A roller coaster starts from rest at its highest point and then descends on its (frictionless) track. Its speed is 20 m/s when it reaches ground level. What was its speed when its height was half that of its starting point

Answers

Answer 1

Answer:

Approximately [tex]14\; {\rm m\cdot s^{-1}}[/tex].

Explanation:

The gravitational potential energy [tex]\text{GPE}[/tex] of this roller coaster is proportional to the height [tex]h[/tex] of the roller coaster.

The kinetic energy [tex]\text{KE}[/tex] of this roller coaster is proportional to the square of speed [tex]v[/tex].

The question states that the track is frictionless. Thus, during the descent, the [tex]\text{GPE}[/tex] of this roller coaster is turned into [tex]\text{KE}[/tex] without any energy loss.

When the roller coaster was at [tex](1/2)[/tex] of the the initial height, only[tex]1 - (1/2) = (1/2)[/tex] of the original [tex]\text{GPE}[/tex] was turned into [tex]\text{KE}[/tex]. The [tex]\text{KE}\![/tex] of this roller coaster at that height would be [tex]1 - (1/2) = (1/2)\![/tex] of the [tex]\text{KE}\!\![/tex] when the roller coaster is at the ground level.

The [tex]\text{KE}[/tex] of the roller coaster is proportional to [tex]v^{2}[/tex] (the square of speed [tex]v[/tex].) Thus, since the [tex]\text{KE}\![/tex] at [tex](1/2)[/tex] the initial height is [tex]1 - (1/2) = (1/2)\![/tex] the [tex]\text{KE}\!\![/tex] at the ground level, the [tex]v^{2}[/tex] at [tex](1/2)\![/tex] the initial height would also be [tex]1 - (1/2) = (1/2)\![/tex] the [tex]v^{2}\![/tex] at the ground level.

Since [tex]v = 20\; {\rm m\cdot s^{-1}}[/tex] at the ground level, [tex]v^{2} = (20\; {\rm m\cdot s^{-1}})^{2}[/tex] at the ground level. The [tex]v^{2}[/tex] at [tex](1/2)[/tex] the initial height would then be:

[tex](1 - (1/2))\times (20\; {\rm m\cdot s^{-1}})^{2}[/tex].

Thus, the speed [tex]v[/tex] at [tex](1/2)[/tex] the initial height would be:

[tex]\begin{aligned}& \sqrt{(1 - (1/2))\times (20\; {\rm m\cdot s^{-1}})^{2}} \\ =\; & \sqrt{\frac{1}{2} \times (20\; {\rm m\cdot s^{-1}})^{2}} \\ =\; & \sqrt{200}\; {\rm m\cdot s^{-1}} \\ \approx\; & 14\; {\rm m\cdot s^{-1}}\end{aligned}[/tex].


Related Questions

Which space mission visited the moon several times?.

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NASA’s Apollo Mission was the ONLY mission which landed humans on the moon, which it did six times. I’m not very sure about several times, though. Hope this helped!

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A 50.0g sample of C-14 has decayed leaving only 3.1g. How much time has elapsed since the original sample was weighed? The half life of C-14 is 5730 years

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A disk with radius of 0. 5 m is free to rotate around its center without friction. A string wrapped around the disk is pulled, as shown above, exerting a 2 n force tangent to the edge of the disk for 1 s. If the disk starts from rest, what is its angular speed after 1 s?.

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For a disk with radius of 0. 5 m is free to rotate around its center without friction,  its angular speed after 1 s is mathematically given as

w=1/(0.5M π^2)

What is its angular speed after 1 s?

Generally, the equation for the Moment of inertia  is mathematically given as

I=0.5mx^2

Where

radius = 0. 5 m

Mass=M

Force on edge=F=2N

Time =t

Hence, Torque

T=0.5*2=1.0Nm

Where

T=Ia

w=W0+at

Hence

W=1/I

In conclusion,  angular speed after 1 s

I=0.5M π^2

w=1/(0.5M π^2)

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Unpolarized light of intensity Io is incident on a stack of 7 polarizing filters, each with its axis rotated 17°cw with respect to the previous filter. Find the ratio between light intensity emerges from the last filter and unpolarized light of intensity Io. It/Io= _________

Answers

The ratio of the intensity between light intensity that emerges from the last filter and unpolarized light of intensity, I₀ is It/I₀ = 0.2925

To answer the question, we need to know what polarization of light is.

What is polarization of light?

This is when the electric field vector of light is oscillating in one plane.

Now for light of intensity I' which is initially unpolarized, its intensity after polarization is I = 1/2I'.Also, for light initially polarized, its intensity after polarization is I"' = I"cos²Ф where Ф is the angle between the initial direction and the direction of polarization.Intensity of light through each polarized filter

Given that we have 7 polarizing filters, each rotated 17° cw with respect to the previous filter.

So, since the light is initially unpolarized,

The intensity through the first polarizing filter is I₁ = 1/2I₀ where I₀ is the initial intensity.The intensity through the second polarizing filter is I₂ = I₁cos²17°= 1/2I₀cos²17°The intensity through the third polarizing filter is I₃ = I₂cos²17° = 1/2I₀cos⁴17°The intensity through the fourth polarizing filter is I₄ = I₃cos²17° = 1/2I₀cos⁶17°The intensity through the fifth polarizing filter is I₅ = I₄cos²17° = 1/2I₀cos⁸17°The intensity through the sixth polarizing filter is I₆ = I₅cos²17° = 1/2I₀cos¹⁰17°The intensity through the seventh polarizing filter is I₇ = I₆cos²17° = 1/2I₀cos¹²17°.The ratio of the intensity between light intensity that emerges from the last filter and unpolarized light of intensity

Since I₇ is the last intensity I₇ = It = 1/2I₀cos¹²17°.

So, It/I₀ = 1/2cos¹²17°

= 1/2(0.9563)¹²

= 1/2 × 0.5850

= 0.2925

So, the ratio of the intensity between light intensity that emerges from the last filter and unpolarized light of intensity, I₀ is It/I₀ = 0.2925

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Examine the distance-time graph.

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Answer:

A

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Answer:

The two helicopters have the same kinetic energy, but a different GPE, or gravitational potential energy.

Explanation:

Which sound wave has higher pitch
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Answer:

Below one has higher pitchLoudness is roughly the same

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Answer: The galaxy's bulge

Explanation:

You are making photoelectric measurements on an electrode of an unknown metal. With zero potential difference applied by the battery, you shine various freqencies of light on the cathode. You detect a small photocurrent for light with wavelength up to 451 nm. What metal is the electrode made of

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Since you detect a small photocurrent for light with wavelength up to 451 nm, the metal the electrode is made of is Sodium.

To solve the question, we need to know what work function is.

What is work function of a metal?

This is the minimum energy at which an electron will be emitted from the surface of a metal.

Since a small photocurrent is detected when ligh of wavelength up to 451 nm is applied with a zero potential difference applied, this is the threshold wavelength which gives the work function of the metal.

So, work function Ф = hc/λ where

h = Planck's constant = 6.63 × 10⁻³⁴ Js, c = speed of light = 3 × 10⁸ m/s and λ = wavelength of light = 451 nm = 451 × 10⁻⁹ m

Substituting the values of the variables into the equation, we have

Ф = hc/λ

Ф = 6.63 × 10⁻³⁴ Js × 3 × 10⁸ m/s ÷ 451 × 10⁻⁹ m

Ф = 19.89 × 10⁻³⁴ × 10⁸ Jm ÷ 451 × 10⁻⁹ m

Ф = 0.0441 × 10⁻¹⁷ J

Ф = 4.41 × 10⁻¹⁹ J

Since 1 eV = 1.602 10⁻¹⁹ J,

Ф = 4.41 × 10⁻¹⁹ J × 1 eV/1.602 10⁻¹⁹ J

Ф = 2.753 eV

From tables, the metal with the work function closet to this value is Sodium.

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An object is sliding down an inclined plane at constant velocity. If the coefficient of kinetic friction between the object and the plane is , what is the angle of the plane?

Answers

The angle of the plane will be 26.57°.Angle of plane is the angle of elevaton at which the body exciute motion on the inclined plane.

What is kinetic friction?

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Force on an object due to the gravitational force will be;

[tex]\rm F = mg[/tex]

For the inclined plane the balance forces will be ;

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Hence the angle of the plane will be 26.57°.

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Which are thought to have formed farthest from the sun?.

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The answer is Kuiper belt comets and in the Kuiper belt there are bits of rock and ice, comets and dwarf planets in the Kuiper Belt. Besides Pluto and a bunch of comets, other interesting Kuiper Belt Objects are Eris, Makemake and Haumea.

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Answer:

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Explanation:

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A ray of light passing through centre of curvature of a concave mirror is incident on its reflecting surface. What is the angle of incidence and reflection of this ray of light?

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The ray of light passes through the center of curvature of a concave mirror it strikes the mirror along the normal ray It incidences on to the mirror at an angle of 90 degrees. The angle of reflection is 90 degrees as well because the angle of reflection and the angel of incidence are the same.
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A system is heated with 134 J of energy and, at the same time, the system expands, doing 89 J of work. What is the change in internal energy of the system, in Joules

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The change in internal energy of the system after the heat is added and the system expands doing work to the surrounding is 45 J.

Change in internal energy of the system

The change in internal energy of the system is determined by applying the first law of thermodynamics as shown below;

ΔU = q - w

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ΔU = 134 J - 89 J

ΔU = 45 J

Thus, the change in internal energy of the system after the heat is added and the system expands doing work to the surrounding is 45 J.

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What is the difference between synchronous and asynchronous?.

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Synchronous communication are phone calls or video meetings. Asynchronous communication happens when information can be exchanged independent of time. It doesn't require the recipient's immediate attention, allowing them to respond to the message at their convenience.

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Answer:synchronous communications are scheduled, real-time interactions by phone, video, or in-person. Asynchronous communication happens on your own time and doesn't need scheduling.

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In straight line path, magnitude of velocity is equal to​

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Acceleration

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The particle is moving in a straight line. That means there’s no change in the path of the particle in the entire trip. It is moving with constant acceleration, meaning the particle doesn’t change its acceleration at all. The acceleration direction is in the same direction of instantaneous velocity

Magnitude of velocity is always equal to SPEED. On any kind of path.
On a straight-line path, magnitude of displacement is equal to distance.

What is the net force that acts on a 5 kg object accelerating at 2m/s

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Answer:

10 N

Explanation:

I assume there is no friction and we are only worrying about the horizontal direction. If so we use the formula F=MA to get F= 2 * 5 = 10 N

F=ma
5x2 = 10N

We use newton’s second rule , to find the force exerted on any object, knowing the rules of newton which are 3 rules are very important in physics.

What is the relationship between frequency and wavelength?

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Answer:

Frequency and wavelength are inversely proportional to each other. The wave with the greatest frequency has the shortest wavelength. Twice the frequency means one-half the wavelength.

Explanation:

Three examples of good hypotheticals

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Answer:

here are some of my favorites

Explanation:

if the world was ending, what would you do?

if you had super powers. what would they be?

if we could go to the moon, would you?

Answer:

If Life was a human, how would you treat him/her?If death was a god would you praise him?And If wishes were dead, would you bring them back alive?

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All masses cannot be measured in kilogram, why ?​

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Answer:

We cannot measure all masses in kg, because there are very small quantities like 1gm nd even smaller, and this will not be an accurate measurement in Kg.

A go-cart is rolling down a hill at 15m/s. If it has 85J of kinetic energy. what is the mass of the go-cart?

0.76kg
0.87kg
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Answer:

the third one

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When the reflection of an object is seen in a flat mirror, the image is.

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Answer:

the image is actually appearing behind the mirror, and not in the mirror.

Energy is the capacity to do work or
produce a change. Energy of position is
called potential energy. Energy of motion
is called kinetic energy.
Which situation best illustrates potential
energy being converted into kinetic
energy?
(1) a baseball landing on the ground
(2) a car coming around a corner
(3) turning off an electric lamp
(4) an apple falling from an apple tree
(5) a jogger running in a race

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Answer:

4

Explanation:

Apple initially has Potential energy due to it's height and mass

  as it falls this PE is converted to KE

An apple falling from an apple tree illustrates potential energy being converted into kinetic energy. So, the correct option is (D).

What is Potential and Kinetic Energy?

Kinetic energy is a type of energy which is possessed by an object due to its motion while Potential energy is the type of energy possessed by an object due to its position or state.

While kinetic energy is relative to the position of other objects in its environment, potential energy is completely independent of its environment.

Kinetic energy can be transferred from one moving object to another while potential energy cannot be transferred. The formula of Kinetic energy is [tex]1/2 mv^2[/tex] while the formula of Potential energy is mgh where m is the mass, v is the velocity, h is the height of an object and g is the acceleration due to gravity. S.I. unit of both is Joules (J). In the given information, the apple which is on the tree is in rest mode i.e. potential energy falls from the tree, changing its motion i.e. kinetic energy.

Thus, an apple falling from an apple tree illustrates potential energy being converted into kinetic energy. So, the correct option is (D).

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Which formula can be used to solve problems related to the first law of thermodynamics? q = w u q = u – deltaw q = u w q = u – w

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"Q = ΔU + W" is the equation is used to solve the questions related to "First law of thermodynamics".

What is the first law of thermodyanamics?

"First law of thermodynamics" states that "energy" neither created nor destroyed, but it can transfer from "one form of energy" to "another form of energy".

This "First law of thermodynamics" is also called as "law of conversation of energy". The formula for "First law of thermodynamics" of a system is that "change in internal energy of a system" is same as the difference of "heat energy" flows across the " boundaries of a system" and the "work done" on the system.

ΔU = Q - W

Q = ΔU + W

Where, "ΔU" is "change in internal energy", "Q" is "heat transferred and "W" is "work done.

Hence "Q = ΔU + W" is the equation is used to solve the questions related to "First law of thermodynamics".

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Which describe the image formed by the convex
mirror? Check all that apply.
-real
-virtual
-inverted
-upright
-smaller
-larger

Answers

Answer:

- Virtual

- Upright

- Smaller

Explanation:

I just did it on Edg22 and I got it correct :D

Answer:

see  the  picture

Explanation:

What were two reasons that the Krystal Beslanowitch case was finally closed?

Answers

Answer:

1. Police Weren't Able To Find Any Real Leads

2. They Didn't Find Any Clues To The Killer Until 18 Years Later

Explanation:

It was unknown at the time, but it would go on to take 18 years for her killer to be arrested and tried for her death. The initial case went on from 1995 to 1997 but ended up closing when the police department was unable to find any real leads.

a toy airplane takes off and flies for a distance of 34 meters at an angle of 26 degrees above the horizontal. what is its altitude when it has flown this distance?

Answers

Answer:

Explanation:

14.9m

The altitude when the airplane flies a distance of 34 m is equal to 14.9 m.

What is the distance?

The distance of an object can be demonstrated as the total length traveled by an object. The distance can be defined as a scalar parameter as it has magnitude, not direction. The distance by an object is always positive (+ve), it can never be zero.

Given, the airplane traveled the distance, BC = 34m as shown in the attached diagram, below:

The angle of the path with horizontal, θ = 26°

From the right angle triangle ΔCBA, we can calculate the BC:

Sin θ = BC/AC

Sin 26° = x/34

x = sin 26° ×34

x = 0.438 × 34

x = 14.9 m

Therefore, the altitude when an airplane has flown this distance is 14.9 m.

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find the work done by the engine of a car which moves at an acceleration of 3 m / s2 for 8s. the mass of the car is 1400 kg, while the coefficient of fecundation of its wheels with the road is 0.03.​

Answers

Explanation:

so that u multiple in this formula

Answer:

362.88 kJ

Explanation:

Given

a = 3 m/s²t = 8 sm = 1400 kgμ(k) = 0.03

Finding Displacement

S = ut + 1/2at²S = 0 + 1/2(3)(8)²S = 32(3) = 96 m

Finding Net Force

Applied Force (F) = ma = 1400 x 3 = 4200 NFriction Force (f) = μmg = 0.03 x 1400 x 10 = 420 NNet Force = F - f = 4200 - 420 = 3780 N

Work Done

W = FS = 3780 N x 96 mW = 362880 JW = 362.88 kJ
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