while standing at the edge of a cliff 45m high, you drop a ball. When the ball has fallen 5m, you throw a second ball straight down. What initial speed must you give the second ball if they are both to reach the ground at the same time?​

Answers

Answer 1

The initial velocity of the second ball is 14.85 m/s

Motion Under Gravity

Motion under gravity is also known as vertical linear motion. The three formula involved are

V = U +/- gth = ut +/- 1/2g\(t^{2}\)\(V^{2}\) = \(U^{2}\) +/- 2gH

Where

V = final velocityU = initial velocityg = acceleration due to gravityt = time

Given that at the edge of a cliff 45m high, you drop a ball. When the ball has fallen 5m, you throw a second ball straight down.

Let first calculate the time for the first ball.

where U = 0

h = ut +/- 1/2g\(t^{2}\)

h = 1/2g\(t^{2}\)

substitute all the parameters

45 = 1/2 x 9.8 x \(t^{2}\)

45 = 4.9\(t^{2}\)

\(t^{2}\) = 45/4.9

\(t^{2}\) = 9.18

t = \(\sqrt{9.18}\)

t = 3.03 s

To calculate initial speed that you must give the second ball if they are both to reach the ground at the same time, we will make g negligible.

U  = h/t

U = 45/3.03

U = 14.85 m/s

Therefore, the initial velocity of the second ball is 14.85 m/s

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Related Questions

What's a good way to start the problem?

Answers

Answer: Start by writing down the problem in your own words using as much detail as possible. Be as specific as possible in your description.

Explanation:

Look at the simple machine shown below and determine the mechanical
advantage.
3.0 m
0.3 m

Look at the simple machine shown below and determine the mechanicaladvantage.3.0 m0.3 m

Answers

Answer:

10.0

Explanation:

Mechanical Advantage = distance moves along the plane/distance moved along the vertical

distance moves along the vertical = 0.3m

distance moves along the plane = 3.0m

Mechanical Advantage = 3.0/0.3

Mechanical Advantage = 10

Hence the mechanical advantage is 10.0

In the attachment there is a density column where there is colour


Question: tell me why is the red at the bottom of the density column if it is the least dense

In the attachment there is a density column where there is colourQuestion: tell me why is the red at

Answers

Answer: The red at the bottom represents the base of the tube, not the red liquid.

Explanation:

The densest materials have more weight per unit of volume.

This means that those elements will always flow to the bottom of the containers, like the one in the image.

The red liquid being the least dense one, can not go to the bottom by its own means.

There could be some cases, like:

The red liquid when solid, is way denser than in its liquid phase, and then the red at the bottom could be solid phase of the red liquid, but there is no mention of this in the question, then we can discard this idea.

Another trivial idea is that the red liquid at the bottom could be trapped by some kind of wall, but again, there is no mention of this, so again we can discard this idea.

The thing that makes sense is that the red at the bottom represents the base of the tube and not the red liquid.

plz help

In a pot of boiling water, what happens to the hot water at the bottom of the pot? What happens to the cold water at the top of the pot?​

Answers

Explanation:

First, the liquid on the bottom of the pot closest to the heat source starts to get hot; as it does, it rises. The rising hot water is replaced by the cooler, more dense water molecules. The water molecules in your pot continually exchange in this way, thanks to gravity, eventually warming the entire pot of liquid.

The water at the bottom of the pot becomes hot and it’s density decreases.Cold water could become water vapor.

Average speed is calculated by dividing distance traveled by
time. How is average velocity calculated?

Answers

Answer:

The average velocity of an object is its total displacement divided by the total time taken. In other words, it is the rate at which an object changes its position from one place to another. Average velocity is a vector quantity. The SI unit is meters per second.

hope this helps you

Answer:

displacement divided by time

Explanation:

Consider the circuit in Figure 5 with e(t) = 12sin(120pit) V. When S1 and S2 are
open, i leads e by 30°. When SI is closed and S2 is open, i lags e by 30°. When S1 and S2 are closed, i has an amplitude 0.5A. What are R, L, and C?

Consider the circuit in Figure 5 with e(t) = 12sin(120pit) V. When S1 and S2 areopen, i leads e by 30.

Answers

Based on the information, it should be noted that the resistance R is 0.5 Ω.

How to calculate the resistance

When S1 and S2 are open, i leads e by 30°. In this case, the circuit consists of only the inductor (L) and the capacitor (C) in series. Therefore, the impedance of the circuit can be written as:

Z = jωL - 1/(jωC)

Since i leads e by 30°, we can express the phasor relationship as:

I = k * e^(j(ωt + θ))

Z = jωL - 1/(jωC) = j(120π)L - 1/(j(120π)C)

Re(Z) = 0

By equating the real parts, we get:

0 = 0 - 1/(120πC)

Let's assume that there is a resistance (R) in series with the inductor and capacitor. The impedance equation becomes:

Z = R + jωL - 1/(jωC)

Z = R + jωL

Im(Z) = ωL > 0

Substituting the angular frequency and rearranging the inequality, we have:

120πL > 0

L > 0

This condition implies that the inductance L must be greater than zero.

When S1 and S2 are closed, i has an amplitude of 0.5 A. In this case, the impedance is:

Z = R + jωL - 1/(jωC)

Since the amplitude of i is given as 0.5 A, we can express the phasor relationship as:

I = 0.5 * e^(j(ωt + θ))

By substituting this phasor relationship into the impedance equation, we can determine the value of R. The real part of the impedance must be equal to R:

Re(Z) = R

Since the amplitude of i is 0.5 A, the real part of the impedance must be equal to 0.5 A: 0.5 = R

Therefore, the resistance R is 0.5 Ω.

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A rock moving in the +x-direction with speed 16.0 m/s has a net force applied to it at time t = 0, and this produces a constant acceleration in the −x-direction that has magnitude 4.00 m/s2. For what three times t after the force is applied is the rock a distance of 24.0 m from its position at t = 0?

Answers

Answer: The rock is (24m) away from the origin at t = 2 s, t = 6 s, and t = 9.29 s

Car A is moving at a speed of 45km/h towards car B which is moving at a speed of 55km/h. if the two car were initially separated at a distance of 150km, determine how long it will take the two cars to meet?​

Answers

The time taken by the cars to meet is 5.4 x 10³ s.

Speed of car A, v₁ = 45 km/h = 12.5 m/s

Speed of car B, v₂ = 55 km/h = 15.27 m/s

Distance between the cars, d = 150 km = 15 x 10⁴m

The expression for the time taken by the cars to meet can be given as,

Time = Distance/Average speed

t = d/(v₁ + v₂)

Applying the values of d, v₁ and v₂.

t = 15 x 10⁴/(12.5 + 15.27)

t = 15 x 10⁴/27.77

t = 5.4 x 10³ s

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which energy resource is renewable

Answers

Explanation:

solar energy is the answer

PLEASE HELP I NEED THE CORRECT ANSWER TODAY

PLEASE HELP I NEED THE CORRECT ANSWER TODAY

Answers

Answer:

The most common oxidation numbers for a given element

An object is placed at the position x1 = 73 cm and a second mass that is 4/3 times as large is placed at x2 = 247 cm. Find the location of the center of mass of the system.

Answers

If An object is placed at the position x1 = 73 cm and a second mass that is 4/3 times as large is placed at x2 = 247 cm, the location is at 172.44cm

How to find the location

The location of he center of the mass of the object would be

73 cm + (4/3 * 247) / 1 + 4/3

= 73 CM + 329.3 / 2.333

= 402.3 /2.33

= 172.44 CM

Hence we can conclude that the location is at If An object is placed at the position x1 = 73 cm and a second mass that is 4/3 times as large is placed at x2 = 247 cm, the location is at 172.44cm

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(2) Put 5kg mass at left side (at 2m). This is fixed throughout the experiment! (3) Try to balance by putting 5kg mass at the right side. Write the position of the 5kg mass. Calculate the net torque. Torque= mass * g*length, and the unit for torque is N.m (4) Try to balance by putting 10kg mass at the right side. Write the position of the 10kg mass. Calculate the net torque. (5) Try to balance by putting 20kg mass at the right side. Write the position of the 20kg mass. Calculate the net torque. (6) What do you conclude?

Answers

We can conclude that as the mass on the right increases, the distance of the mass towards the right decreases. Also when the two masses balance, the net torque is zero.

What is torque

The torque experienced by an object a given position is the product of the applied force and the perpendicular distance of the object.

When 5 kg mass is at 2 m on the left, another 5 kg at 2 m on the right will balance it.

\(\tau _{net} = (2 \times 5 \times 9.8) - (2 \times 5 \times 9.8)\\\\\tau _{net} = 0\)

Position of 10 kg mass on the right

Apply principle of moment

\(F_1r_1 = F_2r_2\\\\(m_1gr_1) = (m_2gr_2)\\\\r_2 = \frac{m_1gr_1}{m_2g} \\\\r_2 = \frac{m_1 r_1}{m_2} \\\\r _2 = \frac{5 \times 2}{10} \\\\r_2 = 1 \ m\)

Net torque

\(\tau_{et} = m_2gr_2 - m_1gr_1\\\\\tau_{et} = (10 \times 9.8 \times 1) - (5 \times 9.8 \times 2)\\\\\tau_{et} = 0\)

Position of the 20 kg mass

\(r_2 = \frac{5 \times 2}{20} \\\\r_2 = 0.5 \ m\)

Net torque

\(\tau_{et} = m_2gr_2 - m_1gr_1\\\\\tau_{et} = (20 \times 9.8 \times 0.5) - (5 \times 9.8 \times 2)\\\\\tau_{et} = 0\)

Thus, we can conclude that as the mass on the right increases, the distance of the mass towards the right decreases. Also when the two masses balance, the net torque is zero.

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Why does spontaneous emission dominate over stimulated emission at normal temperature?​

Answers

Mechanism by which stimulated emission is made to dominate is to have more atoms in excited state than in lower energy state, so that emitted photons are more likely to stimulate emission than to be absorbed.

What is the relationship between spontaneous and stimulated emission?

The ratio of spontaneous emission to stimulated emission is proportional to ν³. Higher is the frequency of light involved, greater is the rate of spontaneous emission over stimulated emission.

During spontaneous emission, internal energy of an electron decreases, and photon is emitted. Stimulated emission takes place when photon, with energy equal to the energy gap of the level interacts with electron.

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IN A FORCE COMPRESSION GRAPH, WHAT IS THE STORED POTENTIAL ENERGY OF THE SPRING WHEN IT'S COMPRESS 0.60M ?​

Answers

Answer:

La energía potencial elástica es la energía asociada con los materiales elásticos. Por ejemplo, un resorte al ser comprimido o elongado almacena energía potencial elástica y, al ser soltado, puede realizar trabajo sobre un objeto.

Para mantener el resorte comprimido o alargado una cierta longitud x, a partir de su largo natural, es necesario que, en este caso, la mano aplique una fuerza F_{M} sobre el resorte; esta fuerza es directamente proporcional a x.

Explanation:

ón conocida como ley de Hooke.

Para encontrar una expresión que describa la energía potencial asociada con la fuerza del resorte, se determina el trabajo que se requiere para comprimir el resorte desde su posición de equilibrio hasta cierta posición final arbitraria x. Debido a que la fuerza varía desde O hasta kx, se utiliza la fuerza promedio \frac{(F_{0}+F_{X})}{2}.

 \[ \bar{F}=\frac{0+K X}{2}=\frac{1}{2}kx \]

fuerza-sobre-un-resorte

Fuerza sobre un resorte. La fuerza para estirar un resorte aumenta linealmente con su elongación .

El trabajo realizado por la fuerza aplicada será: W=\bar{Fx}=\frac{1}{2}kx^{2}

El trabajo realizado se almacena en el resorte comprimido en forma de energía potencial elástica como:

 \[ \boxed{ Ep_{elas}=\frac{1}{2}kx^{2}} \]

Una vez que se ha comprimido o estirado el resorte respecto a su posición de equilibrio, la energía potencial elástica se puede considerar como la energía almacenada en el resorte deformado. Esta energía siempre es positiva en un objeto deformado al depender de x^{2}.

Por ejemplo, en la figura se observa que un resorte realiza trabajo sobre un bloque. El resorte que se encuentra sin deformar (a) cuando es empujado por un bloque de masa m, se comprime una distancia x (b). Cuando el bloque se suelta (c), partiendo del reposo, la energía potencial plástica almacenada en el sistema se transforma en energía cinética del bloque.

energia-potencial

A 21 KG chair initially at rest on a horizontal floor requires a 167 N horizontal force to set it in motion once the chair is in motion a 132 N horizontal force keeps it moving at a
constant velocity.
The acceleration of gravity is 9.81 m/s².
a) What is the coefficient of static friction
between the chair and the floor?
b) what is the coefficient of kinetic friction between the chair and the floor?

Answers

The chair and floor have a static friction coefficient of 7.9523 and a kinetic friction coefficient of 0.8114, respectively.

What causes static friction?

The braking force of an item is static friction. The resistance humans encounter when attempting to move something fastened to the ground without actually moving thier own bodies or the surface that are sitting on is described as static friction.

What causes static friction to form?

Adhesion, a slight chemical attraction between contact objects, is what causes static friction. Friction is also produced by the interaction of the flaws on each surface.

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Electronegativity can best be defined as a) relative measure showing how many bonds an atom will formb) a relative measure showing the degree to which electrons can be removed from an atom c) the degree to which an electron will leave an atom d) the degree to which an atom wants to gain more electrons

Answers

The electronegativity of an element is the tendency of an atom to attract electrons to itself in a chemical compound.

The electronegativity decreases down the group and increases from left to right across the period.

Therefore, electronegativity can best be defined as the degree to which an atom wants to gain more electrons. Hence, option (d) is the correct choice.

A chopper’s speed increases from 35 m/s to 60 m/s in 5 seconds. What is the acceleration of this helicopter?

Answers

A chopper’s speed increases from 35 m/s to 60 m/s in 5 seconds. Therefore, the acceleration of this helicopter is 5m/s².

What do you mean by an acceleration ?

The term an acceleration is the name we supply to any process where the velocity changes.

Therefore, velocity is a speed and a direction, there are only two ways for you to accelerate is change your speed or change your direction or change both.

Given:

Initial speed = 35 m/s

Final speed = 60 m/s

Time = 5 s

v = u + at

60 = 35 + a(5)

60 - 35 = 5a

25 = 5a

a = 5

Thus, the acceleration of this helicopter is 5m/s².

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Particles q1 =+9.33 uC, q2 =+4.22 uC, and q3=-8.42 uC are in a line. Particles q1 and q2 are separated by 0.180 m and particles q2 and q3 are separated by 0.230 m. What is the net force on particle q2?

Answers

The net force on q₂ will be  1.07 x 10⁻² N, pointing to the left.

To find the net force on particle q₂, we need to calculate the force due to q₁  and q₃ individually and then add them up vectorially. We can use Coulomb's law to calculate the force between two point charges:

F = k × (q₁ × q₂) / r²

where F is the magnitude of the force, k is Coulomb's constant (k = 8.99 x 10⁹ Nm²/C²), q1 and q2 are the charges of the two particles, and r is the distance between them.

The force due to q₁ on q₂ can be calculated as:

F₁ = k × (q₁ × q₂) / r₁²

where r1 is the distance between q₁ and q₂ (r₁ = 0.180 m).

Similarly, the force due to q₃ on q₂ can be calculated as:

F₂ = k × (q₃ × q₂) / r₃²

where r₃ is the distance between q₂ and q₃ (r₃= 0.230 m).

The direction of each force can be determined by the direction of the electric field due to each charge. Since q₁ and q₃ have opposite signs, their electric fields point in opposite directions. Therefore, the force due to q₁ points to the left and the force due to q₃ points to the right.

To find the net force, we need to add up the forces vectorially. Since the forces due to q₁ and q₃ are in opposite directions, we can subtract the magnitude of the force due to q₃ from the magnitude of the force due to q₁ to get the net force on q₂:

Fnet = F₁ - F₃

Substituting the values we get:

Fnet = k × (q₁ × q₂) / r₁² - k × (q₃ × q₂) / r₃²

Plugging in the values we get:

Fnet = (8.99 x 10⁹ Nm²/C²) × [(9.33 x 10⁻⁶ C) × (4.22 x 10⁻⁶ C) / (0.180 m)² - (-8.42 x 10⁻⁶ C) × (4.22 x 10⁻⁶ C) / (0.230 m)²]

Fnet = 1.07 x 10⁻² N

Therefore, the net force on q₂ is 1.07 x 10⁻² N, pointing to the left.

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A ball is launched from ground level with an initialupwards velocity of 20 m/s and an initial horizontalvelocity of 30 m/s. How far from its startingposition does the ball land assuming the ground is level?

Answers

Givens.

• The vertical initial velocity is 20 m/s.

,

• The horizontal initial velocity is 30 ms/s.

,

• The gravity is -9.8 m/s^2.

Use the following formula to find the horizontal reach of the projectile.

\(R=\frac{v^2_0\sin 2\theta}{g}\)

First, we need to find the initial speed using the components we already have.

\(\begin{gathered} v_0=\sqrt[]{v^2_x+v^2_y}=\sqrt[]{30^2+20^2}=\sqrt[]{900+400}=\sqrt[]{1300} \\ v_0\approx36(\frac{m}{s}) \end{gathered}\)

Now we need to find the direction of the initial velocity.

\(\begin{gathered} \theta=\tan ^{-1}(\frac{y}{x})=\tan ^{-1}(\frac{20}{30}) \\ \theta\approx33.69 \end{gathered}\)

Once we have the initial velocity and its direction, use the formula to find the horizontal reach.

\(\begin{gathered} R=\frac{(\sqrt[]{1300})^2\cdot\sin (2\cdot33.7)}{-9.8} \\ R=\frac{1300\cdot(-0.99)}{-9.8} \\ R=\frac{-1286.50}{-9.8} \\ R=131.28m \end{gathered}\)

Therefore, the horizontal reach is 131.28 meters, approximately.

Is a compound considered a pure substance?

Answers

Answer:

It depends on which compound you use carbon dioxide can be while helium will not but if you where to sum it up it would be use because simply most compounds are considered pure substance.

Explanation:

A person is 88 J of work lifting a grocery bag straight off the ground to a height of 1.7 m what is a grocery bags mass

Answers

Answer:

5.277 kg

Explanation:

Since the formula for work is W = F * d and we are given distance and work, the force on the grocery bag is 88 = F * 1.7 F = 88 / 1.7 = 51.765 N.

We also know that force follows the equation F = m * a. Since the constant gravitational acceleration on earth is 9.81 m / s^2, we can find the mass through 51.765 = m * 9.81 m = 51.765/9.81 = 5.277 kg

The "Screaming Swing" is a carnival ride that is - not surprisingly - a giant swing. It's actually two swings moving in opposite directions. At the bottom of its arc, a rider in one swing is moving at 34 m/s with respect to the ground in a 46- m -diameter circle. The rider in the other swing is moving in a similar circle at the same speed, but in the exact opposite direction. What is the acceleration, in m/s2 , that riders experience?

Answers

The acceleration, in m/s² , that riders experience is 50.3 m/s²

What is the acceleration, in m/s² , that riders experience?

Since the riders move in a circle, they undergo circular motion and will have a centripetal acceleration.

So, the centripetal acceleration, is given by a = v²/r where

v = speed of rider andr = radius of circle

Given that a rider in one swing is moving at 34 m/s with respect to the ground in a 46- m -diameter circle. We have that

v = speed of rider = 34 m/s and r = radius of circle = 46/2 = 23 m

So, substituting the values of the variables into the equation for the acceleration, we have

a = v²/r

a = (34 m/s)²/23 m

a = 1156 m²/s²/23 m

a = 50.26 m/s²

a ≅ 50.3 m/s²

So, the acceleration, in m/s² , that riders experience is 50.3 m/s²

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What do you mean by the density of ice is 920 kg/m3 ?

Answers

Explanation:

The density of ice is given by the mass/volume of a given amount of ice so what they simply mean is that when a particular cup filled with ice is weighed for it's mass and measured for it's volume and further divided by each other you are going to get 920 kilograms per meter cube

A ball is thrown 24 m/s into the air. How high does it go?
556.4 m
0 m
29.4 m
-556.4 m

Answers

Answer:

option c is correct

Explanation:

we know that

2as=vf^2-vi^2

vf=24 m/s

vi= 0 m/s

a=g= 9.8 m/s^2

s=vf^2-vi^2/2a

s=(24)²-(0)²/2*9.8

s=576/19.6

s=29.4 m

therefore option c is correct

Which statements describe independent assortment? Check all that apply. Independent assortment occurs during meiosis II. Independent assortment happens during fertilization. Independent assortment results in different combinations of genes in sex cells. Independent assortment makes offspring identical to their parents. Independent assortment occurs when chromosomes randomly line up in the middle of the cell.

Answers

Answer:

The CORRECT answer is:

C. Independent assortment results in different combinations of genes in sex cells.

E. Independent assortment occurs when chromosomes randomly line up in the middle of the cell.

The statements describe independent assortment are Independent assortment results in different combinations of genes in sex cells and  Independent assortment occurs when chromosomes randomly line up in the middle of the cell.

The correct options are C and E.

What is independent assortment?

The Principle of Independent Assortment depicts how various qualities autonomously separate from each other when regenerative cells create. Free combination of qualities and their comparing attributes was first seen by Gregor Mendel in 1865 during his investigations of hereditary qualities in pea plants.

So, Independent assortment results in different combinations of genes in sex cells.

Also, Independent assortment occurs when chromosomes randomly line up in the middle of the cell.

Thus, correct options are C and E.

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10. Refraction occurs...
A. only with light waves
B. at any, unpredictable time
C. when a wave changes speed
D. only at a wave front
E. All of the above

Answers

The answer is C! Good luck!

What is the average speed in mph for a car that travels for 5 hours and 20 minutes?

Answers

Answer: If you meant 5 miles in 20 minutes than it’s 1 mile in 5 minutes

Explanation:

The car's average speed is

0.1875 • (the number of miles it covered)

Some dragonflies splash down onto the surface of a lake to clean themselves. After this dunking, the dragonflies gain altitude, and then spin rapidly at about 1100 rpm to spray the water off their bodies. When the dragonflies do this "spin-dry," they tuck themselves into a "ball" with a moment of inertia of 2.0×10−7kg⋅m2 . How much energy must the dragonfly generate to spin itself at this rate?

Answers

The dragonfly must generate approximately 4.8 × 10^-4 Joules of energy to spin itself at a rate of 1100 rpm.

Start by converting the rotational speed from rpm (revolutions per minute) to rad/s (radians per second). Since 1 revolution is equal to 2π radians, we can use the conversion factor:

Angular speed (ω) = (1100 rpm) × (2π rad/1 min) × (1 min/60 s)

ω ≈ 115.28 rad/s

The moment of inertia (I) is given as 2.0 × 10^-7 kg⋅m².

Use the formula for rotational kinetic energy:

Rotational Kinetic Energy (KE_rot) = (1/2) I ω²

Substituting the given values:

KE_rot = (1/2) × (2.0 × 10^-7 kg⋅m²) × (115.28 rad/s)²

Calculate the value inside the parentheses:

KE_rot ≈ (1/2) × (2.0 × 10^-7 kg⋅m²) × (13274.28 rad²/s²)

KE_rot ≈ 1.331 × 10^-3 J

Round the result to the proper number of significant figures, which in this case is three, as indicated by the given moment of inertia.

KE_rot ≈ 4.8 × 10^-4 J

Therefore, the dragonfly must generate approximately 4.8 × 10^-4 Joules of energy to spin itself at a rate of 1100 rpm.

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what are the effects of cooling on the physical properties of a substance​

Answers

When the liquid cools down, it loses heat energy.

What is the physical effect of cooling on liquid?

As the liquid cools, it loses heat energy. As a result, its particles slow down in movement and come closer to one another. Attractive forces begin to hold particles and the crystals of a solid form.

If water is cooled, it can change into ice. If ice is warmed, it can change into a liquid state. Heating a substance makes the molecules move very fast whereas cooling a substance makes the molecules move very slowly.

Heating a liquid increases the speed of the molecules present in it. An increase in the molecule's speed competes with the attraction between molecules and results in the molecules moving apart whereas Cooling a liquid decreases the movement of the molecules.

So we can conclude that the liquid cools down when it loses heat energy.

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In a local park, a pine cone falls off a tree branch (starting at rest) and falls to the ground. We will model the pine cone hitting the ground as if it is a mass going onto a spring (with the ground being a spring). The pine cone has a mass of 0.116 kg, and starts at a height of 7.90 m above the ground. The pine cone compresses the spring (ground) by 0.0148 m, briefly coming to rest at the bottom of its motion. (It then bounces, which is not part of the time period that we'll cover in this problem.) Assume that the pine cone, the Earth and the spring (ground) are a system, and that no net work is done by external forces to the system or by non-conservative forces. Note: these are the assumptions necessary to assume that mechanical energy is conserved. Label the initial time point as the start of the pine cone's drop, and the final time point as the moment when the pine cone is at rest with the spring as compressed as it will get.
1. What is the change in gravitational potential energy from the initial time point to the final time point? Hint: don't forget that the pine cone actually goes slightly below the height of most of the ground. Joules
2. What is the spring constant of the spring? N/m
3. Now, let's look at the time point when the pine cone is 4.24 meters above the ground. You can do this by assuming that this new time point becomes the final time point, and the spring is no longer in the problem. What is the magnitude of the pine cone's velocity at this time point? m/s

Answers

Answer:

1)) ΔU = -8.96 J, 2)    k = 8.18 10⁴ N / m, 3)  v = 8.47 m / s

Explanation:

For this exercise we will use conservation of energy.

Starting point. Point where the pineapple comes out

          Em₀ = U = m g h

where the reference frame is placed on the ground

Final point. Point where pineapple stops

          Em_f = K_e + U = ½ k y² + m g y

1) the change in gravitational potential energy is

           ΔU = U_f - U₀

           ΔU = m g y - m g h

           ΔU = mg (y-h)

         

let's calculate

            ΔU = 0.116 9.8 (0.0148 - 7.9)

            ΔU = -8.96 J

The negative sign indicates that the energy decreases

2) let's use energy conservation

             Em₀ = Em_f

             mg h = ½ k y² + mg y

             k = mg (h-y) \(\frac{2}{y^2}\)

             

let's calculate

             k = 0.116 9.8 (7.9 - 0.0148)    \(\frac{2}{0.0148^2}\)  

             k = 8.18 10⁴ N / m

3) we use the same starting point and as the end point we use this height (y₂ = 4.24 m)

             Em_{f2} = K + U = ½ m v² + mg y₂

             

energy is conserved

             Em₀ = Em_{f2}

              mgh = ½ m v² + m g y₂

              v =\(\sqrt{ 2g(h-y_2)}\)

let's calculate

              v = \(\sqrt{ 2 \ 9.8 \ (7.9-4.24)}\)

              v = 8.47 m / s

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