expression for β gives:

β = [(44.25 g / V(0°C))] [(V(50°C) - V(0°C)) / (50°C - 0°C)] / 2.23 g

Simplifying this expression gives:

β = (V(50°C) - V(0°C)) / (50°C - 0°C) / V(0°C) x 44.25/2.23

β = (V(50°C) - V(0°C)) / (50°C x V(0°C)) x 19.8

We can estimate the change in volume using the linear expansivity of the glass:

ΔV = V(50°C) - V(0°C) = V(0°C) α ΔT

ΔV = V(0°C) (1.0 x 10^-5 K^-1) (50°C)

Substituting this into the expression for β gives:

β = [V(0°C) (1.0 x 10^-5 K^-1) (50°C)] / (50°C x V(0°C)) x 19.8

β = 1.0 x 10^-5 K^-1 x 19.8

β = 1.98 x 10^-4 K^-1

Therefore, the real cubic expansivity of the liquid is 1.98 x 10^-4 K^-1 using linear expansivity.

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The stream's velocity is 1.75 metres per second, and the discharge is 16.8 cubic metres per second.

Discharge has units of feet3/sec or cubic ft per second if length and duration are measured in feet and seconds, respectively (cfs). The cross-sectional area is calculated as Depth times Width. Due to the velocity reduction caused by friction at the channel's edges, the channel's form is crucial.

The cross-sectional area of the stream must be multiplied by the stream velocity in order to determine discharge.

The cross-sectional area of the image is:

A = (8 m) x (1.2 m) = 9.6 m²

1.75 metres per second is listed as the stream velocity.

So the discharge Q is:

Q = A x V

= (9.6 m²) x (1.75 m/s)

= 16.8 m³/s.

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Answer: The direct way that children affect their own acculturation is by peer watching and engagement.

Answer:One direct way in which children impact their own acculturation is through language acquisition. Children who are exposed to a new culture and language at a young age have the opportunity to learn and adopt the new language and cultural norms more easily than adults. As children interact with peers and adults in the new culture and use the new language, they develop their own sense of identity and acculturation, which can be different from that of their parents or other family members. Children may also participate in cultural activities or events, such as holidays or festivals, which further shape their understanding and experience of the new culture. Overall, children can actively participate in and shape their own acculturation process through language acquisition and cultural experiences.

Explanation:

Answer:

The wavelength of the photon can be calculated using the equation E = hc/λ, where E is the energy, h is Planck's constant (6.626 ✕ 10^−34 J s), c is the speed of light (2.998 ✕ 10^8 m/s), and λ is the wavelength.

λ = hc/E = (6.626 ✕ 10^−34 J s) (2.998 ✕ 10^8 m/s) / (3.02 ✕ 10^−19 J) = 656.4 nm

Explanation:

Answer: Both Chemical and physical changes can be measured, chemical changes can be caused by oxygen since its very reactive. Physical Change: There is no addition or deduction of energy during the physical change, but the energy required for completion of change is released when the change is reversed. Chemical Change: Energy like light, pressure, heat energy is required for chemical changes. When physical or chemical changes occur, they are generally accompanied by a transfer of energy. The law of conservation of energy states that in any physical or chemical process, energy is neither created nor destroyed.

Explanation:

Answer:

Explanation:

From  Law of conservation of momentum,

m1u1+m2u2 = m1v1+m2v2 [Law of conservation of momentum]

m1 = 2600kg

u1 = 15m/s

m2 = 1300kg

u2 = -20m/s  [as it is moving in opposite direction]

here, after impact, cars lock with each other so v (final velocity) is the same for both cars, i.e., v1 = v2

(2600)(15)+(1300)(-20) = (2600)v1+(1300)v2

39000-26000 = (2600+1300)v1  [as v1 = v2]

v1 = 13000/3900

v1 = 3.33 m/s

Here, m1v1 = 2600x3.33 = 8658kgm/s

m2v2 = 1300x3.33 = 4329kgm/s

As final momentum of car 1 is higher than that of car 2, both cars will move in direction of car1, that is, west direction.

The capacitor can be used in various home appliances like ceiling fan, electric motor, etc. The total capacitance by connecting a 5.04 µf and 8.02 µf capacitor together in parallel is  13.06 µf.

A two terminal electrical device which is used to store energy in the form of an electric charge is defined as the capacitor. It contains two electrical conductors separated by a distance.

When two capacitors are connected in parallel, then the total capacitance is given as:

C total = C₁ + C₂

C total = 5.04 µf + 8.02 µf

C total = 13.06 µf

Thus the total capacitance is 13.06 µf.

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This may involve carefully measuring and recording the initial and final energies of the system, controlling for external factors such as friction and air resistance, and using appropriate instruments and equipment with minimal energy loss.

What is Energy?

It is a scalar quantity that can be transferred between objects or converted into different forms, such as kinetic, potential, thermal, or electrical energy. Energy cannot be created or destroyed, but it can be transformed from one form to another. The SI unit of energy is the joule (J), but other units such as calories, electronvolts, or British thermal units (BTU) are also commonly used depending on the context. Energy is a fundamental concept in physics and plays a crucial role in many fields, including mechanics, thermodynamics, chemistry, and astronomy.

It is also important to follow the experimental procedure carefully and consistently to ensure that the results are reproducible and consistent. This may involve controlling for variables such as the angle of release, the height of the release, and the distance traveled by the object.

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The radius of a water droplet suspended in an electric field can be calculated using the following formula:

r = (3qE/4πρg)^(1/2)

where r is the radius of the droplet, q is the charge on the droplet, E is the strength of the electric field, ρ is the density of the droplet material (assumed to be that of water, which is 1000 kg/m^3), and g is the acceleration due to gravity.

In this case, q = -1.602 × 10^-19 C (the charge on an electron), E = 300 V/m, ρ = 1000 kg/m^3, and g = 9.81 m/s^2.

Plugging in these values, we get:

r = (3(-1.602 × 10^-19 C)(300 V/m)/(4π(1000 kg/m^3)(9.81 m/s^2)))^(1/2)

= 1.83 × 10^-5 m

Therefore, the radius of the water droplet is approximately 1.83 × 10^-5 meters.

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Revolutions per minute are needed for the space station which is at 385m from center of the planet is 1.52 rev/min

Orbital velocity is also called as critical velocity. It is minimum velocity must be given to the satellite or the body, so that it can revolve around the planet. i.e. orbital velocity is minimum velocity of body to revolve in stable orbit around a planet.

Orbital velocity is given by,

[tex]v_{c} = \sqrt{\frac{GM}{R+h}}[/tex] where  G = Gravitational constant (6.673×10⁻¹¹ Nm²/kg²

                               M = Mass of the planet

                               R = Radius of the planet

                                h = height of the object(satellite)

Orbital velocity depends on mass of the planet, radius of the planet and height of the object(satellite). It is independent of mass of the body(satellite).

Given,

Diameter of space station, D = 770m {Radius (R+h) = 385m}

Acceleration due to gravity [tex]g_{h}[/tex]= 9.8 m/s²

our given equation is,

[tex]v_{c} = \sqrt{\frac{GM}{R+h}}[/tex]

[tex]v_{c}^{2} = \frac{GM}{R+h}}[/tex].........1)

we know that v=rω

v²=r²ω²

where r = (R+h) = Radius of planet + height of space station from surface of the planet.

v²=(R+h)²ω²......2)

with equation 2), equation 1 becomes.

(R+h)²ω² = [tex]\frac{GM}{R+h}}[/tex]

ω² = GM÷ (R+h)³.............3)

we know that [tex]g_{h} = \frac{GM}{(R+h)^{2} }[/tex].....4)

equ 3 becomes,

ω² = [tex]\frac{g_{h}}{(R+h)}[/tex]

Putting all values in equation,

ω² = 9.8 ÷ 385

ω² = 0.025454

ω = 0.1595 ≅ 0.16 rad/s

let,

ω = 2πn

n= ω ÷ 2π

n = 0.02547 rev/s

n= 0.02547*60 = 1.52 rev/min

Hence 1.52 rev/min is needed for space station at artificial gravity of 9.8 m/s

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Answer:

If the natural abundance of boron-11 is 80.1%, then the natural abundance of boron-10, the other stable isotope of boron, is 100% - 80.1% = 19.9%.

To determine how many of the 7,000 boron atoms are the boron-11 isotope, we can use the following steps:

Calculate the number of boron-10 atoms:

19.9% x 7,000 = 1,393

Calculate the number of boron-11 atoms:

80.1% x 7,000 = 5,607

Therefore, out of 7,000 boron atoms, 5,607 are the boron-11 isotope.

Explanation: