2. Four cars are designed to protect passengers in a 16 m/s crash. The characteristics of the cars are shown below. Which car is most likely to do the best job of
protecting the passengers inside?
Car 1
Characteristic
Car mass
Crumple zone length
1,450 kg
110 cm
Car 2
950 kg
50 cm
Car 3
2,000 kg
85 cm
Car 4
1,450 kg
120 cm
200 KN
1,000 KN
50 KN
1,000 KN
4,000 KN
200 KN
2,000 KN
1,000 KN
Crumple zone rigidity
Safety cell rigidity
Seat belt stiffness
Airbag rigidity
20 kN/m
None
11 kN/m
14 kN/m
10 KN
10 KN
None
45 KN
O A Car 1
O B. Car 2
O C Car 3
O D. Car 4

Answer:

The kinetic theory of matter can be used to explain how solids, liquids and gases are interchangeable as a result of increase or decrease in heat energy. When an object is heated the motion of the particles increases as the particles become more energetic

Answer:

it's from gravity because when you throw something up it goes forward a certain distance

Answer:   the acceleration of the masses is given by = 0, which means the angular acceleration of the pulley is zero. This implies that the masses m and 2m move with constant velocity,  they are in equilibrium.

Answer:

Explanation:

Pressure will expand a gas, enlarging its volume and reducing its density and concentration of particles. Pressure will magnify a gas, developing its volume and multiplying its density and concentration of particles.

Increasing the pressure of a gas is exactly the same as increasing its concentration. If you have a given mass of gas, the way you increase its pressure is to squeeze it into a smaller volume. If you have the same mass in a smaller volume, then its concentration is higher.

Answer:

a) T = 0.5 s

b) v = 1.2π m/s ≈ 3.77 m/s

Explanation:

It makes two revolutions in one second so makes one revolution in ½ second

circumference of the circle is

C = 2πr = 0.6π m

which it traverses in one time period

0.6π m / 0.5 s = 1.2π m/s

To solve this, we must be knowing each and every concept related to speed and its calculations. Therefore, the angular speed of a model car moves round a circular path of radius 0.3m at 2 revolutions per secs is 3.77 m/.

Speed may be defined as the distance traveled by an item in the amount of time it requires to travel that distance. In other words, it measures how rapidly an item travels but does not provide direction.

Speed may be calculated in Science. The speed equation is a scientific formula that is used to calculate various types of speed.

Mathematically, the formula for speed can be given as

speed= distance/time

Values that are given

Time period= 0.5 s

Circumference = 2πr = 0.6π m

substituting all the given values in the above equation, we get

speed     =0.6π m / 0.5 s

On calculations, we get

              = 1.2π m/s

              =3.77 m/s

Therefore, the angular speed of a model car moves round a circular path of radius 0.3m at 2 revolutions per secs is 3.77 m/.

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Answer:

if the mean distance 93 million miles then the range of distances has to go from 92.293.8 million miles however the earth goes

When a mass (m) that orbits the earth in a circular path of radius 7480 km (about 1100 km) above the surface of the earth), the period of revolution of the given satellite is approximately 8207 seconds or 2.28 hours.

The period of revolution of a satellite with mass (m) that orbits the earth in a circular path of radius 7480 km (about 1100 km) above the surface of the earth) can be determined by using Kepler's third law which relates the period of revolution of a satellite to the average radius of its orbit.

Kepler's third law states that the square of the period of revolution of a satellite is proportional to the cube of the average radius of its orbit.

Mathematically, the law can be expressed as: T² = (4π² / GM) × R³Where T is the period of revolution, G is the gravitational constant, M is the mass of the earth, and R is the average radius of the orbit of the satellite.

To find the period of revolution of the given satellite, we can substitute the given values in the equation: R = 7480 km + 6370 km = 13850 kmM = 5.97 × 10²⁴ kgG = 6.67 × 10⁻¹¹ Nm²/kg²T² = (4π² / GM) × R³T² = (4π² / (6.67 × 10⁻¹¹ × 5.97 × 10²⁴)) × (13850 × 10³)³T² = 6.7182 × 10¹⁴ seconds²

Taking the square root of both sides, we get:T = 8.2079 × 10³ seconds

Therefore, the period of revolution of the given satellite is approximately 8207 seconds or 2.28 hours.

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The value of the force, F₀, at equilibrium is equal to the horizontal

component of the tension in string 2.

Response:

Given:

The weight of the rod = The sum of the vertical forces in the strings

Therefore;

M·g = T₂·cos(37°) + T₁

The weight of the rod is at the middle.

Taking moment about point (2) gives;

M·g × L = T₁ × 2·L

Therefore;

\(T_1 = \mathbf{\dfrac{M \cdot g}{2}}\)

Which gives;

\(M \cdot g = \mathbf{T_2 \cdot cos(37 ^{\circ})+ \dfrac{M \cdot g}{2}}\)

\(T_2 = \dfrac{M \cdot g - \dfrac{M \cdot g}{2}}{cos(37 ^{\circ})} = \mathbf{\dfrac{M \cdot g}{2 \cdot cos(37 ^{\circ})}}}\)

F₀ = T₂·sin(37°)

Which gives;

\(F_0 = \dfrac{M \cdot g \cdot sin(37 ^{\circ})}{2 \cdot cos(37 ^{\circ})}} = \dfrac{M \cdot g \cdot tan(37 ^{\circ})}{2} \approx \mathbf{0.377 \cdot M \cdot g}\)

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Answer:

C, We're you born. Sorry if I'm wrong :).

Answer:

It's C. Were you born

hope this helps! :D

Explanation:

1.Unit vector in the direction BA: BA/|BA| = (2/3, 2/3, 1/3)

2.The angular velocity (ω) of the body is given as 3 radians per second.

3.Without the position of point P given, it is not possible to write the position vector of P.

4.Left-handed rotation refers to the direction of rotation where the rotation follows the left-hand rule.

5.Position vector of point A: (4, 1, 1)

Position vector of point B: (2, -1, 0)

The direction vector BA = (-2, -2, -1)

1.To determine the unit vector pointing in the direction BA, we subtract the coordinates of point B from the coordinates of point A and normalize the resulting vector.

The direction vector BA is given by:

BA = (4 - 2, 1 - (-1), 1 - 0) = (2, 2, 1)

To obtain the unit vector in the direction of BA, we divide the direction vector by its magnitude:

|BA| = √(2^2 + 2^2 + 1^2) = √(4 + 4 + 1) = √9 = 3

Unit vector in the direction BA: BA/|BA| = (2/3, 2/3, 1/3)

2.The angular velocity (ω) of the body is given as 3 radians per second.

3.Without the position of point P given, it is not possible to write the position vector of P. Please provide the position of point P to proceed with the calculation.

4.Left-handed rotation refers to the direction of rotation where the rotation follows the left-hand rule. In a left-handed coordinate system, if you curl the fingers of your left hand in the direction of rotation, your thumb will point in the direction of the rotation axis. It is the opposite direction to a right-handed rotation.

5.The position vectors of points A and B are:

Position vector of point A: (4, 1, 1)

Position vector of point B: (2, -1, 0)

The direction vector BA can be obtained by subtracting the coordinates of point A from the coordinates of point B:

BA = (2 - 4, -1 - 1, 0 - 1) = (-2, -2, -1)

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The approximate value of the magnitude of the displacement vector 2D - E is roughly  16.88.

In order to find out the magnitude of the displacement vector 2D - E, you can use these steps:

multiplying  D by 2. this would result to

12i + 6j - 2k

subtracting  E from 2D. this would result to

8i + 11j - 10k

The calculation of Step three entails computing the magnitude of 2D - E where   |V| = sqrt(Vi^2 + Vj^2 + Vk^2)

|2D - E| = sqrt((8^2) + (11^2) + (-10^2))

|2D - E| = sqrt(64 + 121 + 100)

|2D - E| = sqrt(285),

|2D - E| = 16.88 when rounded off to two decimal places.

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Answer:

The atomic and molecular interactions unveil the bulk properties of matter in our environment by ways of the fact that everything in the whole universe is made of either atoms, molecules or even ions

How matter is made up of atoms and molecules?

It has been proven practically everything in the whole universe is matter and everything which interact with matter is also matter. This explains to us the reasons why matter could be atoms, molecules or ions.

That being said, some substances (matter) is made up of atoms of elements, some made up of molecules or atoms and molecules and others ions or both. However, matter is anything which has mass and occupies space.

In conclusion, we can now conclude from the explanation above that the properties of matter are as a result of the interaction which exists between matter at the atomic and molecular level.

Answer:

People can capture geothermal energy through: Geothermal power plants, which use heat from deep inside the Earth to generate steam to make electricity. Geothermal heat pumps, which tap into heat close to the Earth's surface to heat water or provide heat for buildings

When the weather is cold, the water or refrigerant heats up as it travels through the part of the loop that's buried underground. Once it gets back above ground, the warmed water or refrigerant transfers heat into the building. The water or refrigerant cools down after its heat is transferred.

The reading on each of the scales on the right is 421.4 N.

The reading on each of the scales on the left is 156.8 N.

The reading on each scale is determined from the distribution of the weight of the woman.

The weight of the board is distributed uniformly and each scale with have equal reading of the weight of the board.

weight of the board = 10 kg x 9.8 m/s² = 98 N

Reading of each due to weight of the board is calculated as;

W₁ = ¹/₂ (98 N) = 24.5 N

The distribution of the weight of the woman on the right scale is calculated as;

W (R) = ( 1.5 m / 2 m) x ( 54 x 9.8 )

W (R) =  396.9 N

The distribution of the weight of the woman on the left scale is calculated as;

W (L) = ( 0.5 m / 2 m) x ( 54 x 9.8 )

W (L) =  132.3 N

Total reading on the scale on the right = 396.9 N + 24.5 N = 421.4 N

Total reading on the scale on the left = 132.3 N + 24.5 N = 156.8 N

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A cesium-133 atom's radiation goes through 1.5 million cycles in around 0.1633 microseconds (or 163.3 nanoseconds).

9,192,631,770 hertz (cycles per second) is the frequency of the microwave spectral line that the isotope cesium-133 emits. The basic unit of time is provided by this. Cesium clocks have an accuracy and stability of 1 second in 1.4 million years.

The radiation emitted by cesium-133 has a frequency of 9,192,631,770 cycles per second, or 9.192631770 109 Hz.

The following formula may be used to determine how long 1.5 million radiation cycles take to complete:

Time is equal to the frequency of cycles.

Plugging in the numbers, we get:

time = 1.5 million / 9.192631770 × 10^9 Hz

time = 1.632995101 × 10^-7 seconds

So it takes approximately 0.1633 microseconds (or 163.3 nanoseconds) for radiation from a cesium-133 atom to complete 1.5 million cycles.

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Answer: In a pulley, the ideal mechanical advantage is equal to the number of rope segments pulling up on the object. The more rope segments that are supporting to do the lifting work, the less pressure that is needed for the job.

Explanation:

Answer:

Time begins, Formation of subatomic particles, Formation of Atoms, Formation of stars, Formation of Galaxies

Explanation:

At the beginning right after the big bang time starts then sub-atomic particles forms i.e. protons, neutrons from this atoms form and after that stars and galaxies form.

Answer:

Total distance covered (scalar quantity) = 23 km

Displacement (vector quantity) = 3 km north from the original starting point

Explanation:

Since he drove 13 km north and then 10 km south, the total distance he cover in his drive was: 13 km + 10 km = 23 km

On the other hand, his displacement was 3 km north from where he started.

Answer:

Explanation:

(m1 + m2)*V1 = m2*V2 + m1*Vx

Vx = ((m1 + m2)*V1 -  m2*V2) / m1

Vx = ((82 + 48)*7.4 - 48*8.6) /82 = 6.7 m/s

For A 53 g ice cube at −30◦C is dropped into a container of water at 0◦C, the amount of water that freezes onto the ice?  is mathematically given as

x = 9.93 g

Where

Energy received = energy given out

Generally, the amount of water is mathematically given as

(53)(0.5)(30) = (80)(x)

Therefore

x = (49)(0.5)(16)/(80)

x = 9.93 g

In conclusion, the mass of water

x = 9.93 g

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1. A complete fitness and exercise program should incorporate three basic components: Endurance (Aerobic), Flexibility, and Strength. Each of these components has specific guidelines, which govern their effectiveness

Answer:

Refer to the step-by-step Explanation.

Step-by-step Explanation:

Simplify the equation with given substitutions,

Given Equation:

\(mgh+(1/2)mv^2+(1/2)I \omega^2=(1/2)mv_{_{0}}^2+(1/2)I \omega_{_{0}}^2\)

Given Substitutions:

\(\omega=v/R\\\\ \omega_{_{0}}=v_{_{0}}/R\\\\\ I=(2/5)mR^2\)\(\hrulefill\)

Start by substituting in the appropriate values: \(mgh+(1/2)mv^2+(1/2)I \omega^2=(1/2)mv_{_{0}}^2+(1/2)I \omega_{_{0}}^2 \\\\\\\\\Longrightarrow mgh+(1/2)mv^2+(1/2)\bold{[(2/5)mR^2]} \bold{[v/R]}^2=(1/2)mv_{_{0}}^2+(1/2)\bold{[(2/5)mR^2]}\bold{[v_{_{0}}/R]}^2\)

Adjusting the equation so it easier to work with.\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2} \Big[\dfrac{2}{5} mR^2\Big]\Big[\dfrac{v}{R} \Big]^2=\dfrac12mv_{_{0}}^2+\dfrac12\Big[\dfrac25mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\)

\(\hrulefill\)

Simplifying the left-hand side of the equation:

\(mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2} \Big[\dfrac{2}{5} mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\)

Simplifying the third term.

\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2} \Big[\dfrac{2}{5} mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2}\cdot \dfrac{2}{5} \Big[mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\)

\(\\ \boxed{\left\begin{array}{ccc}\text{\Underline{Power of a Fraction Rule:}}\\\\\Big(\dfrac{a}{b}\Big)^2=\dfrac{a^2}{b^2} \end{array}\right }\)

\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v^2}{R^2} \Big]\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2 \cdot\dfrac{v^2}{R^2} \Big]\)

"R²'s" cancel, we are left with:

\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v^2}{R^2} \Big]\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5}mv^2\)

We have like terms, combine them.

\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v^2}{R^2} \Big]\\\\\\\\\Longrightarrow mgh+\dfrac{7}{10} mv^2\)

Each term has an "m" in common, factor it out.

\(\Longrightarrow m(gh+\dfrac{7}{10}v^2)\)

Now we have the following equation:

\(\Longrightarrow m(gh+\dfrac{7}{10}v^2)=\dfrac12mv_{_{0}}^2+\dfrac12\Big[\dfrac25mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\)

\(\hrulefill\)

Simplifying the right-hand side of the equation:

\(\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac12\cdot\dfrac25\Big[mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15\Big[mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15\Big[mR^2\Big]\Big[\dfrac{v_{_{0}}^2}{R^2}\Big]\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15\Big[mR^2\cdot\dfrac{v_{_{0}}^2}{R^2}\Big]\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15mv_{_{0}}^2\Big\\\\\\\\\)

\(\Longrightarrow \dfrac{7}{10}mv_{_{0}}^2\)

Now we have the equation:

\(\Longrightarrow m(gh+\dfrac{7}{10}v^2)=\dfrac{7}{10}mv_{_{0}}^2\)

\(\hrulefill\)

Now solving the equation for the variable "v":

\(m(gh+\dfrac{7}{10}v^2)=\dfrac{7}{10}mv_{_{0}}^2\)

Dividing each side by "m," this will cancel the "m" variable on each side.

\(\Longrightarrow gh+\dfrac{7}{10}v^2=\dfrac{7}{10}v_{_{0}}^2\)

Subtract the term "gh" from either side of the equation.

\(\Longrightarrow \dfrac{7}{10}v^2=\dfrac{7}{10}v_{_{0}}^2-gh\)

Multiply each side of the equation by "10/7."

\(\Longrightarrow v^2=\dfrac{10}{7}\cdot\dfrac{7}{10}v_{_{0}}^2-\dfrac{10}{7}gh\\\\\\\\\Longrightarrow v^2=v_{_{0}}^2-\dfrac{10}{7}gh\)

Now squaring both sides.

\(\Longrightarrow \boxed{\boxed{v=\sqrt{v_{_{0}}^2-\dfrac{10}{7}gh}}}\)

Thus, the simplified equation above matches the simplified equation that was given.  

Answer:C, Atoms of iron are different from atoms of nickel.

Explanation:All the atoms that make up each type of element are alike, and they are different from the atoms that make up every other type of element. So the element iron is different from the element nickel because the atoms that make up the iron are different from the atoms that make up the nickel.

Answer:

Explanation:

The correct option that describes a different evolutionary stage of a star like the sun is:

D) It becomes a white dwarf after exploding as a supernova

This is because a star like the sun does not have enough mass to undergo a supernova explosion. After it has exhausted all the fuel in its core, it will evolve into a red giant and then a planetary nebula, leaving behind a small, hot, dense remnant known as a white dwarf. Supernovae occur in much more massive stars that have cores that can collapse to form a neutron star or black hole.

Answer:

The resistance of 4/0 coated copper conductors is given as 0.0626 ohms per 1000 feet. To find the total resistance of the three 4/0 conductors installed in parallel, we can use the formula for combining resistances in parallel.

Since the total length for each of the three conductors is 323 feet, the resistance of each conductor can be calculated as follows:

Resistance of one conductor = (0.0626 ohms / 1000 feet) * 323 feet

To find the total resistance when the conductors are in parallel, we use the formula:

1/Total Resistance = 1/Resistance of Conductor 1 + 1/Resistance of Conductor 2 + 1/Resistance of Conductor 3

Total Resistance = 1 / (1/Resistance of Conductor 1 + 1/Resistance of Conductor 2 + 1/Resistance of Conductor 3)

Substituting the values, we get:

Total Resistance = 1 / (1/((0.0626 ohms / 1000 feet) * 323 feet) + 1/((0.0626 ohms / 1000 feet) * 323 feet) + 1/((0.0626 ohms / 1000 feet) * 323 feet))

Simplifying the expression will give us the total resistance of the three 4/0 conductors installed in parallel.

It is not recommended to fire a gun straight up into the air.

When a bullet is fired into the air, it will eventually come down and can pose a danger to people and property below. The bullet can still be lethal when it reaches the ground, especially if it lands on a hard surface or hits someone directly.

Additionally, firing a gun in a residential area can be illegal and can result in legal consequences. In general, guns should only be fired in designated shooting ranges or in self-defense situations where there is an immediate threat to life. It is important to handle firearms responsibly and follow all safety guidelines to prevent accidents and injuries.

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Answer:

43.88 meters per second

Explanation:

The computation of the speed is shown below:

As we know that

\(Speed = \frac{Distance}{time}\)

where,

Distance is 395,000 meters

Time is 9,000 seconds

Now placing these values to the formula

So, the speed is

\(= \frac{395,000}{9,000}\)

= 43.88 meters per second

As speed shows the relation between the distance and time and the same is to be considered i.e by applying the formula