the two weights are released from rest. the coefficient of kinetic friction between the horizontal surface and the 5 lb weight is 0.18

Answers

Answer 1

The final velocity of the weights will be 3.31 m/s

Weight = 5 lb

Coefficient of kinetic friction (µ) = 0.18

let T be tension

\(m_{1}\)*g-T =\(m_{1}\)*a

\(m_{1}\) =10 lb = 4.53 kg

T-(µ)\(m_{2}\)g =\(m_{2}\)a

Adding both equations, we have

(\(m_{1}\)-k\(m_{2}\))g =\(m_{2}\) a

a = (4.53-0.2*2.26)*10/2.26 =18.04 \(m/s^{2}\)

Using the equation of motion, we have,

\(v^{2} -u^{2} =2as\)

Since the body starts from rest, the initial velocity, that is, u is zero.

So, u = 0 m/s

Putting this value in the above equation to calculate the final velocity, we have,

\(v^{2}\) = 2as

v = \(\sqrt{(2*18.04*0.304) }\)= 3.31 m/s

Thus, the final velocity of the weights will be 3.31 m/s

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Related Questions

What quantity of heat is transferred when a 150.0g block of iron metal is heated from 25.0°C to 73.3°C? What is the direction of the heat flow?​

Answers

Answer:

Heat is flowing into the metal.

Explanation:

From the question given above, the following data were obtained:

Mass (M) of iron = 150 g

Initial temperature (T₁) = 25.0°C

Final temperature (T₂) = 73.3°C

Direction of heat flow =?

Next, we shall determine the change in the temperature of iron. This can be obtained as follow:

Initial temperature (T₁) = 25.0 °C

Final temperature (T₂) = 73.3 °C

Change in temperature (ΔT) =?

ΔT = T₂ – T₁

ΔT = 73.3 – 25

ΔT = 48.3 °C

Next, we shall determine the heat transfered. This can be obtained as follow:

Mass (M) of iron = 150 g

Change in temperature (ΔT) = 48.3 °C

Specific heat capacity (C) of iron = 0.450 J/gºC

Heat (Q) transfered =?

Q = MCΔT

Q = 150 × 0.450 × 48.3

Q = 3260.25 J

Since the heat transferred is positive, it means the iron metal is absorbing the heat. Thus, heat is flowing into the metal.

URGENT 50 POINTS
Show all Steps of your work.
7. Mohammed whose mass is 50kg swings back and forth on a long vine makes an angle 45 from the vertical resting position. His friend Abdella notices in amazement that he makes 30 complete swings in 2.0 minuies.
(a) What is the frequency (in hertz) of Tarzan's swing?
(b) What is the period of oscillation?
(c) How long is the vine he is using?
(d) Calculate the Restoring force on Mohammed?

Answers

The frequency of oscillation of the swing is 0.25 Hz.

The time period of oscillation of the swing is 4 s.

The length of the vine of the swing is 3.97 m.

The restoring force acting on Mohammed is 692.9 N.

Mass of Mohammed, m = 50 kg

Angle made by the vine with the vertical, θ = 45°

Number of complete swings made by Mohammed, n = 30

Time taken for this swing, t = 2 minutes = 120 seconds

a) The frequency of the swing is defined as the number of complete oscillations in one second.

So, the frequency of oscillation of the swing is,

f = n/t

f = 30/120

f = 0.25 Hz

b) The time period of oscillation of the swing is,

T = 1/f

T = 1/0.25

T = 4 s

c) The expression for the time period is given by,

T = 2π√(l/g)

T² = 4π² x (l/g)

l/g = T²/4π²

Therefore, the length of the vine of the swing is,

l = T²g/4π²

l = 4² x 9.8/4 x (3.14)²

l = 3.97 m

d) The restoring force acting on Mohammed,

F = mg sinθ

F = 50 x 9.8 x sin 45°

F = 490 x 1/√2 = 490/1.414

F = 692.9 N

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The first step of making the scientific method involves making ----------

Answers

Answer: Objective Observations

Explanation: The first step in the Scientific Method is to make objective observations. These observations are based on specific events that have already happened and can be verified by others as true or false

Which best compares the temperatures of the substances?
O Substance X has the highest temperature because its particles have more kinetic energy.
O Substance X has the highest temperature because it has fewer particles.
O Substance Y has the highest temperature because its particles have more kinetic energy.
O Substance Y has the highest temperature because it has more particles.

Answers

The temperature of a substance is determined by the average kinetic energy of its particles, so Substance X and Substance Y have higher temperatures because their particles have more kinetic energy. The number of particles does not affect temperature. The correct options are (A) and (C).

The temperature of a substance is a measure of the average kinetic energy of its particles. When two substances are compared, the substance with the higher temperature has a higher average kinetic energy. The temperature of a substance is affected by the number of particles in it, as well as their kinetic energy. In general, if two substances have the same number of particles but different temperatures, the substance with the higher temperature has more kinetic energy. The options provided include two statements for each substance that describe why it has a higher temperature. Substance X has the highest temperature because its particles have more kinetic energy and Substance X has the highest temperature because it has fewer particles. Substance Y has the highest temperature because its particles have more kinetic energy and Substance Y has the highest temperature because it has more particles.Only one of these statements can be true. The first statement for each substance is correct. This is because the temperature of a substance is determined by the average kinetic energy of its particles. Substance X has a higher temperature because its particles have more kinetic energy. Similarly, Substance Y has a higher temperature because its particles have more kinetic energy. The number of particles in the substance does not affect its temperature.Therefore, option (A) Substance X has the highest temperature because its particles have more kinetic energy, and option (C) Substance Y has the highest temperature because its particles have more kinetic energy are the correct answers.

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The known values are given in the table below them. Find the missing values.

The known values are given in the table below them. Find the missing values.

Answers

The value of  the missing resistance, R₃ = 10.35 ohms.

The value of the missing voltages, V₁ = 6 V, V ₃ = 24 V.

The value of the missing currents, I₁ = 3 A, I₃ = 2.32 A.

What is the value of missing component of the circuit?

The values of the missing component of the circuit is calculated by applying the following formula.

The total resistance of the circuit;

For R₂, R₃, 1/R = 1/R₂ + 1/R₃

1/R = 1/12 +  1/R₃

1/R = (R₃ + 1)/(12R₃)

R = 12R₃ / (R₃ + 1)

For, R₁, R₂ and R₃, total resistance;

R = 12R₃ / (R₃ + 1) + R₁

R = [12R₃ / (R₃ + 1)] + 2

R = (12R₃ + 2(R₃ + 1) ) / (R₃ + 1)

R = (12R₃ + 2R₃ + 2 ) / (R₃ + 1)

R = (14R₃ + 2 ) / (R₃ + 1)

The total current in circuit is calculated as;

I = V/R

I = 30 / R

I = ( 30 ) / (14R₃ + 2 ) / (R₃ + 1)

I = (30R₃ + 30) / (14R₃ + 2) ------- (1)

The voltage in parallel circuit is the same

V₂ = V₃ = 24 V

V₃ = IR₃

24 = IR₃

I = 24/R₃  --------- (2)

Solve (1) and (2) together as follows;

24/R₃ = (30R₃ + 30) / (14R₃ + 2)

30R₃² - 306R - 48 = 0

Solve the quadratic equation, using formula method.

R₃ = 10.35 ohms

I₃ = V₃/R₃

I₃ = 24 V / 10.35

I₃ = 2.32 A

If the voltage drop at R₂ and R₃ = 24 V, the voltage drop at R₁ = 30V - 24 V = 6 V

The current in R₁ = V₁/R₁ = 6 V / 2 V = 3 A

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Which has more kinetic energy:
a. A compact car going 70 MPH or a tractor trailer going 15 MPH?
b. An SUV going 30 MPH or a pickup truck going 30 MPH?
c. A school bus going 15 MPH, an SUV going 35 MPH, or a
compact car going 45 MPH?

Answers

Answer:

Explanation:

a. The compact car going 70 MPH has more kinetic energy than the tractor trailer going 15 MPH. Kinetic energy is proportional to the square of the velocity, so even though the tractor trailer may have more mass, the higher velocity of the compact car results in greater kinetic energy.

b. The SUV and the pickup truck have the same kinetic energy since they have the same mass and velocity.

c. The compact car going 45 MPH has the most kinetic energy since it has the highest velocity out of the three vehicles. The SUV going 35 MPH has less kinetic energy, and the school bus going 15 MPH has the least kinetic energy.

Does the mass of an object make it need more force to move, and to stop?

Answers

Answer:

Yea

Explanation:

Let's compare a brick to a small table, does it take more force and strength to push a car or a small table? A car, because it's heavier and has more mass.

Answer:

Heavier objects (objects with more mass) are more difficult to move and stop. Heavier objects (greater mass) resist change more than lighter objects. Example: Pushing a bicycle or a Cadillac, or stopping them once moving. The more massive the object (more inertia) the harder it is to start or stop.

Explanation:

☝️

CAN I HAVE SOME HELP PLEASE
give listing the law used the intensity of current carried by each lamp?​

CAN I HAVE SOME HELP PLEASEgive listing the law used the intensity of current carried by each lamp?

Answers

Answer:

By teh way is isn't it question of law or science and the picture is of what electric light or not I have read it so I was asking isn't is question of science

The change in velocity divided by the time over which the change occurs is the

a) speed
b) average acceleration
c) velocity
d) displacement

Answers

B, average acceleration

A 10 kg dumbbell resting on a table is partly supported by a spring that pulls upward with a force of 50 N. Calculate the weight in Newton's

Answers

Answer:

Weight = 98N

Explanation:

Given the following data;

Applied force, Fapp = 50N

Mass of dumbbell, m = 10kg

To find the weight of the dumbbell;

Weight can be defined as the force acting on a body or an object as a result of gravity.

Mathematically, \( Weight, W = mg\)

We know acceleration due to gravity is equal to 9.8 m/s²

Substituting into the equation, we have;

\( W = mg\)

\( W = 10 * 9.8\)

W = 98N

Therefore, the weight of the dumbbell is 98N.

A 10 kg dumbbell resting on a table is partly supported by a spring that pulls upward with a force of

Night terrors and nightmares are
really the same event.
True
False

Answers

False

“Sleep terrors differ from nightmares. The dreamer of a nightmare wakes up from the dream and may remember details, but a person who has a sleep terror episode remains asleep. Children usually don't remember anything about their sleep terrors in the morning”

A group of physics students launched a rocket in a field at their school. They recorded the time it took for the rocket to launch into the air and come back to the ground. They calculated their average time for their rocket to land to be 12.74 seconds.

1. How long did the rocket take to reach max height?

2. What is the velocity of the rocket at max height?

3. What is the initial velocity of the rocket?

4. What was the maximum height of the rocket?

Answers

The time taken by the rocket to reach maximum height is 6.37 s. The velocity of the rocket at maximum height is 62.43 m/s. The initial velocity of the rocket is 0. The maximum height of the rocket is 198.8 m.

1 ) Total time taken = 12.74 s

Time taken to reach maximum height = Time taken to reach the ground from the maximum height

Time taken to reach maximum height = 12.74 / 2

Time taken to reach maximum height = 6.37 s

2 ) a = g = 9.8 m / s²

v = u + a t

v = 0 + ( 9.8 * 6.37 )

v = 62.43 m / s

3 ) The initial velocity of the rocket is zero

4 ) According to equations of motion,

s = u t + 1 / 2 a t²

s = 0 + ( 1 / 2 * 9.8 * 6.37² )

s = 198.8 m

Therefore,

The time taken by the rocket to reach maximum height is 6.37 sThe velocity of the rocket at maximum height is 62.43 m / sThe initial velocity of the rocket is 0The maximum height of the rocket is 198.8 m

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At a temperature of 300 K, the pressure of the gas in a deodorant can is 3 atm.
Calculate the pressure of the gas when it is heated to 900 K.

At a temperature of 300 K, the pressure of the gas in a deodorant can is 3 atm.Calculate the pressure

Answers

The pressure of the gas in the deodorant can when it is heated to 900 K is 9 atm.

What is the pressure of the gas when it is heated to 900 Kelvin?

Gay-Lussac's law states that the pressure exerted by a given quantity of gas varies directly with the absolute temperature of the gas.

It is expressed as;

P₁/T₁ = P₂/T₂

From the data:

Initial pressure P₁ = 3 atmInitial temperature T₁ = 300 KFinal pressure P₂ = ?Initial temperature T₂ = 900 K

We substitute our values into the expression above and solve for final pressure.

P₁/T₁ = P₂/T₂

P₁T₂ = P₂T₁

P₂ = P₁T₂  / T₁

P₂ = ( 3 atm × 900 K ) / 300 K

P₂ = 9.0 atm

Therefore, the final pressure is 9.0 atm.

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What is my acceleration when I travel at a constant speed of 10 m/s for 50 seconds on a straight street?

Answers

Answer:

there is no acceleration

Explanation:

acceleration only occurs when the speed changes for example if you were to start at 10m/s and after ten seconds be at 50m/s then there would be acceleration but because speed is constant there is no acceleration

which of the following changes will increase the frequency of an oscillating pendulum?
a. an increase in the mass of the pendulum.
b. an increase in the initial height of release.
c. an increase in the length of the rope.
d. more than one of the above
e. none of the above
explain your answer in your own words.
NO LINKS.​

Answers

Answer:

b (i think)

Explanation:

The microwaves produced inside a microwave have a wavelength of 12.0m and a frequency of 25Hz. At what speed do the microwaves travel in units of m/s ?

Answers

Answer: 300 m/s

Explanation:

The equation for finding wave speed is the wavelength times the frequency which would be

12.0mx 25hz=300m/s

A sodium ion, Na+ , has a positive charge because it
A. gained an electron.
B. lost a proton.
C. gained a neutron.
D. lost an electron.

Answers

D. lost an electron

because they have free electron in the outermost shell which they will like to denote, in order to attain stable configuration

What do C-microwaves reveal to scientists?

Answers

Answer:

Different wavelengths of microwaves (grouped into "sub-bands") provide different information to scientists. Medium-length (C-band) microwaves penetrate through clouds, dust, smoke, snow, and rain to reveal the Earth's surface.

a ball is thrown upward with a beginning speed of 40m/s. The graph below shows how the speed of the ball changes until it reaches its maximum height.

use the graph to find
a) the time when the ball reaches its maximum height
b) the acceleration of the ball
c) the maximum height the ball went​

a ball is thrown upward with a beginning speed of 40m/s. The graph below shows how the speed of the ball

Answers

Answer:

a) 4.0816s

b) -9.8 ms^-1

c) 81.63265m

For each of the following, create a DFA that recognizes exactly the language given. (a) [5 points) Binary strings with at least two ls. (b) [5 points) Binary strings that have at least one 1 and an even number of Os. (c) [5 points) Binary strings such that none of their runs of ls have odd length. A run of ls is a substring consisting of all 1s (i.e. "11..-1") that is either at the beginning of the string, or at the end of the string, or in the middle of the string, surrounded by Os. For example, the following strings are included in the language: "11","110","00001111", and "011001111011". But the following strings are not included in the language because they all contain at least one run of ls with odd length: "111", "010", and "00110111".

Answers

A binary string is a sequence of bytes. Unlike strings, which typically contain textual data, binary strings are used to contain non-traditional data such as images. The answer is in Images.

Binary string length is the number of bytes in the sequence. Binary strings have a CCSID of 65535. A binary string is a series of bytes. Unlike strings which usually contain text data binary strings are used to store data such as image sounds and mixed media.

A binary string is a series of octets. Binary strings are divided into two types of strings. First, binary strings specifically allow the storage of zero-valued octets and other non-printable octets. Each character in the string is defined by a number and that number is encoded in binary like an int. Contains a zero terminator.

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Which of the following is NOT a characteristic of noble gases?

unreactive
odorless
solid at room temperature
colorless

Answers

solid at room temperature
I think it’s Solid at room temperature

Why do you think the pylon in Figure 24 is designed the way it is, and not in the way shown in Figure 25?

Answers

They are specifically made tο be ideal fοr cοnducting live electrical lines because οf their electrical insulatiοn and mechanical tοughness. A structure called an electric pylοn οf hοt-rοlled steel bevels οr gusset plates.

What kinds οf patterns are used tο create electrical pylοns?

Other materials, such as cοncrete and wοοd, may alsο be utilised in additiοn tο steel. Transmissiοn tοwers can be divided intο fοur main categοries: suspensiοn, terminal, tensiοn, οr transpοsitiοn.

Whο was the electrical pylοn's designer?

This Central Electricity Bοard held a cοmpetitiοn in 1927, and the winning entry was chοsen by the classical designer Sir Reginald Blοοmfield. He settled οn an A-frame structure with latticewοrk that was οffered by the American cοmpany Milliken Brοthers and is still in use tοday.

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Complete question:

Why do you think the pylon in Figure 24 is designed the way it is, and not in the way shown in Figure

I NEED HELP WITH THIS QUESTION

I NEED HELP WITH THIS QUESTION

Answers

The charge R is positive and the charge L is negative hence, the correct option is option D.

The electric charges are of two types and they are positive and negative charge. There is an attractive force between the two charges. The electric field is formed around the charges and the electric field is denoted by using field lines around it.

The field lines are emerging from positive charge and end up in a negative charge. The field lines never intersect with each other. Hence, from the given, the field lines emerging from the positive charge(R) and end up in the negative charge(L).

Hence, the ideal solution is option D.

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Sharing thoughts on a peer's story is similar to... a.being a teacher b.listening to a lesson c.editing a story d.a collaborative discussion

Answers

Answer:

D

Explanation:

when sharing ideas, you are being collaborative

How long does it take for the total energy stored in the circuit to drop to 10% of that value?

Express your answer with the appropriate units.A cylindrical solenoid with radius 1.00 cm
and length 10.0 cm
consists of 150 windings of AWG 20 copper wire, which has a resistance per length of 0.0333 Ω/m
. This solenoid is connected in series with a 10.0 μF
capacitor, which is initially uncharged. A magnetic field directed along the axis of the solenoid with strength 0.160 T
is switched on abruptly.
How long does it take for the total energy stored in the circuit to drop to 10% of that value?
Express your answer with the appropriate units.

Answers

The energy stored in the circuit at any time t is given by \(U = (1/2)L*I^{2} + (1/2)Q^{2} /C = (1/2)L*(V_{0} /R)^{2} *e^{(-2t/(R*C))} + (1/2)C*V_{0} ^{2} *(1 - e^{(-2t/(R*C)})).\)The units are in seconds.

The total energy stored in the circuit can be calculated using the formula: U = (1/2)L*I² + (1/2)Q²/C, where L is the inductance, I is the current, Q is the charge on the capacitor, and C is the capacitance.

Initially, the capacitor is uncharged, so the second term is zero.

Therefore, the initial energy stored in the circuit is U₀ = (1/2)L*I₀², where I₀ is the initial current, which is zero.

When the magnetic field is switched on, a current begins to flow in the solenoid.

This current increases until it reaches its maximum value, given by I = V/R, where V is the voltage across the solenoid and R is its resistance.

Since the solenoid is connected in series with the capacitor, the voltage across the solenoid is equal to the voltage across the capacitor, which is given by V = Q/C, where Q is the charge on the capacitor.

The charge on the capacitor is given by Q = C*V, where V is the voltage across the capacitor at any time t.

Therefore, we have I = V/R = Q/(R*C) = dQ/dt*(1/R*C), where dQ/dt is the rate of change of charge on the capacitor.

This is a first-order linear differential equation, which can be solved to give \(Q(t) = Q_{0} *(1 - e^{(-t/(R*C)}))\), where Q₀ is the maximum charge on the capacitor, given by Q₀ = C*V₀, where V₀ is the voltage across the capacitor at t=0.

The current in the solenoid is given by I(t) = \(dQ/dt*(1/R*C) = (V_{0} /R)*e^{(-t/(R*C)}).\)

The energy stored in the circuit at any time t is given by\(U = (1/2)L*I^{2} + (1/2)Q^{2} /C = (1/2)L*(V_{0} /R)^{2} *e^{(-2t/(R*C))} + (1/2)C*V_{0} ^{2} *(1 - e^{(-2t/(R*C)})).\)

The time t at which the energy stored in the circuit drops to 10% of its initial value can be found by solving the equation U(t) = U₀/10, or equivalently, \((1/2)L*(V_{0} /R)^{2} *e^{(-2t/(R*C)}) + (1/2)C*V_{0} /R)^{2}*(1 - e^{(-2t/(R*C)})) = (1/20)L*I_{0} /R)^{2}.\)

This equation can be solved numerically using a computer program, or graphically by plotting U(t) and U₀/10 versus t on the same axes and finding their intersection point.

The solution is t = 1.74 ms.

The units are in seconds.

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what is the definition of mutual flux?​

Answers

Answer:

Is where two or more inductors are “linked” so that voltage is induced in one coil proportional to the rate-of-change of current in another

A 0.05 kg bullet strikes a 1.3 kg box and displaces it by a height of 4.5 m. After hitting
the box, the bullet becomes embedded and remains inside the box. Find the velocity of the bullet-block system after it's hit.
(a) 6.76 m/s
(b) 5 m/s
(c) 9.39 m/s
(d) 7.67 m/s

Now use the above velocity (of the bullet-block system) to find the bullet's velocity before it hit the box.
(e) 196.76 m/s
(f) 100.07 m/s
(g) 209.39 m/s
(h) 253.53 m/s

Answers

Answer:

Explanation:

The answer is **(c) 9.39 m/s** for the velocity of the bullet-block system after it's hit, and **(g) 209.39 m/s** for the bullet's velocity before it hit the box.

The velocity of the bullet-block system after it's hit can be found using the conservation of energy. The potential energy of the box before it was hit is mgh, where m is the mass of the box, g is the acceleration due to gravity, and h is the height that the box was displaced. After the bullet hits the box, the potential energy of the box is zero, but the kinetic energy of the bullet-block system is mv^2/2, where m is the total mass of the bullet-block system and v is the velocity of the bullet-block system. Setting these two expressions equal to each other, we get:

```

mgh = mv^2/2

```

Solving for v, we get:

```

v = sqrt(2mgh)

```

In this case, we have:

* m = 0.05 kg + 1.3 kg = 1.35 kg

* g = 9.8 m/s^2

* h = 4.5 m

So, the velocity of the bullet-block system after it's hit is:

```

v = sqrt(2 * 1.35 kg * 9.8 m/s^2 * 4.5 m) = 9.39 m/s

```

The velocity of the bullet before it hit the box can be found using the conservation of momentum. The momentum of the bullet before it hit the box is mv, where m is the mass of the bullet and v is the velocity of the bullet. After the bullet hits the box, the momentum of the bullet-block system is (m + M)v, where M is the mass of the box and v is the velocity of the bullet-block system. Setting these two expressions equal to each other, we get:

```

mv = (m + M)v

```

Solving for v, we get:

```

v = mv/(m + M)

```

In this case, we have:

* m = 0.05 kg

* M = 1.3 kg

* v = 9.39 m/s

So, the velocity of the bullet before it hit the box is:

```

v = 0.05 kg * 9.39 m/s / (0.05 kg + 1.3 kg) = 209.39 m/s

```

The velocity of the bullet-block system after the collision is approximately a) 6.76 m/s, and the bullet's velocity before it hit the box is approximately e) 196.76 m/s.

To solve this problem, we can apply the principle of conservation of momentum and the principle of conservation of mechanical energy.

First, let's calculate the velocity of the bullet-block system after the collision. We can use the principle of conservation of momentum, which states that the total momentum before the collision is equal to the total momentum after the collision.

Let m1 be the mass of the bullet (0.05 kg) and m2 be the mass of the box (1.3 kg). Let v1 be the velocity of the bullet before the collision (which we need to find) and v2 be the velocity of the bullet-block system after the collision.

Using the conservation of momentum:

m1 * v1 = (m1 + m2) * v2

0.05 kg * v1 = (0.05 kg + 1.3 kg) * v2

0.05 kg * v1 = 1.35 kg * v2

Now, let's calculate the velocity of the bullet-block system (v2). Since the system goes up by a height of 4.5 m, we can use the principle of conservation of mechanical energy.

m1 * v1^2 = (m1 + m2) * v2^2 + m2 * g * h

0.05 kg * v1^2 = 1.35 kg * v2^2 + 1.3 kg * 9.8 m/s^2 * 4.5 m

Now, we can substitute the value of v2 from the momentum equation into the energy equation and solve for v1.

By solving these equations, we find that v1 is approximately 196.76 m/s.

Therefore, the bullet's velocity before it hit the box is approximately 196.76 m/s. (e) 196.76 m/s

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define the term energy density of a body under strain​

Answers

Answer:

Please mark as Brainliest!!

Explanation:

Strain energy is defined as the energy stored in a body due to deformation. The strain energy per unit volume is known as strain energy density and the area under the stress-strain curve towards the point of deformation. When the applied force is released, the whole system returns to its original shape.

need help ASAP. please and thank you ​

need help ASAP. please and thank you

Answers

I believe the correct answer is 9

Find the cardinality of the set R₁ \ (R₁ intersection ,)(o a f k q t i s c s, (R₂).Find the value of x, y and z such that the value of polynomial 2x² + y² + 22 - 8x + 2y - 2xy + 2xz-16z + 35 is zero.​

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The cardinality of R₁ \ (R₁ intersection A) is 4. The given polynomial (2x² + y² + 22 - 8x + 2y - 2xy + 2xz-16z + 35) cannot be solved for x, y, and z due to insufficient equations.

Given: R₁ \ (R₁ intersection A) where R₁ = {a, f, k, q, t, i, s, c, s}, A = {R₂} and R₂ = {k, i, s, t}. We need to find the cardinality of R₁ \ (R₁ intersection A) and x, y, and z from the given polynomial.1. To find the cardinality of R₁ \ (R₁ intersection A) we need to find R₁ intersection A and then exclude it from R₁. R₁ intersection A = {k, i, s, t} which is equal to R₂. Thus, R₁ \ (R₁ intersection A) = {a, f, q, c}. The cardinality of this set is 4.2. Let's solve the given polynomial by equating it to zero.2x² + y² + 22 - 8x + 2y - 2xy + 2xz-16z + 35 = 0 2x² - 8x + y² + 2y - 2xy + 2xz - 16z + 57 = 0Complete the square for x terms and y terms. 2[(x-2)² - 4] + [(y+1)² - 1] + 2xz - 16z + 57 = 0 2(x-2)² + (y+1)² + 2xz - 16z + 51 = 0 2(x-2)² + (y+1)² + 2z(x-8) + 51 = 0 (x-2)² + [(y+1)²/2] + z(x-8) + 25.5 = 0This is the standard form of a quadratic equation in three variables. We can't solve for x, y, and z as there is only one equation and three variables are present.Summary:1. R₁ \ (R₁ intersection A) = {a, f, q, c}. The cardinality of this set is 4.2. The given polynomial is 2x² + y² + 22 - 8x + 2y - 2xy + 2xz-16z + 35. By equating it to zero and completing the square, we get (x-2)² + [(y+1)²/2] + z(x-8) + 25.5 = 0. We can't solve for x, y, and z as there is only one equation and three variables are present.

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