How much would a spring scale with a spring constant of 120 N/m stretch if it had 3.75 J of work done on it?

The final velocity of the ball 2 if the collision is perfectly elastic is 5.87 m/s.

The final velocity of the ball 2 if the collision is perfectly elastic  7.12 m/s.

The final velocity of the ball 1 if the collision is perfectly inelastic 4.4 m/s

The final velocity of the ball 2 if the collision is perfectly inelastic 4.4 m/s

Momentum is defined as product of mass and velocity of the body. It is denoted by letter p and it is expressed in kg.m/s. Mathematically p = mv. it discuss the moment of the body. body having zero mass or velocity has zero momentum. The dimensions of the momentum is [M¹ L¹ T⁻¹].

according to conservation law of momentum,

momentum before collision is equal to momentum after collision.

for elastic collision,

m₁v₁ +m₂v₂ = m₁v₁' + m₂v₂'

for inelastic collision,

m₁v₁ +m₂v₂ = (m₁+ m₂)v

where,

mass of the ball 1 m₁ = 110g = 0.11 kg

mass of the ball 2 m₂ = 340 g = 0.34kg

initial velocity of ball 1 v₁ = 15 m/s

initial velocity of ball 2 v₂ = 0 m/s

final velocity of ball 1 v₁' = ?

final velocity of ball 2 v₂' = ?

velocity of both ball v = ?

for elastic collision,

m₁v₁ +m₂v₂ = m₁v₁' + m₂v₂'

putting all the values,

0.11× 15 = 0.11v₁' + 0.34v₂'

1.65 = 0.11v₁' + 0.34v₂' _______1)

According to conservation energy in elastic collision,

1/2m₁v₁² + 1/2m₂v₂² = 1/2m₁v₁'² + 1/2m₂v₂'²

1/2×0.11×15² = 1/2×0.11×v₁'² + 1/2×0.34×v₂'²

12.37 = 0.055×v₁'² + 0.17×v₂'²______2)

Solving this simultaneous equation we get,

v₁' = 5.87 m/s

v₂'= 7.12 m/s

for inelastic collision,

m₁v₁ +m₂v₂ = (m₁+ m₂)v

0.11×18 + 0 = (0.11 + 0.34 )v

v = 4.4 m/s

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The total resistance in the circuit is 30 ohms. Option d is correct.

In an electric circuit, resistors can be connected in different ways, such as in series or parallel. When resistors are connected in series, the total resistance is equal to the sum of the individual resistances. This is because the same current flows through each resistor, and the total voltage across the resistors is divided among them.

The resistances in series is the sum of all resistances. The three resistances are, 10 ohms, 15 ohms and 5 ohms. Therefore,

Total Resistance = 10 ohms + 15 ohms + 5 ohms = 30 ohms.

Hence, option d is correct.

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An astronaut measure the period of a mass spring system on Earth.

The period of a mass spring system on the moon would be longer than the period on Earth. This is because the period of a mass spring system is dependent on the square root of the ratio of the mass to the spring constant, and the acceleration due to gravity. Since the acceleration due to gravity on the moon is only 1/6th of that on Earth, the restoring force on the mass will be weaker, resulting in a longer period. Therefore, the astronaut would measure a longer period for the same mass spring system on the moon than on Earth.

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The charge required for the fixed point charge is approximately [tex]4.8032 * 10^{-10} C[/tex].

The electrostatic force between the fixed point charge and the electron is equal in magnitude to the gravitational force between the electron and the Earth, so we can set these two forces equal to each other and solve for the charge of the fixed point charge.

Electrostatic force between two point charges is given by Coulomb's law:

[tex]F = k * q1 * q2 / r^2[/tex]

The gravitational force between two masses is given by Newton's law of gravitation:

[tex]F = G * m1 * m2 / r^2[/tex]

Setting these two forces equal to each other and solving for q2, we get:

[tex]k * q1 * q2 / r^2 = G * m_e * m\_earth / r^2[/tex]

Solving for q2, we get:

[tex]q2 = G * m_e * m\_earth / k[/tex]

Substituting the given values, we get:

[tex]q2 = (6.67430 * 10^{-11} N * m^2 / kg^2) *\\ (9.10938356 *10^{-31} kg) *\\ (5.9722 *10^{24} kg) / (8.98755 * 10^9 N * m^2 / C^2)[/tex]

[tex]q2 = 4.8032 * 10^{-10} C[/tex]

Therefore, the charge required for the fixed point charge is approximately [tex]4.8032 * 10^{-10}[/tex]C.

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The student measured the length of a wire four times and the total length from the reading is 18.55 m.

From the given,

The length of the wire measured by the student using a meter rule is :

l₁ = 18.6 m

l₂ = 18.5m

l₃ = 18.6m

l₄ = 18.5 m

The total length of the wire is obtained from the average values of length.

Total length (L) = (l₁ + l₂ + l₃ + l₄)/4

                     L  = (18.6 + 18.5 + 18.6 + 18.5) / 4

                         = 74.2 /4

                         = 18.55

Hence, the actual length of the wire = 18.6 m.

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Answer: B

Explanation:

A student creates a dichotomous key to identify common household pets. The wrong  key is option  C. A pet can have a hairy body and live in a cage, or can be hairless and not live in a cage.

A dichotomous key is an instrument utilized for the classification and identification of living organisms by examining their visible traits. It is comprised of a sequence of decisions or actions which guide the user towards accurately identifying the organism.

Every decision or move involves selecting between two alternative options or features that are contradictory to each other. Furthermore, the correct answer identified as option C acknowledges that pets can possess different traits and may not necessarily conform to a specific classification.

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The diagram to show behavior of magnetic poles is given.

Magnetic poles can be either north or south. Opposite magnetic poles (i.e., north and south) attract each other, while like magnetic poles (i.e., north and north, or south and south) repel each other. This behavior is due to the alignment of the magnetic fields around the poles.

The strongest part of a magnet's magnetic field is at the poles, while the weakest part is at the sides. Magnetic field lines flow out of the north pole and into the south pole, forming a loop around the magnet. The closer the field lines are to each other, the stronger the magnetic field is in that region.

Overall, this behavior of magnetic poles is a result of the interaction of magnetic fields, and is essential to many technological applications of magnets, such as in electric motors and generators.

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The child's speed at the lowest point is 5.42 m/s.

At the highest point of the swing, the child is momentarily at rest and has only potential energy. At the lowest point, the child has only kinetic energy.

Using the conservation of mechanical energy, we can write:

Potential energy at highest point = Kinetic energy at lowest point

mgh = (1/2)mv²

where m is the mass of the child, g is the acceleration due to gravity, h is the height of the swing at the highest point, and v is the speed of the child at the lowest point.

First, we need to find the height of the swing at the highest point. Since the swing is supported by two chains, the height of the swing at the highest point is half the length of the chains:

h = (1/2)3.00 m = 1.50 m

Next, we can solve for the child's speed at the lowest point:

mgh = (1/2)mv²

40.0 kg * 9.81 m/s² * 1.50 m = (1/2) * 40.0 kg * v²

588 J = 20.0 kg * v²

v² = 29.4 m²/s²

v = 5.42 m/s

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a) The order in which the objects reach the bottom of the slope depends on their moments of inertia, b) All three shapes will reach the bottom of the slope in approximately the same amount of time, which is around 0.42 seconds, c) The solid cylinder has the greatest moment of inertia, d) All three objects have the same linear acceleration of approximately 1.52 m/s^2, and e) All three objects have the same tangential (linear) velocity of approximately 1.52 m/s.

A slope is a slanted surface that connects two different levels or elevations.

a) The order in which the objects reach the bottom of the slope depends on their moments of inertia. The object with the smallest moment of inertia will reach the bottom first, followed by the object with the next smallest moment of inertia, and so on.

b) The time it takes each shape to reach the bottom of the slope can be calculated using the formula:

t = sqrt(2h/(g*sin(theta)))

where h is the height of the slope (1 m), g is the acceleration due to gravity (9.81 m/s^2), and theta is the angle of the slope (20°).

For the given values, we have:

t_ring = sqrt(21/(9.81sin(20°))) ≈ 0.42 s

t_sphere = sqrt(21/(9.81sin(20°))) ≈ 0.42 s

t_cylinder = sqrt(21/(9.81sin(20°))) ≈ 0.42 s

Therefore, all three shapes will reach the bottom of the slope in approximately the same amount of time.

c) The moment of inertia of a ring, sphere, and solid cylinder can be calculated using the formulas:

I_ring = m*r^2

I_sphere = (2/5)mr^2

I_cylinder = (1/2)mr^2

where m is the mass of the object and r is its radius.

Since all three objects have the same mass and are made from the same material, their radii must be different in order for their moments of inertia to be different. Therefore, the object with the greatest radius will have the greatest moment of inertia. In this case, the solid cylinder has the greatest radius, so it has the greatest moment of inertia.

d) The linear acceleration of each object can be calculated using the formula:

a = gsin(theta)(1 - mu*cos(theta))

where mu is the coefficient of static friction between the object and the slope.

For the given values, we have:

a_ring = 9.81sin(20°)(1 - 0.3cos(20°)) ≈ 1.52 m/s^2

a_sphere = 9.81sin(20°)(1 - 0.3cos(20°)) ≈ 1.52 m/s^2

a_cylinder = 9.81sin(20°)(1 - 0.3*cos(20°)) ≈ 1.52 m/s^2

Therefore, all three objects have the same linear acceleration.

e) The tangential (linear) velocity of each object can be calculated using the formula:

v = r*omega

where omega is the angular velocity of the object, which can be calculated using the formula:

omega = a/r

where a is the linear acceleration of the object and r is its radius.

For the given values, we have:

v_ring = r*omega = r(a/r) = a ≈ 1.52 m/s

v_sphere = r*omega = r(a/r) = a ≈ 1.52 m/s

v_cylinder = r*omega = r(a/r) = a ≈ 1.52 m/s

So, all three objects have the same tangential (linear) velocity.

Therefore, a) The order in which the objects reach the bottom of the slope depends on their moments of inertia, b) All three shapes will reach the bottom of the slope in approximately the same amount of time, which is around 0.42 seconds, c) The solid cylinder has the greatest moment of inertia, d) All three objects have the same linear acceleration of approximately 1.52 m/s^2, and e) All three objects have the same tangential (linear) velocity of approximately 1.52 m/s.

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Answer:

equator

Explanation:

in south & north pole you could have 20+ hours daylight or night, everyday!

The sacrifice involved in making one decision over another  is known as opportunity cost.

The opportunity cost of a choice is described as  the value of the best alternative forgone where, given limited resources, a choice needs to be made between several mutually exclusive alternatives.

When talking about an opportunity cost, it is referred to as those benefits that exist when making a decision which  could either be in business or a personal decision.

The law of increasing opportunity cost sates that as you increase the production of one good, the opportunity cost to produce the additional good will increase . It is always recommended to make a cost-benefit analysis to contemplate all the benefits.  

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#complete question:

What is the sacrifice involved in making one decision over another ?

The mass of the Ball B is 1.35 x 10⁻⁶ kg.

Gravitational Force is described by Newton's law of universal gravitation, which states that the force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

The law of universal gravitation is important in many fields, including astronomy, physics, and engineering.

The gravitational force F between two objects of masses m1 and m2 separated by a distance r is given by:

F = G(m₁m₂)/r²

where G is the gravitational constant.

We can rearrange the equation to solve for the mass of Ball B:

m₂ = Fr²/Gm₁

Substituting the given values, we get:

m₂ = (8.7 x 10⁻¹⁰ N)(3.0 m)²/(6.6743 x 10¹¹ N(m^2/kg²))(30 N)

m₂ = 1.35 x 10⁻⁶ kg

Therefore, the mass of Ball B is approximately 1.35 x 10⁻⁶kg.

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The net electric force on charge q2 is 28.7 N.

The net electric force on charge q2 is calculated by applying Coulomb's law of electrostatic force.

F(net) = F(12) + F(23)

The force on q2 due to charge 1 is calculated as;

F(12) = -(9 x 10⁹ x 8 x 10⁻⁶ x 3.5 x 10⁻⁶ )/(0.1²)

F(12) = 25.2 N

The force on q2 due to charge 3 is calculated as;

F(23) = (9 x 10⁹ x 2.5 x 10⁻⁶ x 3.5 x 10⁻⁶ )/(0.15²)

F(23) = 3.5 N

The net force on q2 is calculated as;

F(net) = 25.2 N + 3.5 N = 28.7 N

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The ball will strike the ground after 8.04 seconds.

Using the kinematic equation for displacement:

y = y0 + v0t - 1/2g*t^2

where:

We want to findt, let's substitute the values:

0 = 58.52 + 19.50t - 1/2(9.81)*t^2

4.905t^2 - 19.50t - 58.52 = 0

Using the quadratic formula:

t = (-b ± sqrt(b^2 - 4ac)) / 2a

where:

t = (-(-19.50) ± sqrt((-19.50)^2 - 4(4.905)(-58.52))) / 2(4.905)

t = (19.50 ± 31.37) / 9.81

The two possible solutions are:

t1 = 5.61 s (ball on the way up)

t2 = 8.04 s (ball on the way down)

Since the question is asking for when the ball strikes the ground, we take the larger solution, which is:

t = 8.04 s

In other words, the ball will strike the ground after 8.04 seconds.

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The coefficient of static friction between the block of wood and the table is 0.449.

The weight of the block of wood is Mg = 4.0 kg × 9.81 m/s^2 = 39.24 N.

The coefficient of static friction μs is given by the equation μ_s = fs/N, where N is the normal force from the table.

Since the block is not accelerating vertically, we know that N = Mg, so we have:

μs = fs/N = 17.64 N / 39.24 N = 0.449

Therefore, the coefficient of static friction between the block of wood and the table is 0.449.

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A mercury barometer gives the local atmospheric pressure as 750 mmHg, then the absolute pressure of carbon dioxide is 89.87 kPa.

A vacuum gage indicates that the pressure of carbon dioxide in a closed tank is −10 kPa. A mercury barometer gives the local atmospheric pressure as 750 mmHg.

To determine the absolute pressure of carbon dioxide, we need to add the atmospheric pressure to the pressure indicated by the vacuum gauge.

Converting the atmospheric pressure from mmHg to kPa

750 mmHg x (101.3 kPa / 760 mmHg) = 99.87 kPa

Absolute pressure of carbon dioxide

-10 kPa + 99.87 kPa = 89.87 kPa

Therefore, the absolute pressure of carbon dioxide is 89.87 kPa.

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The force required to stop the car of mass 3250 kg is -12195.12 N.

Force is the product of mass and acceleration.

To calculate the force required to stop the car, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

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Answer: A vertical column of water can be supported to a height of about 10.3 meters (33.8 feet) by standard atmospheric pressure.

- This is because the weight of the column of water is balanced by the pressure exerted by the air above it. This phenomenon is known as hydrostatic pressure, and it is the reason why water towers and barometers work.

The initial volume of the liquid is 31.4 cm³. The volume coefficient of thermal expansion of the liquid is 0.002 per degree Celsius. A temperature increase of 109.5°C is needed for the liquid to rise to a height of 49cm.

The initial volume of the liquid can be found using the formula for the volume of a cylinder:

V = πr²h

where r is the radius (half the diameter), h is the height, and π is approximately 3.14. Plugging in the given values, we get:

V = π(0.5 cm)²(40 cm)

V = 31.4 cm³

The volume coefficient of thermal expansion (β) is defined as the fractional change in volume per degree Celsius change in temperature. It can be calculated using the formula:

β = ΔV/(VΔT)

where ΔV is the change in volume, V is the initial volume, and ΔT is the change in temperature. We can rearrange this formula to solve for ΔV:

ΔV = βVΔT

We know that ΔT = -10°C (a decrease of 10°C) and that the height decreased from 40cm to 37cm, or by 3cm. The change in volume can be found using the formula for the volume of a cylinder again, with the new height of 37cm:

ΔV = π(0.5 cm)²(40 cm - 37 cm)

ΔV = 0.59 cm³

Plugging in all the values, we get:

0.59 cm³ = β(31.4 cm³)(-10°C)

β = 0.002

To find the change in temperature needed for the liquid to rise to a height of 49cm, we can use the same formula as before, but solve for ΔT:

ΔT = ΔV/(βV)

We know that ΔV is the difference between the initial volume and the volume at the new height, which is:

ΔV = π(0.5 cm)²(49 cm - 40 cm)

ΔV = 6.86 cm³

Plugging in all the values, we get:

ΔT = 6.86 cm³/(0.002)(31.4 cm³)

ΔT = 109.5°C

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A student measured the length of a wire four times using a meter rule, then average length will be 18.55 cm

A student measured the length of a wire four times using a meter rule and obtained the following reading 18.6,18.5,18.6,18.5.

To determine the length of the wire, we need to calculate the average of the four measurements.

Wadding up all the readings and dividing by the number of readings.

Average length = (18.6 + 18.5 + 18.6 + 18.5) / 4

Average length = 74.2 / 4

Average length = 18.55 cm

Therefore, the length of the wire is approximately 18.55 cm.

The question is incomplete and the complete question is

'' A student measured the length of a wire four times using a meter rule and obtained the following readings: 18.6 cm; 18.5 cm and 18.6 cm. Determine the length the length the student should record''.

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The minimum stopping distance is determined as 8 m.

The minimum stopping distance of the car is calculated as follows;

d = (u²)/(2a)

where;

when the minimum stopping distance = 2 m, initial velocity = 40 km/hr = 11.11 m/s

2 = (11.11²)/(2a)

a = (11.11²)/(2 x 2)

a = 30.86 m/s²

when the speed becomes 80 km/h, the minimum stopping distance is calculated as;

u = 80 km/h = 22.22 m/s

d = (22.22² )/ (2 x 30.86)

d = 8 m

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The plant structure that increases the probability of successful reproduction is flower. So, option B.

The reproductive organs of flowering plants are flowers. The possibility of successful pollination and fertilization is increased by the presence of both male and female reproductive structures in them.

In the flowers, the pollen is considered as the male sex cells. The female part, i.e., the pistil, consists of the ovary, which produces female sex cells or eggs.

There are specialized plant structures in flowers, such as brightly colored petals to attract potential pollinators and extended stamens that require animals to brush against the plants in order to receive the nectar.

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1. The terrestrial planets experience quakes; the gas giants do not. 4.Terrestrial planets experience tectonic activity; gas giants do not.

6. Activity in molten interior of the terrestrial planets results in tectonic activity. Correct options are: 1, 4, 6.

Terrestrial planets, such as Earth, Mars, and Venus, have a solid surface that is broken into several pieces called tectonic plates. Gas giants like Jupiter and Saturn, on  other hand, do not have a solid surface and, therefore, do not experience quakes. For example, is responsible for the formation of mountains, ocean basins, and other geological features. Heat generated by decay of radioactive elements within Earth's core causes convection currents, which move the tectonic plates around. Hence Correct answer: 1,4,6.

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--The complete Question is, Which statements accurately compare the tectonic activity of the planets?

Check all that apply.

1. The terrestrial planets experience quakes; the gas giants do not.

2. The gas giants have multiple plates; the terrestrial planets do not.

3. The gas giants have no true surfaces, so they experience tectonic activity.

4. Terrestrial planets experience (or experienced) tectonic activity; gas giants do (or did) not. 5. Mountains and volcanoes are found on the gas giants, not on terrestrial planets.

6. Activity in the molten interior of the terrestrial planets results (or resulted) in tectonic --

The record will rotate through an angle of 1.24°.

Angular speed of the record, ω = 38.9 rev/min = 0.65 rev/s

Time taken for the rotation, t = 1.9 s

Motion in a circular path or around the circumference of a circle is referred to as circular motion. It may rotate at a particular speed and angular rate or it may rotate at a variable rate, making it either uniform or non-uniform circular motion.

The angular speed is the rate of change of angular displacement.

Therefore, angular displacement of the record,

θ = ωt

θ = 0.65 x 1.9

θ = 1.24°

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The velocity of the ball just before it hits the ground is 14.0 m/s

Let's solve the problem using the given equation:

[tex]v^2 = u^2 + 2as[/tex]

We know that u (initial velocity) is zero, s (distance traveled) is 10 meters, and a (acceleration due to gravity) is 9.81 m/s^2. We want to find the final velocity (v) just before the ball hits the ground.

Plugging in the given values, we get:

v^2 = 0 + 2(9.81)(10)

v^2 = 196.2

Taking the square root of both sides, we get:

v = sqrt(196.2)

v = 14.0 m/s

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--The complete Question is, A ball is dropped from a height of 10 meters. What is its velocity just before it hits the ground, assuming no air resistance? (Assume that the acceleration due to gravity is 9.81 m/s^2)

Hint: You can use the equation v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity (which is zero in this case), a is the acceleration due to gravity, and s is the distance traveled.--

The ratio of their rotational kinetic energies is 4/5 or 0.8.

Let's denote the mass and radius of the cylinder and sphere as "m" and "r", respectively. At the top of the incline, both objects have only potential energy, which is then converted to kinetic energy. At the bottom of the incline, both objects have both translational and rotational kinetic energy.

For a uniform solid cylinder, the rotational inertia is[tex]1/2 * m * r^2[/tex]. For a uniform sphere, the rotational inertia is[tex]2/5 * m * r^2[/tex]. Therefore, the ratio of their rotational kinetic energies is:

(rotational kinetic energy of sphere) / (rotational kinetic energy of cylinder)

[tex]= (2/5 * m * r^2 * (v/r)^2) / (1/2 * m * r^2 * (v/r)^2)[/tex]

= (4/5)

Therefore,  rotational kinetic energy of  sphere is 80% of  rotational kinetic energy of the cylinder at  bottom of the incline.

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--The complete Question is, A uniform solid cylinder and a uniform sphere with the same mass and radius are released from rest at the top of an incline. They both roll without slipping down the incline and reach the bottom with the same translational speed. What is the ratio of their rotational kinetic energies at the bottom of the incline?--

The experiment to measure the speed of sound will involve recording the time for the loudest sound to be heard.

The dependent variable in the experiment is the time and the independent variable is the frequencies of the tuning fork.

Some potential reasons for the two lab groups in different locations coming up with different results include:

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