A car equipped with a massless spring in front collides with a stationary car as shown in the diagram. The mass of the incoming car is three times the mass of the target car. While the spring is being compressed, the cars are moving closer together, and while it is expanding they are moving farther apart, but at the instant that the spring is fully compressed, they have no relative motion, which means they are moving at the same speed. At this instant, the cars are moving with a speed of 2.4 m/s.
(a) Find the speed of the incoming car before the collision.
(b) Find the fraction of the system’s energy that is stored in the spring when
it is fully compressed.
(c) Find the final speed and direfction for both cars after the spring expands and the cars separate.

Answers

Answer 1

Answer:

Explanation:

Let m be target car mass

a)

conservation of momentum

(3m)u + m(0) = (3m + m)(2.4)

               3u = 4(2.4)

                u = 3.2 m/s

b)

system energy is originally in the striking car as kinetic energy

KE = ½(3m)3.2² = 15.36m J

at full compression, kinetic energy is

½(3m + m)2.4² = 11.52m J

so spring potential energy fraction of total energy is

(15.36 - 11.52)/15.36 = 0.25 or 25%

c)

The center of mass (CoM) is moving at 2.4 m/s

The CoM sees the larger mass car approach at

3.2 - 2.4 = 0.8 m/s and will see it depart at - 0.8 m/s

so a ground based observer would see it moving at

v₁ = 2.4 + -0.8 = 1.6 m/s in its original direction

The CoM sees the smaller mass car approach at

0 - 2.4 = -2.4 m/s and will see it depart at + 2.4 m/s

so a ground based observer would see it moving at

v₂ = 2.4 + 2.4 = 4.8 m/s in its original direction of the larger car

so the relative velocity of approach at 3.2 - 0 = 3.2 m/s

equals the relative velocity of departure at 4.8 - 1.6 = 3.2 m/s

checks.


Related Questions

a force is something that ___ an object to ____

Answers

Answer:

which can cause an object with mass to change its volocity

What s the kinetic energy of a 0.100 kg baseball thrown at 20.0 m/s?

1: 40.0 J
2: 1.00 J
3: 2.00 J
4; 20.0 J
5: 4.00 J

Answers

Answer:

KE = ½mv² = ½(0.100)20.0² = 20.0 J

Explanation:

i really need help with this. cant anyone help me?

Answers

(A)

Explanation:

The number of atoms for each element on the left side must equal that on the right side. Only (A) satisfies that condition. The other other choices have mismatching number of atoms on either side.

I need HELP ASAP please!!!

Answers

Answer: A

Explanation:i took this one

no links never ever in the world give me a link just answer now without links What is the lithosphere? please write a full paragraph

Answers

Answer:

The lithosphere is the Earth's stable outer layer. The lithosphere is made from the brittle top mantle and the crust, which are the Earth's outermost layers. The atmosphere above it and the asthenosphere (another issue of the top mantle) underneath it define its limitations. even though the rocks of the lithosphere are nevertheless taken into consideration elastic, they may be not viscous. The asthenosphere is viscous, and the lithosphere-asthenosphere boundary (LAB) is the component in which geologists and rheologists—scientists who study the drift of depend—mark the difference in ductility among the 2 layers of the top mantle. Ductility measures a strong cloth’s ability to deform or stretch under strain. The lithosphere is a long way less ductile than the asthenosphere.

Explanation:

Plagarism checked, 100% unique [I think, if not sorryyyyeeeeee]

Hope this helps!

Byeeee have a nice day

A 100 Hz sound wave is traveling through the air. If we increase the frequency to 200 Hz, this will _____ the wavelength.

Answers

Answer:

reduce

Explanation:

It will reduce the wavelenth

How are the parts of birds and fish similar in structure and function?

Answers

Answer:

Birds and fish both have a backbone structure, which makes them structurally and functionally similar.

Explanation:

Suppose an object is traveling in a circle of radius 10 m. if the object has a period of 6 s, what is its orbital speed (in m/s)

Answers

The orbital speed of the object moving around the circle is 10.5 m/s

Speed is the ratio of total distance to total time taken. Speed is given by:

Speed = distance / time

Given that the object is traveling in a circle of radius 10 m. The distance along the circle is:

Distance along circle = 2π * radius = 2π * 10 m = 62.83 m

The orbital speed = distance / time = 62.83 m / 6s = 10.5 m/s

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Why did the physicist conclude that cats can be either liquid or solid?

Answers

Answer:

Explanation:

https://www.science.org/content/article/cats-behave-liquids-tampons-play-music-and-other-advances-honored-ig-nobel-prizes

Answer:

Liquid or Both

Explanation:

Cats exist in their own three states of matter: loaf, cinnamon roll, and liquid. The last category is certainly the most confusing because cats should be solids — and of course, they can be.

3. How do you record your score in the 3-Minute Step Test? A record the 60-second heart rate before activity B. record the 30-second heart rate after the activity C. record the 60-second heart rate after the activity D. record the 60-second heart rate during7 the activity ?? plss po nid ko ngayon​ plsss free piont makakasagot neto

Answers

Answer:

d

Explanation:

you record it during the test

If the gas was instead in a cylinder with a floating, massless, frictionless piston, what would the volume of the gas be (in liters) at STP

Answers

The volume of the gas at standard temperature and pressure (STP) is 1,239.2 L.

The given parameters;

volume of the gas, V₁ = 9.5 Lpressure of the gas, P₁ = 140 atmtemperature of the gas, T₁ = 20 ⁰C = 273 + 20 = 293 Kpressure of gas at standard condition, P = 1 atmtemperature of gas at standard condition, T = 0⁰C = 273 K

The volume of the gas at standard condition is calculated by applying general gas law as shown below;

[tex]\frac{PV}{T} = \frac{P_1V_1}{T_1} \\\\V = \frac{P_1V_1T}{T_1P} \\\\V = \frac{140 \times 9.5 \times 273}{293 \times 1} \\\\V = 1,239.2 \ L[/tex]

Thus, the volume of the gas at standard temperature and pressure (STP) is 1,239.2 L.

"Your question is not complete, it seems be missing the following information;"

A compressed air tank carried by scuba divers has a volume of 9.5 L and a pressure of 140 atm at 20∘C.

If the gas was instead in a cylinder with a floating, massless, frictionless piston, what would the volume of the gas be (in liters) at STP.

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im board lolololololololololol​

Answers

Answer:

noice me too U n U

Explanation:

Hello, I wanted an answer from a mathematician. The number 1.04 is closer to the number 1, 2, 1.25 or 1.5.

Answers

Answer:

Explanation:

Of the 4 numbers given, the answer is 1 or A

If you take the absolute value of abs(1 - 1.04) you get 0.04.

(2 - 1.04) = 0.96

1.25 - 1.04 = .21

1.5 - 1.04 = 0.46

The last three are all larger than 0.04

Note: absolute value means the positive difference between 2 numbers (even  though it is negative). If it is negative, absolute value makes it positive.

3. A ferry boat is 4.0 m wide and 6.0 m long. When a truck pulls onto it, the boat sinks 4.00 cm in the water. What is the weight of the truck?

Answers

Answer:

Explanation:

The weight of the truck will equal the weight of the displaced water.

Assuming fresh water and that the sides of the ferry are vertical,

The volume of the water displaced is

6.00(4.00)(0.0400) = 0.960 m³

that volume of water weighs

0.960 m³(1000 kg/m³)(9.81 N/kg) = 9,417.6 = 9.42 kN

Including reaction time, the stopping distance is more than 20 feet at 10 miles per hour, at 20 miles per hour it will be about:
30 feet
63 feet
40 feet
75 feet

Answers

Answer:

A. 30 feet

Explanation:

Including reaction time, the stopping distance is more than 20 feet at 10 miles per hour, at 20 miles per hour it will be about 63 feet. Option B is correct.

What is speed?

Speed is defined as the rate of change of the distance or the height attained. it is a time-based quantity.

Given conditions;

10 miles per hour ⇒ 20 feet

1 mile per hour ⇒ 2 feet

20 miles per hour ⇒ 20 × 2 feet

20 miles per hour ⇒ 20 × 2 feet

20 miles per hour ⇒40 feet

If the stopping distance is more than 20 feet at 10 miles per hour at 20 miles per hour it must be more than 40 feet.So that the correct answer is 63 feet.

Hence option B is correct.

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The reaction is at dynamic equilibrium.
N2 + 3H2 = 2NH3
Which statement is correct?
(1 point)
a. The solution has the same concentrations of nitrogen gas and ammonia.
b. Nitrogen and hydrogen combine at the same rate that ammonia breaks down.
c. The solution has the same concentrations of nitrogen and hydrogen gases.
d. Both directions of the reaction have stopped.

Answers

Answer:

Nitrogen and hydrogen combine at the same rate that ammonia breaks down.

Explanation:

If 8.90 kg of ice at -5.00°C is added to 12.0 kg of water at 15°C, compute the final temperature.
(in deg C)

How much ice remains, if any? (in Kg)

Answers

Answer:

6.93 kg

Explanation:

m1 = 8.90 kg

T1 = -5°C

m2 = 12 kg

T2 = 15°C

constant needed:

c (ice) = 2100 J/kg °C

c (water) = 4200 J/kg °C

L (Latent Heat) = 336 000 J/kg

Black Principle

Q (release) = Q (absorbs)

Q (release) max = m2 c(water) ∆T2

Q (release) max = 12 x 4200 x (15-0)

Q (release) max = 756 000 J

Q (absorbs) = m1 c(ice) ∆T1 + m1 L

Q (absorbs) = 8.9 x 2100 x (0-(-5)) + 8.9 x 336 000

Q (absorbs) = 93 450 + 2 990 400 = 3 083 850 J

since Q (absorbs) is much much bigger than Q (release), only a few litlle ice melting. So we need to see how much ice melting and how many left.

Q (release) - Q (absorbs) ice -5°C to ice 0°C = 756000 - 93450 = 662550

mass of melting Ice

Q (absorbs) melting ice = m(melting) L

662 550 = m(melting x 336 000

m (melting) = 662 500/336 000

m (melting) = 1.977 kg

so the ice remains is 8.90 - 1.97 = 6.93 kg

cells science crossword

Answers

where's the crossword?

d. The soccer player accelerates from rest at a rate of 3.1 m/s2. How far does he
run in 1.5 seconds? (1 point)

Answers

Answer:

= 6.975 m

Explanation:

3.1 m = 1 s2

? = 2.25 s2

(3.1 * 2.25)/1

= 6.975m

A hiker is at the bottom of a canyon facing the canyon wall closest to her. She is 280.5 meters from the wall and the sound of her voice travels at 340 m/s at that location. How long after she shouts will she hear her echo? (Be careful to consider why echoes happen.)

Answers

Answer:

4.80 seconds

Explanation:

The velocity of sound is obtained from;

V= 2d/t

Where;

V= velocity of sound = 329.2 ms-1

d= distance from the wall = 790.5 m

t= time = the unknown

t= 2d/V

t= 2 × 790.5/ 329.2

t= 4.80 seconds

The time is taken by the sound to reach the hiker will be  t= 4.80 seconds

What is sound velocity?

The sound velocity is defined as the distance traveled by the sound wave in a particular direction with respect to time.

The velocity of sound  is given by the formula:

[tex]V=\dfrac{2d}{t}[/tex]

Here;

V= velocity of sound = 329.2  [tex]\frac{m}{s^2}[/tex]

d= distance from the wall = 790.5 m

t= time = the unknown

The time will be calculated as:

[tex]t=\dfrac{2d}{V}[/tex]

[tex]t=\dfrac{2\times 790.5}{329.2}[/tex]

[tex]t=4.80\ seconds[/tex]

Hence the time is taken by the sound to reach the hiker will be  t= 4.80 seconds

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The speed of a motorcycle changed from 5m/s to 20m/s the ratio of initial and final kinetic energy is?

Answers

Answer:

Explanation:

½m5² / ½m20² = 25/400 = 1/16 = 0.0625

The inclined plane in the figure above has two sections of equal length and different roughness. The dashed line shows where section 1 ends and section 2 begins. A block of M is placed at different locations on the incline. The coefficients of kinetic and static friction between the block and each section are shown in the table below.

If the block is at rest on section 1 of the incline, what is the magnitude of the force of static friction exerted on the block by the incline?

Answers

The static friction exerted on the block by the incline is [tex]\mu _ s _1 Mgcos \ \theta[/tex].

The given parameters;

mass of the block, = Mcoefficient of static friction in section 1, = [tex]\mu_s_1[/tex]angle of inclination of the plane, = θ

The normal force on the block is calculated as follows;

Fₙ = Mgcosθ

The static friction exerted on the block by the incline is calculated as follows;

[tex]F_s = \mu_s F_n\\\\F_s = \mu _s_1(Mg cos\ \theta)\\\\F_s = \mu _s_1 Mgcos\ \theta[/tex]

Thus, the static friction exerted on the block by the incline is [tex]\mu _ s _1 Mgcos \ \theta[/tex]

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please answer ASAP .
a body slides down an inclined plane which makes an angle of 30° with the horizontal, neglecting friction. calculate the velocity of the body after sliding 10 m from rest​

Answers

Answer:

Explanation:

a = gsinθ

a = 9.8sin30

a = 4.9 m/s²

v² = u² + 2as

v² = 0² + 2(4.9)(10)

v² = 98

v = √98 = 9.8994949...

v = 9.9 m/s

The chart shows data for a moving object.
Which conclusion is best supported by the information
in the chart?
Time (s)
Velocity (m/s)
2
4
6
8
8
8
O The object has negative displacement.
O The object has negative acceleration.
O The object does not have displacement
O The object is not accelerating
Mark this and return
Save and Exit
Next
Submit

Answers

Answer:

the object is not accelerating

car accelerates at a rate of 4.00 m/s?. How long will it take the car to speed up from 20 m/s to 50 m/s?

Answers

The distance that will take the car to speed yup from 20m/s to 50m/s is 262.5 meters

The first step is to write out the parameters given in the question are

acceleration= 4

initial velocity= 20

final velocity= 50

The distance can be calculated as follows

V²= U² + 2as

50²= 20² + 2(4)(s)

2500= 400= 8s

2500-400= 8s

2100= 8s

s= 2100/8

s= 262.5 meters

Hence the distance is 262.5 meters

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From the definition of acceleration, the time it will take the car to speed up is 7.5 seconds

Given that a car accelerates at a rate of 4.00 m/s^2. To calculate how long it will take the car to speed up from 20 m/s to 50 m/s, let us first mark out the needful parameters.

Acceleration a = 4 m/[tex]s^{2}[/tex]

Initial velocity U = 20 m/s

Final Velocity V = 50 m/s

Time t = ?

From the definition of acceleration, acceleration is the rate of change of velocity. That is,

a = (V - U)/ t

Substitute all the parameters into the formula above.

4 = ( 50 - 20) / t

Cross multiply

4t = 30

Make t the subject of formula

t = 30/4

t = 7.5 t

Therefore, the time it will take the car to speed up is 7.5 seconds

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A steam pipe is covered with 1.50-cm thick insulating material of thermal conductivity of 0.200 cal/cm · °C · s. How much energy is lost every second when the steam is at 195°C and the surrounding air is at 20.0°C? The pipe has a circumference of 800 cm and a length of 40.0 m. Neglect losses through the ends of the pipe.

Answers

This question involves the concepts of Fourier's law of heat conduction and heat loss per unit time.

The heat energy loss per second is "3.12 x 10⁸ W".

Applying Fourier's Law of Heat Conduction here, we get:

[tex]Q = -kA\frac{\Delta T}{\Delta x}[/tex]

where,

Q = heat energy loss per unit time = ?

k = thermal conductivity = 0.2 cal/cm.°C.s [tex](\frac{4.184\ J}{1\ cal})(\frac{100\ cm}{1\ m})[/tex] =  83.68 J/m.°C.s

A = Surface area = (circumference)(length) = (8 m)(40 m) = 320 m²

ΔT = difference in temperature = 20°C - 195°C = -175°C

Δx =thickness of insulation = 1.5 cm = 0.015 m

Therefore,

[tex]Q = -(83.68\ J/m.^oC.s)(320\ m^2)(\frac{-175\ ^oC}{0.015\ m})\\\\[/tex]

Q = 3.12 x 10⁸ W = 312 MW

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Unless otherwise stated, all objects are located near the Earth's surface, where g = 9.80 m/s. A girl pushes a 21 kg lawn mower as shown in the figure


a)If F = 32 N and θ = 45 ∘ what is the acceleration of the mower? Ignore friction.


b)What is the normal force exerted on the mower by the lawn?

Answers

Newton's second law allows us to find the result for the acceleration of the mower is:

         a = 0.8 m / s²

Newton's second law says that the net force is proportional to the mass and the acceleration of the bodies.

             ∑ F = m a

 

where the bold letters indicate vectors, F is the force, m the mass and the acceleration of the bodies.

A free-body diagram is a schematic where the forces are drawn if the details of the bodies, see attached.

Let's write Newton's equation.

x-axis

         Fₓ = ma

y-axis

         N - F_y - w = 0

Let's use trigonometry to find the components of the force.

         Cos 45 = [tex]\frac{F_x}{F}[/tex]  

         sin 45 = [tex]\frac{F_y}{F}[/tex]  

         Fₓ = F cos 45

         F_y = F sin 45

Let's substitute.

         F cos 45 = m a

         a = [tex]\frac{F \ cos45}{m}[/tex]

Let's calculate.  

         a = [tex]\frac{32 \ cos 45}{21}[/tex]  

         a = 0.8 m / s²

In conclusion using Newton's second law we can find the result for the acceleration of the mower is:

         a = 0.8 m / s²

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The acceleration of the mower is 1.1m/s^2. The normal force exerted on the mower by the lawn is 145.5 N.

a) The force that moves the lawn mower in the horizontal direction is Fcosθ.

Where;

F = 32 N

θ = 45∘

Effective force that moves the mower forward = 32 N cos 45∘ = 22.6 N

Now;

F = ma

m = mass of the lawn mower

a = acceleration

a = F/m

a =  22.6 N/21 kg

a = 1.1 m/s^2

b) The normal force = mgcosθ

FN = 21 kg × 9.80 m/s × cos 45 ∘

= 145.5 N

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What is being transferred as you do work?
A. Energy
B. Power
C. Heat
D. Strength

Answers

[tex]\huge\bold{\purple{\bold{⚡A. Energy⚡}}} [/tex]

[tex]\huge\underline\mathtt\colorbox{cyan}{Reason:}[/tex]

When a force causes a body to move, work is done on the object by the force. Work is the measure of the energy transfer when a force 'F' moves an object through a distance 'd'. So we say that energy is transferred from one energy store to another when work is done, and therefore, energy transferred = work done.

i’m pretty sure the answer is energy because as you do ur work energy is the ability of a person or an object to do work or to cause a change. When you do work on an object, some of your energy is transferred to the object. You can think of work as the transfer of energy.

Why did the brain name itself? 100 points

Answers

The human brain did not “give itself” the name “brain”. A network of brains (i.e. society) agreed over time on calling the gray think-tank in our skulls a “brain”. Different networks in other environments agreed on other terms to label the same object. Over time these networks evolved, constantly creating slightly-tweaked yet new names, based contextually on what they were already calling other objects (these constitute what we know as linguistic relationships).

Answer:

In the remote past, people had no notion what function the brain has in the human organism. They saw “mush” and called it accordingly. Since brain was a borrowed word, those who began to use it, must at one time have had a native name for the content of heads.

does this help?

thanks for the points!

Kaya is riding her dirt bike eastward on a dirt road. She spots a pothole ahead.
Kaya slows her car from 14.0 m/s to 5.5 m/s in 6.0 s. What is her acceleration?

Answers

Answer: The acceleration of Kaya is .

Explanation:

Answer:

Kaya's acceleration is 1.41666667.

Explanation:

To find the acceleration we need to subtract the starting speed to the slowed speed. So 14 - 5.5 = 8.5.

Now we divide 8.5 by the time, 6 seconds.

Our final answer is 1.41666667, or rounded, 1.42.

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