1. A bullet of mass 0.02-kg is shot horizontally into a wooden log, striking it with a
velocity of 200
a) If it penetrates 4-cm before stopping, what is the stopping
force i.e friction force? (work = change in kinetic energy)
b) What is the acceleration of the bullet while slowing in the log.
c) How long does it take for the bullet to stop?

every atom has at least one free electron.

Because the free electrons in metals are not bound to the atoms, they are free to flow between the atoms.

Due to the size of metals' lattice structures, there are many electrostatic forces.

The size of broken is enormous.

because the delocalized electrons in them cause the metal to conduct electrical charge.

related to its temperature

Iron 9.70×10−8 1.03×107

Because at least one electron per atom is free, metals are effective heat and electricity conductors.

Free electrons that are not bound to the atoms exist in metals. These electrons are unrestricted in the metal, interacting with the metal atoms to effectively transmit heat to them. As a result, metals are superior heat conductors than the majority of other materials.

By allowing free electrons to travel between the atoms, metals conduct electricity.

Metals have high melting and boiling temperatures because they have massive lattice structures and must break a huge number of electrostatic forces.

Because of their delocalized electrons, which transmit electrical charge through the metal, metals are electrical conductors, and their structure and bonding explains these characteristics.

According to the Wiedemann-Franz law, a metal's temperature directly affects how much thermal conductivity there is compared to electrical conductivity.

These eight electrons are the reason why iron metal has a high electrical conductivity.

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Answer:

Explanation:

momentum of sedan of 1600 kg = 1600x v , where v is its velocity

momentum of suv of 2300 kg = 2300 x u where u is its velocity .

force of friction = ( 1600 + 2300 ) x 9.8 x  .75 ( fiction = μ mg )

= 28665 N

distance by which friction acted = √ (5.54² + 6.19²)

= 8.3 m

work done by friction

= 28665 x 8.3

= 237919.5 J

Total kinetic energy of cars = work done by friction

1/2 x 1600 x v² + 1/2 x 2300 u² = 237919.5

16 v² + 23 u² = 4758.4

1600 x v / 2300 u = 6.19 / 5.54

v / u = 1.6

v = 1.6 u

putting this equation in fist equation

40.96 u² + 23 u² = 4758.4

= 63.96 u² = 4758.4

u² = 74.4

u = 8.62 m /s

v = 13.8  m /s

Answer:

The new charge is \(k = 2 Q\)

Explanation:

From the question we are told that

The initial charge of the first one is \(+Q\)

The charge on the sphere closest to the rod is \(-Q\)

Generally at the point the charge was redistributed the charge on each sphere is \(+ \frac{Q}{2}\)

Also from the question we are told that the new charge on one of the sphere is -Q

So this mean that

\(\frac{ Q}{2} + \frac{Q}{2} = -Q + k\)

Here k is the charge on the other sphere

=>      \(k =  2 Q\)

Answer:

convection currents

Explanation:

The volume in mL is 11.62 ml.

We know that V = M/d

V = 50/4.3=11.62 ml.

The relationship between mass and volume can be easily determined using density; for example, the mass of a body is equal to its volume multiplied by the density (M = Vd), whereas the volume is equal to the mass divided by the density (V = M/d).

Density is the mass of a material substance per unit volume. d = M/V, where d is density, M is mass, and V is volume, is the formula for density. Grams per cubic centimeter are a typical unit of measurement for density. For instance, while Earth has a density of 5.51 grams per cubic centimeter, water has a density of 1 grams per cubic centimeter. Another way to state density is in kilograms per cubic meter (in metre-kilogram-second or SI units). For instance, air weighs 1.2 pounds per cubic metre. In textbooks and manuals, the densities of typical solids, liquids, and gases are stated.

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In a tractor pull, a tractor put 250,000 J of work into pulling a large mass. The tractor pulls the mass using 98,000N of force. The tractor pulled the mass to a distance of 2.55 meters

We may use the work done formula to solve this problem:

Work = Force  x Distance x Cosine (angle between force and displacement)

Yet, because the force and displacement are applied in the same direction, the angle between them is zero, and the cosine of zero is one. As a result, we may reduce the formula to:

Work = Force x Distance

Because we know the work done is 250,000 J and the force exerted is 98,000 N, we can rewrite the formula to solve for distance:

Distance = Work / Force

Distance = 250,000 J / 98,000 N

Distance = 2.55 meters

As a result, The tractor pulled the mass to a distance of 2.55 meters

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The running of a clock at the top of a tower at the equator would be predicted by special relativity to be slow, and by general relativity to be fast.

The equator, which separates Earth's Northern and Southern hemispheres, is a circle of latitude with a radius of around 40,075 kilometers (24,901 mi). Halfway between the North and South poles, at 0 degrees latitude, is a fictitious line. Any other roughly spherical celestial body can likewise be referred to by this name.

The equator of a spinning spheroid, such as a planet, is the parallel (circle of latitude) where latitude is defined to be 0° in astronomical (3D) spatial geometry. It is a fictitious line that divides the spheroid into its northern and southern hemispheres and runs parallel to its poles. It is, in other words, the point at which the spheroid intersects the plane that is perpendicular to its axis of rotation.

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Answer:

Explanation:

Option C. The heat absorbed or lost by a substance while it's changing state  correctly describes latent heat

Latent heat is the heat absorbed or lost by a substance while it is changing state.

The latent heat is a type of heat that is transferred during phase change, i.e., while a substance undergoes a change of state.

For example, when ice melts into liquid water, or when liquid water evaporates into water vapor, heat is absorbed from the surroundings.

Latent heat is not associated with a temperature change; rather, it's associated with a change of state.

For instance, the temperature of water remains at 100°C while boiling.

When water is boiling, the latent heat of vaporization is absorbed and utilized to break the hydrogen bonds holding water molecules together to change water from the liquid phase to the gaseous phase.

When the water is boiling, adding more heat won't increase the water's temperature, instead, the extra heat will be absorbed to change the phase of water molecules.

Therefore, the correct answer to the given question is option C: The heat absorbed or lost by a substance while it is changing state.

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Answer:

3.3 rad/sec.

Explanation:

The term '' average angular velocity'' can be defined as the rate at which the angular velocity changes. Kindly note that the rate in which the angular velocity changes is in radian per seconds[rad/sec]. So, without mincing words let's dive straight into the solution to the question above.

The radius of the blowing ball = 12cm, the initial angular velocity = 5.0 rad/s, the final angular velocity =  1.5 rad/s and the angle of rotation = 5.5 radians.

Therefore, from the definition of average angular velocity given above, the mathematical representation can be written as given below:

The average angular velocity  = [ the  initial angular velocity] + [the final angular velocity] / 2.

Thus, the average angular velocity = [ 5.0 rad/s + 1.5 rad/s] / 2 = 3.3 rad/s.

Before she jumped from the cliff, her gravitational potential energy was

GPE = (her weight) x (height of the cliff) .

That's exactly the GPE that she lost on the way down to the water.  So we can write

24,500 J = (her weight) x (44.0 m)

Divide each side by 44.0 m:

Her weight = 24,500 J / 44 m

Her weight = 556.8 Newtons

(about 125 pounds)

From conservation of linear momentum, the final velocity is 15.7 m/s and the time taken is 1.6 s

Velocity can be defined as a distance travel in a specific direction per time taken. It is a vector quantity.

Given that 30kg metal ball is dropped from a height of 12.5 m.  

a.  Find the final velocity when the ball  hits the ground.

The maximum K.E of the ball at it final velocity will be equal to its maximum P.E at height 12.5 m. That is,

K.E = P.E

1/2mv² = mgh

Where

Substitute all the parameters

1/2 × 30 × v² = 30 × 9.8 × 12.5

v² = 245

v = √245

v = 15.65 m/s

b. The time it takes for the ball to hit the ground can be found through

h = ut + 1/2gt²

but u = 0

h = 1/2gt²

Substitute all the necessary parameters

12.5 = 1/2 × 9.8 × t²

12.5 = 4.9t²

t² = 12.5/4.9

t² = 2.55

t = √2.55

t = 1.6 s

Therefore, the final velocity when the ball hits the ground is 15.65 m/s and the time it takes for the ball to hit the ground is 1.6 s

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Answer:

The spheres do not move.

Explanation:

Both spheres start neutral, meaning they have an equal number of positive and negative words.

The spheres are metal, so they are conductors. When the positively-charged rod touches sphere A, the negative charges in both spheres are attracted towards the rod, and the positive charges in both spheres are repelled away.

When the rod is removed, sphere A will have a negative charge, and sphere B will have a positive charge. The electrostatic force will pull the spheres together. Since they are already touching, the spheres will not move.

The weight of the elephant is approximately 19,780.2 Newtons, calculated by multiplying its mass (2019 kg) by the acceleration due to gravity (9.8 m/s²).

To calculate the weight of the elephant in Newtons, we need to use the formula:

Weight = Mass x Acceleration due to gravity

Given that the mass of the elephant is 2019 kg and the acceleration due to gravity is 9.8 m/s^2, we can substitute these values into the formula:

Weight = 2019 kg x 9.8 m/s^2

By multiplying these values, we find that the weight of the elephant is approximately 19,780.2 Newtons.

The weight of an object is the force with which it is attracted towards the center of the Earth due to gravity. The unit of weight is Newtons, and it represents the force required to support the object against gravity. In this case, the weight of the elephant tells us the force exerted by the Earth on the elephant, and it is approximately 19,780.2 Newtons.

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8.27 x 1013 meres is the orbital radius.

Jupiter's mass, 1.9 x 1027 kg, and the time interval, 16.9 days, are equal to 1.46 x 106 seconds. The radius is needed, thus r. Solution

The moon must be held in its orbit by a gravitational force equal to the centripetal force between Jupiter and the moon.

6.67 x 10⁻¹¹ N/m²kg

2 x 1.9 x 10/27 x 1.46 x 10'6 / 4 r = 6.85 x 102'7 G = 6.67 x 10'11 N/m2kg2 r = 8.27 x 10'7

The second-largest moon in Jupiter's orbit and the third-largest moon in the solar system is called Callisto. Of all the objects in our solar system, its surface has the most craters.

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20Kg x 1000g x 1 Equals 20000 gram of water. 10 000 gram times a temperature range of 40 to 80 is 12000 calories. 5023200 joules are equal to 10,000 gram times 4.186 joules at 40 or 80 degrees.

kilojoules (kJ), energy. A equation E Equals mc2, were E is already in joules, m is now in kilogrammes, and c seems to be the light speed in metres per second, can be used to recall the base unit conversion. To view the outcomes displayed in the table, enter the quantity of kJ you wish to convert into the text box.

Heat has kJ of energy (or BTU). The quantity of heat transmitted per unit of time is known as the rate of heat transfer. Heat has a magnitude, a direction, and an action point because it is a direction (or vector) quantity. Heat transmission quantity is noted as Q (kJ).

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Answer:

Both of these minerals precipitate from water as a chemical sediment. Both minerals are used commercially.

Explanation:

Given,

The mass of the bike and the rider, m=62 kg

The initial velocity of the bike and the rider, u=4 m/s

The final velocity of the bike and the rider, v=14 m/s

The work done in accelerating an object from its initial velocity to its final velocity is given by the change in its initial and final kinetic energy.

Therefore the work done by the rider is,

On substituting the known values,

Therefore the work done by the rider is 5580 J

Answer:

Kinetic and potential

potential (didnt say its moving)

Kinetic and potential

kinetic

kinetic

kinetic

potential

kinetic and potential

kinetic (might have potential)

kinetic

The kinetic energy of the bullet will be 24.5 Joules and the average stopping force will be 490 Newtons.

The kinetic energy of an object is the energy present in an object due to the motion of object. Kinetic energy is directly proportional to the mass and velocity of the object. Kinetic energy can be converted into potential energy when an object comes at rest.

KE = 1/2 mv²

KE = 1/2 × 0.01 × 70 (10 g = 10/1000 = 0.01 kg)

KE = 24.5 J

Now, work done in stopping the bullet must be 24.5J

W = F × s

24.5 = F × 5/100

F = 490 N

Therefore, the average stopping force will be 490 N.

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Answer:

B - to the right

Explanation:

Since the team on the right pulls with greater force than the team to the left, the rope will move to the right.

Answer:

The complete question is

NASA is giving serious consideration to the concept of solar sailing. A solar sailcraft uses a large, low-mass sail and the energy and momentum of sunlight for propulsion. (a) Should the sail be absorbing or reflective? Why? (b) The total power output of the sun is 3.9 x 10^26  W. How large a sail is necessary to propel a 10,000-kg spacecraft against the gravitational force of the sun? Express your result in square kilometers. (c) Explain why your answer to part (b) is independent of the distance from the sun.

a) The sail should be reflective because, an incident electromagnetic wave, in this case, light wave, impacts twice the energy density on a reflective sail, and hence twice the force on a totally reflective sail as would be impacted on a sail that is totally absorbing.

For totally reflective, F = (2I/c)A    ....1

for totally reflective, F = (I/c)A       ....2

where I is the intensity of the light

c is the speed of light = 3 x 10^8 m/s

A is the area the sail

b) The intensity of the light from the sun = power/area

==> I = \(\frac{3.9*10^{26}}{4\pi r^{2} }\)

where r is the distance from the sun and the sail

The Force from the sail from equation 1  is therefore

\(F\) = \(\frac{2*3.9*10^{26}*A}{4\pi r^{2} *3*10^{8}}\) = \(2.069*10^{17}\frac{A}{r^{2}}\)

gravitational force between the sail and the sun \(F_{g}\) = \(\frac{GMm}{r^{2}}\)

where

G is the gravitational constant = 6.67 x 10^−11 m^3⋅s−2⋅kg−1.

m is the mass of the sail = 10000 kg

M is the mass of the sun = 1.99 x 10^30 kg.

==> \(F_{g}\) = \(\frac{6.67*10^{-11}*1.99*10^{30}*10000}{r^{2}}\) = \(\frac{1.33*10^{24}}{r^{2}}\)

Equating the forces, we have

\(2.069*10^{17}\frac{A}{r^{2}}\)  =  \(\frac{1.33*10^{24}}{r^{2}}\)

the distance cancels out

A = (1.33 x 10^24)/(2.069 x 10^17) = 6428226.196 m^2

==> 6428.2 km^2

c) The force of the solar radiation is proportional to the intensity of the sun from the light, and the intensity is inversely proportional to the square of the distance from the source. Also, the force of gravitation  is inversely proportional to the square of the distance, so they both cancel out.

The kinetic energy of the flywheel after 1 minute of rotation, given that it has a mass of 50 and radius of 40 cm is 32.4 KJ (Option D)

We'll begin by obtaining the velocity of the flywheel. This is shown below:

v = at

v = 0.6 × 60

v = 36 m/s

Finally, we shall determine the kinetic energy of the flywheel. Details below:

KE = ½mv²

KE = ½ × 50 × 36²

KE = 25 × 1296

KE = 32400 J

Divide by 1000 to express in KJ

KE = 32400 / 1000

KE = 32.4 KJ

Thus, the kinetic energy is 32.4 KJ (Option D)

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Answer:

Explanation:

temperature is a scalar quantity

The charge of the particle on the aluminum rod is 9.26 x 10^-6 C.

When a charged particle moves through a magnetic field, it experiences a force known as the Lorentz force. The Lorentz force is given by the equation F = qvBsinθ, where F is the force, q is the charge of the particle, v is the velocity of the particle, B is the magnetic field strength, and θ is the angle between the velocity vector and the magnetic field vector.

In this scenario, an aluminum rod with a mass of 0.946 g is passed between the poles of a 0.41-T permanent magnet at a speed of 4.05 m/s at a 90o angle. Since aluminum is a conductor, it is expected that electrons in the metal will be free to move, allowing for a current to flow through the rod.

We can calculate the charge of the particle by using the equation F = ma, where F is the Lorentz force, m is the mass of the particle, and a is the acceleration of the particle.

The acceleration of the aluminum rod can be calculated using the equation a = F/m. Since the rod is moving at a constant velocity, the force due to air resistance can be ignored. Therefore, the force acting on the rod is solely due to the Lorentz force. Thus, we can write: a = F/m = qvBsinθ/m, Solving for q, we get: q = ma/vBsinθ = (0.946 x 10^-3 kg x 4.05 m/s)/(0.41 T x sin90o) = 9.26 x 10^-6 C.

Therefore, the charge of the particle on the aluminum rod is 9.26 x 10^-6 C.

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Answer:

Current = 5.45amps

Power = 654 watts

Explanation:

E =120V

I =?

R = 22.02 Ohms

I= E/R

I= 120/22.02

I = 5.45AmPs

P = ?                    P= E x R

E = 120V              P= 120x5.45

I = 5.45 AmPs      P=  654W