19. Two objects of equal masses collide head-on while moving in the opposite directions and join together. Show that the fractional loss of original KE of the objects is given by the 1 expression.
E=(1/2)+(V1V2/V1²+V2²)

Answers

Answer 1

Answer:

Explanation:

mass of each object = m

momentum conservation: mv₁ + mv₂ = 2mv, so v = (v₁ + v₂)/2

Initial KE = mv₁²/2 + mv₂²/2 = m(v₁² + v₂²)/2

final KE = (2m)v²/2 = m(v₁ + v₂)²/4

Change in KE = m(v₁² + v₂²)/2 - m(v₁ + v₂)²/4 = m(v₁ + v₂)²/4

= m(v₁² + v₂² + 2v₁v₂)/4 = (1/2) m(v₁² + v₂²)/2 + mv₁v₂/2

Fraction loss = change in KE / initial KE = 1/2 + v₁v₂/(v₁² + v₂²)


Related Questions

Define kinetic Energy and thermal energy. Describe what happens to each as the temperature of a substance is increases.

Answers

Explanation:

Kinetic energy is the energy by virtue of

object's motion whereas Thermal energy is

the internal energy of an object due to the

kinetic energy of its atoms.

On Increasing temperature, they both

increases

2.27 A gas is compressed from V1= 0.3 m3, p1=1 bar to V2= 0.1 m3, p2 =3 bar. The pressure and
the volume are related linearly during the process. For the gas, find the
work, in kJ.
2.29 A gas expands from an initial state where p1=500kPa and V1=0.1m3 to a state
end where p2= 100 kPa. The relationship between pressure and volume during the process is
pV=constant. Schematize the process in a p-V diagram and determine the work, in
kJ.

Answers

Answer:

-40 kJ

80 kJ

Explanation:

Work is equal to the area under the pressure vs volume graph.

W = ∫ᵥ₁ᵛ² P dV

2.27) Pressure and volume are linearly related.  When we graph P vs V, the area under the line is a trapezoid.  So the work is:

W = ½ (P₁ + P₂) (V₂ − V₁)

W = ½ (100 kPa + 300 kPa) (0.1 m³ − 0.3 m³)

W = -40 kJ

2.29) Pressure and volume are inversely proportional:

pV = k

The initial pressure and volume are 500 kPa and 0.1 m³.  So the constant is:

(500) (0.1) = k

k = 50

The final pressure is 100 kPa.  So the final volume is:

(100) V = 50

V = 0.5

The work is therefore:

W = ∫ᵥ₁ᵛ² P dV

W = ∫₀₁⁰⁵ (50/V) dV

W = 50 ln(V) |₀₁⁰⁵

W = 50 (ln 0.5 − ln 0.1)

W ≈ 80 kJ

Think about the way your body works when you eat an ice cream cone. Provide an explanation of how organs are working together as a system to help you eat the cone. Describe one organ system and how its parts combine to get your body nutrition from the food.

PLZ HELP

Answers

Answer:

Explanation:

BAHAHAHAH karely omg HAHAHA un idke

A ball is launched directly upward and ultimately reaches a height of 40 ft on a day when the wind is gusting in different directions. From the time the ball is launched until it reaches a height of 20 ft off the ground the wind is blowing at constant 20 mph to the right. From that time to the time the ball has reached the top and traveled back down to a height of 20 ft the wind is blowing at constant 20 mph to the left. As it travels from 20 ft high back to the ground the wind again blows at a constant 20 mph to the right, where will the ball land?

Answers

Recall that

v² - u² = 2 ax

where u and v are initial and final velocities, respectively; a is acceleration; and ∆x is the change in position.

We can use this formula to determine the launch speed of the ball. In the vertical direction, the ball has acceleration g in the downward direction, where g = 32.2 ft/s². At its maximum height, the ball has 0 vertical velocity. So we have

0² - u² = 2 (-32.2 ft/s²) (40 ft)

==>  u ≈ 50.75 ft/s

Now, the ball's height y at time t is given by

y = u t - 1/2 g t²

Find at which time t the ball covers the first 20 ft of its trajectory:

20 ft = (50.75 ft/s) t - 1/2 g t²

==>  t ≈ 0.462 s

(there is a second solution, t ≈ 2.69 s, which corresponds to the time it takes for the ball to return to this height as it's falling back down)

During this first interval, the ball's horizontal position x is

x = (20 mph) t ≈ (29.33 ft/s) t

so that at the moment the ball reaches a height of 20 ft, it will have moved

x = (29.33 ft/s) (0.462 s) ≈ 13.5 ft

to the right. (So we've take the right to be positive and the left to be negative.)

In the upper half of its trajectory, when the wind changes direction, the ball's horizontal position is given by

x = 13.5 ft - (29.33 ft/s) t

Note that t = 0 here means we now take the ball's current position to be the "initial" one. So the time we found earlier for when the ball has a height of 20 ft as it's falling back down is actually t = 2.69 s - 0.462 s ≈ 2.23 s. At this point, the ball's horizontal position is

x = 13.5 ft - (29.33 ft/s) (2.69 s - 0.462 s) ≈ -51.8 ft

or about 51.8 ft to the left of where it started.

The wind changes direction again, so that the ball's position at time t is now

x = -51.8 ft + (29.33 ft/s) t

Solving y = 0 for t gives the time when the ball reaches the ground:

0 = (50.75 ft/s) t - 1/2 g t²

==>  t ≈ 3.15 s

Again, this is the time it takes for the ball to reach the ground since it was launched, while the position function takes t = 0 to refer to the moment the ball is 20 ft above the ground. So once it hits the ground, it will be

x = -51.8 ft + (29.33 ft/s) (3.15 s - 2.69 s) ≈ -38.3 ft

which means the ball lands on the ground about 38.3 ft to the left of where it started.

Two insulated copper wires of similar overall diameter have very different interiors. One wire possesses a solid core of copper, with a circular cross section of radius 1.53 mm. The other wire is composed of 19 strands of thin copper wire bundled together. Each strand has a circular cross section of radius 0.306 mm. The current density ???? in each wire is the same. ????=1750 A/m2 Two circles. One circle is solid, whereas the other contains 19 tightly packed smaller circles How much current does each wire carry? solid wire current: A stranded wire current: A The resistivity of copper is ????=1.69×10−8 Ω·m. What is the resistance of a 3.25 m length of each wire? solid wire resistance: Ω stranded wire resistance: Ω

Answers

Answer:

a

 Solid Wire     [tex]I  =   0.01237 \  A [/tex]      

  Stranded  Wire  [tex]I_2  =   0.00978 \  A [/tex]

b

  Solid Wire   [tex]R  = 0.0149 \ \Omega [/tex]

   Stranded  Wire  [tex]R_1  = 0.0189 \ \Omega [/tex]

Explanation:

Considering the first question

From the question we are told that

  The  radius of the first wire is  [tex]r_1  = 1.53 mm = 0.0015 \  m[/tex]

  The radius of  each strand is  [tex]r_0 =  0.306 \ mm =  0.000306 \ m[/tex]

  The current density in both wires is  [tex]J  =  1750 \  A/m^2[/tex]

Considering the first wire

     The  cross-sectional area of the first wire is

      [tex]A   = \pi  r^2[/tex]

= >  [tex]A   = 3.142 *  (0.0015)^2[/tex]

= >  [tex]A   = 7.0695 *10^{-6} \  m^2 [/tex]

Generally the current in the first wire is    

     [tex]I  =  J*A[/tex]

=>  [tex]I  =  1750*7.0695 *10^{-6}[/tex]

=>  [tex]I  =   0.01237 \  A [/tex]

Considering the second wire  wire

The  cross-sectional area of the second wire is

     [tex]A_1  =  19 *  \pi r^2[/tex]

=>     [tex]A_1  =  19 *3.142 *  (0.000306)^2[/tex]

=>  [tex]A_1  =  5.5899 *10^{-6} \  m^2[/tex]

Generally the current is  

      [tex]I_2  =  J  *  A_1[/tex]

=>    [tex]I_2  =   1750  *  5.5899 *10^{-6} [/tex]

=>    [tex]I_2  =   0.00978 \  A [/tex]

Considering question two  

 From the question we are told that

     Resistivity is  [tex]\rho  =  1.69* 10^{-8} \Omega \cdot m[/tex]

     The  length of each wire  is  [tex]l =  6.25 \  m[/tex]

Generally the resistance of the first wire is mathematically represented as

    [tex]R  =  \frac{\rho *  l  }{A}[/tex]

=> [tex]R  =  \frac{  1.69* 10^{-8} * 6.25 }{ 7.0695 *10^{-6} }[/tex]

=> [tex]R  = 0.0149 \ \Omega [/tex]

Generally the resistance of the first wire is mathematically represented as

    [tex]R_1  =  \frac{\rho *  l  }{A_1}[/tex]

=> [tex]R_1  =  \frac{  1.69* 10^{-8} * 6.25 }{5.5899 *10^{-6} }[/tex]

=> [tex]R_1  = 0.0189 \ \Omega [/tex]

1-4 help pls if u know it

Answers

Answer:

c,B,a,d i guess i m not sure it is the guessing

Assignment 1. Define Couple?

Answers

two individuals of the same sort considered together

The ratio of carbon-14 to nitrogen-14 is an artifact is 1:3. Given that half-life of carbon-14 is 5730years, how old is the artifact?

Answers

Answer:

9155 years old

Explanation:

We use the following expression for the decay of a substance:

[tex]N = N_0\,\,e^{-k*t}[/tex]

So we first estimate the value of k knowing that the half-life of the C14 is 5730 years:

[tex]N = N_0\,\,e^{-k*t}\\N_0/2=N_0\,\,e^{-k*5730}\\1/2 = e^{-k*5730}\\ln(1/2)=-k*5730\\k= 0.00012[/tex]

so, now we can estimate the age of the artifact by solving for"t" in the equation:

[tex]1/3=e^{-0.00012*t}\\ln(1/3)= -0.00012*t\\t=9155. 102[/tex]

which we can round to 9155 years old.

what is E=mc^2?
please explain..

Answers

Answer:

In physics, mass–energy equivalence is the principle that anything having mass has an equivalent amount of energy and vice ve

The statement "All Romans are Italians" means the same as "If you are Roman, then you are Italian"

True

False

Answers

False hope this helps you have a brainly day!!

Which of the following is a description of the Remote Associates Test (RAT)?

Answers

Answer:

The description is outlined throughout the clarification section following, and according to the given word.

Explanation:

Throughout the 1960s, Sarnoff Mednick created the RAT as a tool used for testing imaginative convergent thought. Through each RAT test query lists a set of terms, which demands that we have a single additional term that will tie any of the others around.  Those other words may also be related in something like a variety of ways, such as through creating a compound word or perhaps a semantic connexon.

Lana's class is studying the various kinds of energy found on a playground
Which of the following would be the BEST way to test for an equal transformation of energy on a playground?
СА
Using the slide, Lana could measure her kinetic energy when she was climbing up the ladder, measure her potential energy before she slid down, and her total energy used at the bottom of the slide. If the amount of potential
energy and kinetic energy added up to equal the total amount of energy used, it would show an equal transformation of energy
OB
Using the slido, Lana could measure her potential and kinetic energy sitting at the top of the slide, and then she could measure her kinetic and potential energy at various points while sliding to the bottom of the total value of
her potential energy and her kinetic energy were equal at every measuremont, it would show that there had been an equal transformation
C
Using the swing, Lana could measure her potential energy when she was sitting still on the swing, and she could measure her kinetic energy when the swing was in motion. If the kinetic energy was twice the amount of her
potential energy, it would show there had boon an equal transformation of potential energy to kinetic energy
D
Using the soesaw, Lana could measure her potential energy when she was in motion, and she could measure her kinetic energy when she was resting. If her kinetic and potential energy were equal, it would show that there
had been an equal transformation

Answers

If the amount of potential energy and kinetic energy added up to equal the total amount of energy used, it would show an equal transformation of energy.

What is Energy?

This can be defined as the ability or capacity to do work. The potential and kinetic energy equals the total amount of energy involved when Lana was on the playground.

This depicts an equal transformation of energy which is why the most appropriate choice in this scenario is option A.

Read more about Energy here  https://brainly.com/question/582060

22/22 is an even number greater than 20?

Answers

Answer:

yes

Explanation:

becuse it is an even  that is 2 number then 20

Answer:

Yes

Explanation:

It is because 22 is greater than 20

I will give you branilest
Mrs. LaCross leaves school and accidentally leaves her coffee mug on the roof of her car as shown in the picture below.



She was traveling at a constant pace until a student rushes in front of her not using the sidewalks and crosswalks and she had to slam on her brakes. What will happen to her coffee mug?
[ Select ]
a. The mug will move side by side
b. The mug will move backwards
c. The mug will move forward
d. The mug will not move

Answers

Answer:

the mug will moveforwards

what is the diffrence between scalar and vector physical quantites write all examples that you know about each of them​

Answers

Answer:

Scalar quantity is defined as the physical quantity with magnitude and no direction.

There are plenty of scalar quantity examples, some of the common examples are:

Mass

Speed

Distance

Time

Area

Volume

Density

Temperature

A vector quantity is defined as the physical quantity that has both direction as well as magnitude.

Vector quantity examples are many, some of them are given below:

Linear momentum

Acceleration

Displacement

Momentum

Angular velocity

Force

Electric field

Polarization

metal sphere having an excess of +5 elementary charges has a net electric charge of

Answers

Answer:

[tex]q=+8.01\cdot 10^{-19}\ coulombs[/tex]

Explanation:

Elementary charge

The elementary charge, denoted by the symbol e is the electric charge carried by a proton or, equivalently, the magnitude of a negative electric charge carried by an electron, which has charge −e.

The value of the elementary charge is a fundamental constant in physics:

[tex]\mathbf{e}=1.60217662 \cdot 10^{-19}\ coulombs[/tex]

If a metal sphere has an excess of +5 elementary charge, then it has a net charge of:

[tex]q=5*\mathbf{e}=+5*1.60217662 \cdot 10^{-19}\ coulombs[/tex]

[tex]\boxed{q=+8.01\cdot 10^{-19}\ coulombs}[/tex]

5
Find the resultant of the following four forces.
A= 25 N due north
B = 50 N due east
C= 30 N due west
D=40 N due south

Answers

25+50-30-40 = 0

north and east are positive directions, south and west are negative

hope this helps

also hope u enjoy a pic of my crush lol

Amoving object is in equilibrium. Which best describes the motion of the object if no forces change?
a. It will change directions.
b. It will slow down and stop.
c. It will maintain its state of motion.
d. It will speed up and then slow down.​

Answers

I think the answer is c

PLEASE PROVIDE EXPLANATION.

THANK YOU!!

Answers

Answer:

11,000 kg

(a) 11.2 m/s

(b) 1.6 m/s

Explanation:

Momentum is conserved.

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

(2200 kg) (60.0 km/h) + m (0 km/h) = (2200 kg) (10 km/h) + m (10 km/h)

132,000 kg km/h = 22,000 kg km/h + m (10 km/h)

110,000 kg km/h = m (10 km/h)

m = 11,000 kg

Momentum is conserved.

m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂

(m) (-v) + (2m) (5v) = (m) (v₁) + (2m) (v₂)

-mv + 10mv = m v₁ + 2m v₂

9mv = m (v₁ + 2 v₂)

9v = v₁ + 2 v₂

Since the collision is elastic, kinetic energy is also conserved.

½ m₁u₁² + ½ m₂u₂² = ½ m₁v₁² + ½ m₂v₂²

m₁u₁² + m₂u₂² = m₁v₁² + m₂v₂²

(m) (-v)² + (2m) (5v)² = m v₁² + (2m) v₂²

mv² + 50mv² = m v₁² + 2m v₂²

51mv² = m (v₁² + 2 v₂²)

51v² = v₁² + 2 v₂²

We know v = 1.60 m/s.  So the two equations are:

14.4 = v₁ + 2 v₂

130.56 = v₁² + 2 v₂²

Solve the system of equations using substitution.

130.56 = (14.4 − 2 v₂)² + 2 v₂²

130.56 = 207.36 − 57.6 v₂ + 4 v₂² + 2 v₂²

0 = 6 v₂² − 57.6 v₂ + 76.8

0 = v₂² − 9.6 v₂ + 12.8

v₂ = [ 9.6 ± √(9.6² − 4(1)(12.8)) ] / 2(1)

v₂ = 1.6 or 8

If v₂ = 1.6 m/s, then v₁ = 14.4 − 2 v₂ = 11.2 m/s.

If v₂ = 8 m/s, then v₁ = 14.4 − 2 v₂ = -1.6 m/s.

We know v₁ can't be -1.6 m/s, since that would mean puck A didn't change speeds after the collision.  Therefore, v₁ = 11.2 m/s and v₂ = 1.6 m/s.

how does energy transfer between objects​

Answers

Answer:

Object A runs into Object B. The force that object A has will transfer from Object A to Object B. But during this transfer you will loose some energy, therefore object B will not travel as fast.

Explanation:

Energy is transferred from one object to another when a reaction takes place

what are the applications of measurement?​

Answers

Things like thermometers, barometers, and water, gas, and electric meters, automotive speedometer and fuel gage, and compasses.

Question 4
5 pts
What is microscopic and floats in the ocean?
Plankton
Benthos
Nekton
© Fish

Answers

Answer:

Plankton is the correct answer I think

A cloth hat and large rock are dropped at at the same time on the moon

Answers

Answer:

What’s the question??

Explanation:

In a photoelectric effect experiment, light from a blue LED (wavelength = 405 nm) is directed onto a piece of sodium. It is observed that when V = 0.52 volts, the current measured at the collector drops to zero. What is the work function of the sodium? (a) 0.85 eV (b) 2.5 eV (c) 1.6 eV (d) 3.6 eV (e) 0.088 eV 100% What is the highest velocity of an ejected electron, just above the surface of the sodium? (a) 680000 m/s (b) 300000 m/s (c) 430000 m/s 100% Now we decrease the power of the LED, keeping the wavelength fixed. Which of the following statements is true? (a) The maximum velocity of any ejected electrons will decrease. (b) The minimum possible time to eject an electron (relative to when the LED is turned on) will increase.

Answers

Answer:

1. (b) 2.5 eV

2. (c) 430000 m/s

3. (a) The maximum velocity of any ejected electrons will decrease.  

Explanation:

1)

From Einstein's Photoelectric Equation:

hc/λ = K.E + ∅

∅ = hc/λ - K.E

∅ = hc/λ - eV

where,

e = charge on electron = 1.6 x 10⁻¹⁹ C

V = Stopping Potential = 0.52 volts

h = 6.625 x 10⁻³⁴ J.s

c = speed of light = 3 x 10⁸ m/s

λ = wavelength = 405 nm = 4.05 x 10⁻⁷ m

∅ = Work Function = ?

Therefore,

∅ = (6.625 x 10⁻³⁴ J.s)(3 x 10⁸ m/s)/(4.05 x 10⁻⁷ m) - (1.6 x 10⁻¹⁹ C)(0.52 volts)

∅ = 4.9 x 10⁻¹⁹ J - 0.832 x 10⁻¹⁹ J

∅ = (4.075 x 10⁻¹⁹ J)(1 eV)/(1.6 x 10⁻¹⁹ J)

∅ = 2.5 eV

therefore, correct answer is"

(b) 2.5 eV

2)

K.E = (1/2)mv² = eV

where,

m = mass of electron = 9.1 x 10⁻³¹ kg

v = speed = ?

therefore,

(1/2)(9.1 x 10⁻³¹ kg)v² = (1.6 x 10⁻¹⁹ C)(0.52 volts)

v = √(0.18 x 10¹² m²/s²)

v = 0.43 x 10⁶ m/s = 430000 m/s

Correct option is:

(c) 430000 m/s

3.

The decrease in power at constant wavelength means decrease in voltage, that results in the decrease of kinetic energy of electrons. So, correct option is:

(a) The maximum velocity of any ejected electrons will decrease.

If electrons are added to an object the object becomes
charge.
negative
positive
neutral
nothing happens

Answers

Answer:

It can be either, depending on how much and how you add the electrons

a strong inductive argument must have true premises

True

False

Answers

That is true imo not false

A block is 10cm long, 5cm wide and 2cm high and weighs 100g. What is the volume of the block? What is the density?

Answers

Answer:

1gm/cm^3

Explanation:

its the answer

If a car with a mass of 4000 kg is accelerating at a rate of 2 ms and hits a tree what force does it have

Answers

That depends on the car's speed at the moment of impact, and how long it takes to stop after the impact.

It is NOT 8,000N. That answer would come from a totally incorrect application of " F = m a " . 8,000 Newtons is what it takes to accelerate that car in the first place, long before it hits the tree.

Force can be described as either a pull or a push

Now when a body with mass and acceleration hits an object, we say a collision has taken place, hence there will be transfer of energy within the system

Give data

mass = 4000kg

acceleration = 2m/s^2

We know that force is given as

Force = mass x acceleration

Substitute our given data into the expression for force

Force = 4000 x 2Force = 8000N

For more information on force kindly visit

brainly.com/question/18038995

calculate the monentun pf 75 kg bicycle and boy who has ghe velocitg of 3m/s

Answers

Explanation:

n=75 kg

v=3m/s

m=n×v

m=75x3

m= 225n

) The square plates of a 5000-pF parallel-plate capacitor measure 50 mm by 50 mm and are separated by a dielectric that is 0.23 mm thickand totally fills the region between the plates. The voltage rating (the maximum safe voltage) of the capacitor is 400 V. What is the maximum energy that can be stored in this capacitor without damaging it

Answers

Answer:

4 x 10⁻⁴ J

Explanation:

C = 5000 pF, V = 400 V

Energy = CV²/2 = 5000 x 10⁻¹² x 400²/2 = 4 x 10⁻⁴ J

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