find ds in terms of dv and approximate the change in the surface when the volume change from 1,000 m3 to 999 m3 .

(a) The height of the roller coaster at 120,000 potential energy is 122.45 m.

(b) The velocity of the roller coaster at 0 J kinetic energy is 0.

(c) The height of the roller coaster at 60,000 potential energy is 61.23 m.

(d) The velocity of the roller coaster at 60,000 J kinetic energy is 34.64 m/s.

(e) The height of the roller coaster at 40,000 potential energy is 40.82 m.

(f) The velocity of the roller coaster at 80,000 J kinetic energy is 40 m/s.

The given parameters:

When the kinetic energy = 0 and potential energy = 120,000 J

The height of the roller coaster is calculated as follows;

P.E = mgh

\(h = \frac{P.E}{mg}\\\\h = \frac{120,000}{100 \times 9.8} \\\\h = 122.45 \ m\)

Since the kinetic energy = 0, the velocity of the roller coaster = 0

When the potential energy, P.E = 60,000 J, the kinetic energy, K.E is calculated as;

P.E + K.E = M.A

P.E + K.E = 120,000

60,000 + K.E = 120,000

K.E = 120,000 - 60,000

K.E = 60,000 J

The height of the roller coaster at 60,000 potential energy is calculated as follows;

\(h = \frac{P.E}{mg} \\\\h = \frac{60,000}{100 \times 9.8} \\\\h =61.23 \ m\)

The velocity of the roller coaster at 60,000 J kinetic energy is calculated as follows;

\(K.E = \frac{1}{2} mv^2\\\\v^2 = \frac{2K.E}{m} \\\\v = \sqrt{ \frac{2K.E}{m}} \\\\v = \sqrt{ \frac{2\times 60,000}{100}}\\\\v = 34.64 \ m/s\)

When the potential energy, P.E = 40,000 J, the kinetic energy, K.E is calculated as;

P.E + K.E = M.A

40,000 + K.E = 120,000

K.E = 120,000 - 40,000

K.E = 80,000

The height of the roller coaster at 40,000 potential energy is calculated as follows;

\(h = \frac{P.E}{mg} \\\\h = \frac{40,000}{100 \times 9.8} \\\\h = 40.82 \ m\)

The velocity of the roller coaster at 80,000 J kinetic energy is calculated as follows;

\(v = \sqrt{\frac{2K.E}{m} } \\\\v = \sqrt{\frac{2\times 80,000}{100} } \\\\v = 40 \ m/s\)

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Answer:

1.21 m/s

Explanation:

Given :

2 loudspeakers

F2 - F1 = 2.86 Hz

Speed of sound, V = 343

Fo = frequency when listener is at rest = 406Hz

To obtain the walking speed Vo, speed as observer moves away from speaker ;

Vo = [(F2 - F1) * V] ÷ 2 * Fo

Vo = [2.86 * 343] ÷ (2 * 406)

Vo = 980.98 / 812

Vo = 1.2081034

Vo = 1.21 m/s

Explanation:

You want  N/m

 N = 66 * 9.81

 m = 2.3 x 10^-2 m

66* 9.81 / 2.3 x 10^-2  = 28150 =  28 000 N/m    to two S D

Answer:

I can't do your work for you but I can explain the last question;

The want you to tell them (In at least 3 sentences) Why you think your answers are correct or how your answer's match your hypothesis.

A hypothesis (for a little more help)  is an idea or explanation that you then test through study and experimentation.

Outside science, a theory or guess can also be called a hypothesis. A hypothesis is something more than a wild guess but less than a well-established theory. Anyone who uses the word hypothesis is making a guess.

Explanation:

Sorry I didnt give you the exact answer but I hope this helps :)

Scientists typically collect ozone samples from the stratosphere, which is the atmospheric layer located between about 10 and 50 kilometers (6 to 30 miles) above the Earth's surface.

The stratosphere is the layer of the Earth's atmosphere located above the troposphere and below the mesosphere. It extends from about 10 kilometers (6 miles) to about 50 kilometers (30 miles) above the Earth's surface.

The stratosphere is characterized by a gradual increase in temperature with altitude, due to the absorption of ultraviolet radiation by ozone in the stratosphere.

This is where most of the Earth's ozone is found and where the ozone layer is located. The ozone layer absorbs harmful ultraviolet (UV) radiation from the sun, protecting life on Earth from its harmful effects. Scientists collect air samples from this layer using airplanes or weather balloons equipped with specialized instruments.

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It is not recommended to fire a gun straight up into the air.

When a bullet is fired into the air, it will eventually come down and can pose a danger to people and property below. The bullet can still be lethal when it reaches the ground, especially if it lands on a hard surface or hits someone directly.

Additionally, firing a gun in a residential area can be illegal and can result in legal consequences. In general, guns should only be fired in designated shooting ranges or in self-defense situations where there is an immediate threat to life. It is important to handle firearms responsibly and follow all safety guidelines to prevent accidents and injuries.

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The velocity of longitudinal waves in a metallic rod depends on its elastic modulus, density, atomic structure, and temperature. These factors collectively determine the ability of the rod to transmit and propagate longitudinal waves.

1. Elastic modulus: The velocity of longitudinal waves is directly proportional to the elastic modulus of the material. Elastic modulus refers to the stiffness or rigidity of the material. In metals, a higher elastic modulus corresponds to a higher velocity of longitudinal waves.

2. Density: The density of the metal also affects the velocity of longitudinal waves. Generally, higher density metals tend to have slower wave velocities.

3. Atomic structure: The arrangement and bonding between atoms in a metal impact the velocity of longitudinal waves. The crystal structure, grain boundaries, and defects in the metal can influence wave propagation.

4. Temperature: Temperature affects the speed of sound in a material, including the velocity of longitudinal waves in a metallic rod. As temperature increases, the atomic vibrations within the metal increase, leading to a higher velocity of longitudinal waves.

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Answer:

C

Explanation:

The most commonly accepted theory of muscle growth states that microscopic tears within a muscle activate an inflammatory response process that causes dormant cells to build and regenerate muscle tissue; this is option c.

It has negative consequences on the muscle, and it is also known as "microtrauma," which occurs as a result of muscle contraction and is a normal part of the muscle repair and growth process. Here, the fibers in the muscle are damaged, and in response, the body initiates a repair process. This leads to muscle growth and increased strength and is helpful for muscle repair.

Hence, the most commonly accepted theory of muscle growth states that microscopic tears within a muscle activate an inflammatory response process that causes dormant cells to build and regenerate muscle tissue; this is option c.

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If a Catatlyst was added the values affected would be 2, 3, 4

A catalyst is a substance that speeds up the rate of a chemical reaction without undergoing any permanent change itself. It facilitates the reaction by providing an alternative pathway with lower activation energy, which allows the reaction to occur more readily.

Catalysts work by interacting with the reactant molecules and weakening the existing bonds or creating new ones, making it easier for the reaction to proceed.

Catalysts are typically specific to certain reactions and can be used in small amounts relative to the reactants. They play a crucial role in many industrial processes and are essential for efficient chemical transformations.

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According to Chargaff's rule, the amounts of adenine (A), thymine (T), and guanine (G) in the DNA molecule are equal to each other. The amounts of cytosine (C) and guanine (G) are also equal.

Erwin Chargaff was a biochemist, author, Bucovinian Jew who immigrated to America during the Nazi era, and professor of biochemistry at Columbia University's medical school.

Chargaff found patterns among the four bases, or chemical building blocks, of DNA, which are directly related to DNA's function as the genetic material of living things.

He was born in Austria-Hungary. Heraclitean Fire: Sketches from a Life Before Nature, an autobiography he penned, received positive reviews.

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If an airplane is  is accelerating down a runway at 2.5 m/s². It's velocity changes 2.5 m/s in each second.

Acceleration is the rate at which speed and direction of velocity vary over time. A point or object going straight ahead is accelerated when it accelerates or decelerates.

Even if the speed is constant, motion on a circle accelerates because the direction is always shifting. Both effects contribute to the acceleration for all other motions.

Hence, the velocity of the airplane changes 2.5 m/s in each second  when it  is accelerating down a runway at 2.5 m/s².

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Answer:

The target was higher than the cannon

Explanation:

Given that a cannon ball is launched with initial speed 56 m/s, and hits a target at speed 35 m/s.

The initial velocity must be 56 m/s, while the final velocity will be 35 m/s.

When an object is thrown upward with an initial velocity, the object continues to move upwards with decreasing in magnitude of velocity till it reaches the maximum height where the final velocity will be equal to zero.

In this question, since the final velocity is less than the initial velocity, we can conclude that the target is higher.

Therefore, the target was higher than the cannon.

Answer:

In a solar eclipse, the sun is completely blocked because the moon moves between the earth and the sun. Although the moon is much smaller than the sun because it is located so far away from the earth, the moon can completely block sunlight from the earth's point of view.

Answer:

Explanation:

The time taken to travel from Fort Worth to Dallas is:

t = 3:23 pm - 2:41 pm = 42 minutes = 0.7 hours

The distance covered is:

d = 58 km

The average speed is:

v = d/t = 58 km / 0.7 hours = 82.86 km/h

To convert km/h to m/s, we can use the conversion factor:

1 km/h = 0.2778 m/s

Therefore, the average speed in m/s is:

v = 82.86 km/h × 0.2778 m/s/km = 23.06 m/s (rounded to two decimal places)

So the average speed is 23.06 m/s.

Answer:

How is hydrogen obtained and separated from other nearby substances?

photoelectrolysis, a photoelectrochemical cell submerged in water uses sunlight to separate the water into hydrogen and oxygen bubbles. In the thermochemical cycle, water is heated to 800 to 1,000 °C, with the molecule. splitting to release hydrogen. The main drawback of this method is that it requires nuclear power

How is Hydrogen used?

Hydrogen can be used in fuel cells to generate electricity, or power and heat. Today, hydrogen is most commonly used in petroleum refining and fertilizer production, while transportation and utilities are emerging markets

What products are made from Hydrogen?

Hydrogen is a very useful element. It is used to make ammonia for fertilizers, refining metals, and methanol for making artificial material like plastics. Hydrogen is also used as a rocket fuel where liquid hydrogen is combined with liquid oxygen to produce a powerful explosion.

Any environmental concerns about the use of Hydrogen?

Emissions of hydrogen lead to increased burdens of methane and ozone and hence to an increase in global warming. Therefore, hydrogen can be considered as an indirect greenhouse gas with the potential to increase global warming.

Answer:D

The momentum of an object is defined as the product of its mass and velocity. So, to calculate the momentum of an object with a mass of 750 kg and a velocity of 15 m/s, we can use the following formula:

Momentum = mass x velocity

Momentum = 750 kg x 15 m/s

Momentum = 11,250 kg m/s

Therefore, the momentum of the object is 11,250 kg m/s.

ANSWER

EXPLANATION

From the previous part, we have that the index of refraction of the liquid is 1.37, so we have to replace this in the equation and solve,

And then, take the inverse of the sine to find the critical angle,

Hence, the critical angle is 46.9°, rounded to the nearest tenth.

Therefore, the ball hits the water 30.1 meters from the bottom of the cliff.

A vector is a mathematical object that has both magnitude (size) and direction. It can be used to represent physical quantities that have both a numerical value and a direction, such as velocity, force, or acceleration. A vector can be represented graphically as an arrow, with its length representing its magnitude and its direction indicating its direction. The tail of the arrow represents the starting point of the vector, while the head represents the endpoint. In addition to their graphical representation, vectors can also be described algebraically using components.

Here,

To find the distance from the bottom of the cliff where the ball hits the water, we need to find the time it takes for the ball to hit the water and then use this time to find the vertical displacement of the ball at that time.

First, we can find the time it takes for the ball to hit the water by setting the y-coordinate of its position vector equal to zero (since the water is at ground level):

-4.9t² + 40 = 0

Solving for t, we get:

t = √(40/4.9) = 2.03 seconds

So the ball hits the water after 2.03 seconds.

Next, we can use this time to find the vertical displacement of the ball at that time by plugging in t = 2.03 seconds into the y-component of its position vector:

r_y = -4.9(2.03)² + 40 = 30.1 meters

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Answer:

d) The box’s initial potential energy is transformed into kinetic energy and

thermal energy.

Explanation:

Let us analyze the situation first. Initially we have a box at rest placed at some height on a ramp. So, the three energies associated with the box will be:

Kinetic Energy = 0 (due to zero velocity)

Thermal Energy = 0 (due to not temperature change)

Potential Energy = Greater than zero value (due to height)

Now, when the box is released to slide down the ramp with friction, the energies become:

Kinetic Energy = Increasing (due to increase in velocity)

Thermal Energy = Increasing (due to increase in temperature, because of friction)

Potential Energy = Decreasing (due to decrease in height)

So, from Law of Conservation of Energy, we can write:

Loss of Potential Energy = Gain in Kinetic Energy + Gain in Thermal Energy

So, the correct option is:

d) The box’s initial potential energy is transformed into kinetic energy and  thermal energy.

Answer:

\(a_{c} = 13.46\ m/s^2\)

Explanation:

The motion of the tethered ball around the pole can be modeled as uniform circular motion. The acceleration of the objects executing uniform circular motion is due to the change in direction of their velocity. This is called centripetal acceleration. It is given by the following formula:

\(a_{c} = \frac{v^2}{r}\)

where,

ac = centripetal acceleration = ?

v = speed of ball = 3.5 m/s

r = distance of ball from center of rotation = 0.91 m

Using these values in equation, we get:

\(a_{c} = \frac{(3.5\ m/s)^2}{0.91\ m}\\\\a_{c} = 13.46\ m/s^2\)

The momentum of the Van whose velocity and mass has been given would be =4.8×10⁴kgm/s

To calculate the momentum of a moving object, the formula that should be used is given below as follows:

p = MV

where;

M = mass = 1.5×10³kg

V = Velocity= 32 m/s

P = momentum = 32×1.5×10³ = 4.8×10⁴kgm/s

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High tides occur when the sun and moon are at right angles to one another. This is because the gravitational pull of the moon and the sun combine to create larger-than-normal tides, known as spring tides. The correct option is A.

Gravitational pull is the force of attraction that exists between two objects with mass. The greater the mass of an object, the greater its gravitational pull.

Option B, "Low tides occur when the sun and moon are at right angles to one another," is incorrect. Low tides occur when the sun and moon are at a 90-degree angle (or "quarter moon") to each other, but this position also results in high tides on the opposite side of the Earth.

Option C, "The gravitational pull of the sun and moon combined creates larger than normal tides," is partially correct. The gravitational pull of both the sun and moon does contribute to the tides, but the specific position depicted in the image (sun and moon at right angles to each other) does not necessarily create larger than normal tides.

Option D, "The gravitational pull of the sun reduces the moon's gravitational pull to create moderate tides," is also incorrect. The sun's gravitational pull does have an effect on the tides, but it does not reduce the moon's gravitational pull. Rather, the combined gravitational pull of the sun and moon creates the tides we observe.

Therefore,The accurate description of the tide represented by the image below is option A: "High tides occur when the sun and moon are at right angles to one another."

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(A) The spring constant of the spring is 4.94 N.

(B) The speed of the cart after pushing it is 0.47 m/s.

(C) The force applied to the cart is 0.75 N.

ω = √k/m

where;

0.5 rev/s = 0.5(2π) rad/s = π rad/s = 3.142 rad/s

ω² = k/m

k = mω²

k = 0.5 x (3.142)²

k = 4.94 N/m

E = ¹/₂kA²

where;

A is amplitude

E = ¹/₂(4.94)(0.15)²

E = 0.056 J

E = ¹/₂mv²

2E = mv²

v² = 2E/m

v² = (2 x 0.056)/(0.5)

v² = 0.224

v = √0.224

v = 0.47 m/s

E = ¹/₂FA

2E = FA

F = 2E/A

F = (2 x 0.056)/(0.15)

F = 0.75 N

Thus, the spring constant of the spring is 4.94 N. The speed of the cart after pushing it is 0.47 m/s. The force applied to the cart is 0.75 N.

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Answer:

  2.38 mW

Explanation:

Power is work per unit time. Work is the product of force and distance. That means ...

  \(\text{power}=\dfrac{\text{force}\times\text{distance}}{\text{time}}=\text{force}\times\dfrac{\text{distance}}{\text{time}}\\\\\text{power}=\text{force}\times\text{velocity}\)

Using the given values of force and velocity, the tadpole's power output is ...

  P = (0.028 N)(0.085 m/s) = 0.00238 W = 2.38 mW

The tadpole's power output is about 2.38 mW.

The nature of the image formed by the convex lens is virtual, the position of the image is 30 cm away from the lens on the same side as the object, and the size of the image is twice the size of the object. The magnification is 2, meaning the image is magnified.

Given:

Object height (h) = 5 cm

Focal length of the convex lens (f) = 10 cm

Object distance (u) = 15 cm (positive since it's on the same side as the incident light)

To determine the nature, position, and size of the image, we can use the lens formula:

1/f = 1/v - 1/u

Substituting the given values:

1/10 = 1/v - 1/15

To simplify the equation, we find the common denominator:

3v - 2v = 2v/3

Simplifying further:

v = 30 cm

The image distance (v) is 30 cm. Since the image distance is positive, the image is formed on the opposite side of the lens from the object.

To find the magnification (M), we use the formula:

M = -v/u

Substituting the values:

M = -30 / 15 = -2

The magnification is -2, indicating that the image is inverted and twice the size of the object.

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Answer:

KE=1/2 mv² = FD

where FD =umgd , thus,

1/2mv²= umgd

1/2v² =ugd

v² = 2 ugd

v =√2ugd

v=√2(0.3)(9.81)(78)

v=21.4m/s

Answer:

The displacement of the pendulum from equilibrium position is 0.855 of the length of the pendulum.

Explanation:

A pendulum's motion can be modelled as a simple harmonic motion and the differential equation describing simple harmonic motion is given as

(d²x/dt²) + (k/m)x = 0

(d²x/dt²) = acceleration of the pendulum

x = displacement of the pendulum from equilibrium position

k = spring constant of the pendulum = (mg/L) = (0.006×9.8/L) = (0.0588/L)

L = length of the pendulum

m = mass of the pendulum = 6 g = 0.006 kg

(k/m) = (g/L) = (9.8/L)

To calculate the pendulum's acceleration

Initial velocity of the car = 0 mph = 0 m/s

Final velocity of the car = 60 mph = 26.822 m/s

Time taken for velocity change = 3.2 s

Acceleration = (Δv/Δt) = (26.822/3.2) = 8.382 m/s²

(d²x/dt²) + (k/m)x = 0

Becomes

8.383 + (9.8/L)x = 0

(9.8x/L) = -8.382

9.8x = -8.382L

x = -(8.382/9.8) = -0.855 L (the minus sign shows the direction of movement of the pendulum)

Ignoring the sign and only focusing on the magnitude of the pendulum's displacement from equilibrium position, the displacement of the pendulum from equilibrium position is 0.855 of the length of the pendulum.

Hope this Helps!!!

Answer:

198785.714286 Joules

Explanation:

\(W=f*d\)

\(F=ma\\F=516.326530612*-14\\F=-7228.57142857 N\\\)

To find work:

Now that the force and the distance are known, plug and chug:

\(W=f*d\\W=-7228.57142857*27.5\\W=-198785.714286J\)

Note that the question is asking for the magnitude of work, so the negative can be discarded as it is a directional component.

So, your answer is

198785.714286 Joules