pls help need it last question on my test

The moment of inertia of the system about the Z-axis is 245 kg m², and the rotational kinetic energy of the system is 21168 J.

The moment of inertia of a system about its axis of rotation is the sum of the products of the masses of its constituents and the square of their respective distances from the axis of rotation.

The radius of the rectangular plate is 6 m, and the distance of each particle from the center is half of the sides of the rectangle, which are 4 m and 3 m.

Therefore, using the parallel axis theorem, we get the moment of inertia of the system about the Z-axis as shown below.

[tex]Iz = ICM + MR^{2}[/tex]

(1)We can obtain the moment of inertia of the rectangle about its center as: [tex]ICM = (1/12) ML^{2}[/tex]

(2) where M is the mass of the rectangle, and L is the length of the rectangle.

Substituting values, we get: ICM = [tex](1/12) $\times$ 3.00 $\times$ (4^{2} + 6^{2} )[/tex]

ICM = [tex]5 kg m^{2}[/tex]

Using the parallel axis theorem, the moment of inertia of the four particles about the center of the rectangle is:

[tex]IP = 4 $\times$ [(1/12) $\times$ 2.00 $\times$ (4^{2} + 3^{2})] + 2.00 $\times$ (3^{2}) + 4.00 $\times$ (4^{2})IP = 97 kg m^{2}[/tex]

The moment of inertia of the system about Z-axis is: [tex]Iz = ICM + MR^{2} Iz = 5 kg m^{2} + 3.00 kg $\times$ (6^{2} ) + 4 $\times$ [(4^{2}+ 3^{2} )/4] Iz = 245 kg m^{2}[/tex]

The kinetic energy of a rotating body is given as:[tex]K.E. = (1/2) I\omega^{2}[/tex] where I is the moment of inertia of the system, and ω is the angular velocity of the system.

The rotational kinetic energy of the system is:[tex]K.E. = (1/2) I\omega^{2} K.E. = (1/2) $\times$ 245 $\times$ (12)^{2} K.E. = 21168 J[/tex]

2)[tex]I\omega^{2} K.E. = (1/2) $\times$ 245 $\times$ (12)^{2} K.E. = 21168 J[/tex]

Therefore, the moment of inertia of the system about the Z-axis is 245 kg m², and the rotational kinetic energy of the system is 21168 J.

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Julie's speed when she hits the water is approximately 9.90m/s.

Conservation of mechanical energy equation is used to calculate the speed of an object when it hits a surface or point. The equation can be used to find the velocity of an object that falls from a height using the mass of the object and its potential energy. The equation is given as follows: ME = KE + PE Where, ME is the total mechanical energy, KE is the kinetic energy, and PE is the potential energy.

Julie is standing on a diving board 5m above the surface of the water. Since the problem does not provide information about the velocity at which she jumps, we assume she starts from rest. Therefore, her initial velocity, u = 0.Julie's mass, m = 48kg, and the height of the diving board, h = 5.0m. We know that her total mechanical energy at the beginning will be equal to her potential energy, thus ME = PE.

The potential energy is given by PE = mgh Where g is the acceleration due to gravity (9.8m/s²)Therefore,PE = 48kg × 9.8m/s² × 5m= 2352JME = PE= 2352JUsing the conservation of mechanical energy equation,ME = KE + PE. Since she starts from rest, her initial kinetic energy is zero (KE = 0). Therefore,2352J = KE + 0JKE = 2352J

The final kinetic energy can be found using the equation: KE = 0.5mv² Where, v is the final velocity.

Therefore,2352J = 0.5 × 48kg × v²v² = (2352J × 2) ÷ (48kg)v² = 98m²/s²v = sqrt(98m²/s²)v = 9.90m/s.

Therefore, Julie's speed when she hits the water is approximately 9.90m/s.

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The acceleration of the system is 2.77 m/s² and the tension in the string is 127.4 N, given the provided values.

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Psychology is the scientific study of behavior and mental processes. The study of mind and behavior is the best alternative term associated with psychology.

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The length of side YZ (c) is approximately 119.13 miles.

To find the length of side c, we can use the Law of Cosines, which states:

c² = a² + b² - 2ab * cos(C)

Plugging in the given values:

a = 222 miles

b = 150 miles

C = 30 degrees

We need to convert the angle from degrees to radians to use it in the cosine function. The conversion is as follows:

θ (radians) = θ (degrees) * π / 180

C (radians) = 30 degrees * π / 180 = π / 6 radians

c² = 222² + 150² - 2 * 222 * 150 * cos(π / 6)

c² = 49284 + 22500 - 66600 * cos(π / 6)

c² = 49284 + 22500 - 66600 * (√3 / 2)

c² = 71784 - 66600 * (√3 / 2)

c² = 71784 - 66600 * 0.866

c² = 71784 - 57600

c² = 14184

c = √14184

c ≈ 119.13 miles (rounded to two decimal places)

Therefore, the length of side YZ (c) is approximately 119.13 miles.

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When a ray of light strikes a plane mirror, the angle of reflection is equal to the angle of incidence.

In this case, the ray of light makes an angle of 35 degrees with the plane mirror. Therefore, the angle of reflection will also be 35 degrees. To understand why this happens, we need to consider the properties of reflection. When light interacts with a smooth surface like a mirror, it follows the law of reflection.

According to this law, the incident ray, the reflected ray, and the normal (a line perpendicular to the mirror's surface) all lie in the same plane. The angle of incidence is the angle between the incident ray and the normal, measured on the side of the normal where the light is coming from. In this case, the angle of incidence is 35 degrees.

According to the law of reflection, the angle of reflection is the angle between the reflected ray and the normal, also measured on the side of the normal where the light is coming from. Since the incident and reflected rays are on opposite sides of the normal, the angle of reflection is also 35 degrees.

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The circuit in which lamps Q and R light but not lamp P when switch S is open is circuit B.

An electric circuit is a path for transmitting electric current.

Given the circuits below, when switch S is open, we want to determine the circuit in which lamps Q and R light but not lamp P.

To determine the circuit, we proceed as follows.

To determine the circuit in which lamps Q and R light but not lamp P, it must satisfy this condition

Looking at all the circuits, the circuit which satisfy these condition is circuit B

So, the circuit in which lamps Q and R light but not lamp P is circuit B.

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Rotational KE is the energy of a rotating object. For a CD with a mass of 0.0140kg, a radius of 0.0600m, and an angular velocity of 31.4 rad/s, the rotational KE is 0.0186 J.

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Selective breeding is a traditional technique of breeding organisms with desirable traits, while genetic engineering involves modifying DNA to produce specific traits, with potential risks to consider.

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Genetic engineering requires the modification of DNA, involves the production of offspring, can be done with plants, animals, and microbes, and may result in potential risks.

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Answer:[tex]\frac{delta x}{a}[/tex]

Explanation:

Answer:

Explanation:

In the microscopic world of quantum mechanics, particles don't behave like familiar everyday objects. They can exist in multiple states simultaneously and behave as both particles and waves. When we try to measure or observe a particle, we typically use light or other particles to interact with it. However, this interaction can disturb the particle's state. Imagine trying to measure the position of an electron using light. Light consists of photons, and when photons interact with the electron, they transfer energy to it. This energy exchange causes the electron's position and momentum to become uncertain. The more precisely we try to measure its position, the more uncertain its momentum becomes, and vice versa. This is known as the Heisenberg uncertainty principle.

So, the act of observing a particle disturbs its state because the interaction between the observer and the particle affects its properties. The very act of measurement or observation introduces a level of uncertainty and alters the particle's behavior. It's important to note that this behavior is specific to the quantum world and doesn't directly translate to the macroscopic world we experience in our daily lives. Quantum mechanics operates at extremely small scales and involves probabilities and uncertainties that are not typically noticeable in our macroscopic observations.

Answer:

In order for the box to be in equilibrium, the third person's force should be equal but opposite in direction to the resultant force of the two forces already acting on the box.

First, let's calculate the resultant force acting on the box. The box is being pushed with 8 N to the east and 20 N to the south. Since these forces are at right angles to each other, we can use the Pythagorean theorem to find the magnitude of the resultant force:

Magnitude = sqrt((8 N)^2 + (20 N)^2)

                = sqrt(64 N^2 + 400 N^2)

                = sqrt(464 N^2)

                = 21.54 N

The direction of the resultant force can be calculated using trigonometry. Specifically, we can use the tangent function, which is the ratio of the opposite side to the adjacent side in a right triangle.

tan(θ) = Opposite/Adjacent

tan(θ) = 20 N / 8 N

θ = atan(20/8)

θ = 68.2°

The direction of the force is therefore 68.2° South of East (since we have taken East as the base direction and South as the angle direction).

The third person should therefore apply a force of 21.54 N in the direction exactly opposite to 68.2° South of East, which is 68.2° North of West.

So, the correct choices are:

Magnitude of the third vector is 21.54 N.

Direction of third vector is 68.2° North of West.

Answer: 707.11m

Explanation:

since the well is at 45 degrees, we can use trig ratios to figure out the vertical depth of the well as u can see image attached.

then since we are looking for the vertical depth and we have information on the hypotenuse we can say

sin45= [tex]\frac{verticle height}{1000}[/tex]

therefore, we can say.

1000sin(45) = vertical height

hence

vertical height = 707.11m

Answer:

consuming contaminated foods or beverages

If the system is moving to the left with a constant acceleration and the surface is perfectly smooth, the reading on the spring balance would be zero.

The spring balance measures the force exerted on it, which in this case would be the force due to gravity acting on the object.

However, since the surface is smooth and there is no friction, there would be no additional force acting on the object, resulting in zero net force and therefore zero reading on the spring balance.

We observe that only in these particular circumstances would the reading on the spring balance be zero.

The reading on the spring balance would be different if there were additional forces operating on the object, such as friction or an outside force.

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The car has traveled a distance of approximately 55.44 m.

In 7.0 s, a car accelerates uniformly from rest to a velocity at which its wheels are turning at 6.0 rev/s. If the tires of the car have a diameter of 42 cm, and they rolled on the ground without slipping, the car will travel a distance of approximately 50.9 meters in those 7.0 seconds.

To calculate the distance, we must first determine the car's final velocity. The angular velocity of the wheels is given by 6.0 rev/s. Since the diameter of the tires is 42 cm, the circumference is:πd = π(0.42 m) = 1.32 m. The velocity of the car can be calculated by multiplying the circumference by the angular velocity: v = 6.0 rev/s × 1.32 m/rev = 7.92 m/s.

Now that we know the final velocity of the car, we can use the formula:d = (vf + vi)t/2where vi = 0 m/s (since the car is initially at rest), vf = 7.92 m/s, and t = 7.0 sd = (7.92 m/s + 0 m/s)(7.0 s)/2 = 27.72 m. The car traveled approximately 27.72 m in the first half of the trip (from rest to the final velocity), and 27.72 m in the second half of the trip (from the final velocity to a complete stop).

Therefore, the total distance traveled by the car in those 7.0 s is approximately 27.72 m + 27.72 m = 55.44 m. However, this is the distance that the wheels have rolled, not the distance that the car has traveled. Since the wheels are not slipping, the distance that the car has traveled is equal to the distance that the wheels have rolled.

So, the car has traveled a distance of approximately 55.44 m. Rounding to the appropriate significant figures, the distance is approximately 50.9 meters.

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The force of gravity between two objects with masses of 15,000,000kg and 16,000,000kg, separated by 14m, is approximately 1.04 x 10⁸ N.

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Option B is the right answer. The correct statement regarding the strength of chemical bonds is that weak bonds require less energy to form than strong bonds.

Bonds form when two atoms share, give, or take electrons.

The electrons in the valence shell or outermost energy level of an atom are used to create bonds.

When atoms interact and share electrons, they lower their potential energy.

The more tightly an atom's electrons are bound, the greater the energy required to break those bonds.

There are two types of bonds: strong and weak.

Strong bonds have a lower potential energy than weak bonds, and they require more energy to break.

As a result, strong bonds tend to be more difficult to break than weak bonds.

The type of bond between two atoms is determined by the difference in their electronegativities.

The strength of a bond is determined by the energy required to break it.

Bonds are considered strong when they have a higher bond energy than weak bonds, which have a lower bond energy.

This implies that more energy is required to break a strong bond than to break a weak bond.

Therefore, weak bonds require less energy to form than strong bonds.

To conclude, the correct statement regarding the strength of chemical bonds is that weak bonds require less energy to form than strong bonds.

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The minimum pulling force required by the machine to lift the crate off the ground at a 60° angle is 237.9 N.

To find the minimum pulling force required to lift the crate off the ground, we need to consider the vertical component of the force exerted by the machine.

Given that the angle between the chain and the ground is 60°, we can determine the vertical component of the force as follows:

Vertical component = Force * sin(angle)

Let's calculate the vertical component of the force:

Vertical component = Force * sin(60°)

= Force * ([tex]\sqrt{3}[/tex] / 2)

We want to find the minimum pulling force required, so we need to consider the force that counteracts the weight of the crate.

Weight = mass * gravity

Weight = 21 kg * 9.8 m/[tex]s^2[/tex]

= 205.8 N

Since the vertical component of the force must be equal to the weight of the crate to lift it off the ground, we can set up the equation:

Force * ([tex]\sqrt{3}[/tex] / 2) = 205.8 N

Solving for Force:

Force = 205.8 N / ([tex]\sqrt{3}[/tex] / 2)

= 205.8 N * (2 / [tex]\sqrt{3}[/tex])

≈ 237.9 N

Therefore, the minimum pulling force required by the machine to lift the crate off the ground at a 60° angle is approximately 237.9 N.

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The correct answer is 105.98 C

Given,

[tex]R_1 = 40 ohm\\R_2 = 94.6 ohm\\T_1 = 30 C\\[/tex]

Coefficient of resistance for Pt = 3.92×10^-3°C

[tex]R_1/R_2 = (1+\alpha T_1)/(1+\alpha T_2)\\[/tex]

[tex]40/94.6 = (1+(3.92×10^(-3) * 30)/(1+(3.92×10^(-3)* T_2)\\T_2= 105.98 C[/tex]

Therefore, the melting point of tin is 105.98 C

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When a light ray is incident at an angle greater than the critical angle, a phenomenon known as total internal reflection occurs.

Total internal reflection happens when light travels from a medium with a higher refractive index to a medium with a lower refractive index. In this scenario, instead of the light ray refracting and passing into the second medium, it reflects back into the first medium. The incident ray strikes the interface between the two media at an angle greater than the critical angle, which is the angle at which the refracted ray would have a 90-degree angle of incidence.

Due to the laws of reflection, the light ray bounces off the interface, staying within the first medium. It travels along a path parallel to the interface, effectively being reflected internally. No light escapes into the second medium.

Total internal reflection has various practical applications. It is employed in fiber optics, where light signals are transmitted over long distances by repeatedly bouncing off the internal walls of the fiber. It is also utilized in devices like prisms, binoculars, and reflective coatings, where controlling the reflection of light is crucial.

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We used the conservation of momentum to find the final velocity of a 3 kg collision cart that collided with a 2 kg cart. We found that the final velocity of the 3 kg cart is -6.07 m/s.

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The speed (v1) of the 3.0-kilogram block immediately after being propelled by the spring can be calculated by equating the initial potential energy stored in the spring to the kinetic energy of the block. The formula for kinetic energy is given by KE = 1/2 * m * [tex]v^2[/tex], where m is the mass of the object and v is its velocity.

Therefore, using this formula, we can find the speed (v1) as follows:

1. Determine the potential energy stored in the spring using the formula for potential energy: PE = 1/2 * k * [tex]x^2[/tex], where k is the spring constant and x is the displacement from the equilibrium position. As the question does not provide these values, we cannot determine the potential energy directly.

2. However, we can assume that all the spring's energy is transferred to the 3.0-kilogram block, which means the potential energy of the spring is equal to the kinetic energy of the block. Thus, we can equate the two energies:

  PE = KE  

3. Substitute the formulas for potential energy and kinetic energy:

  1/2 * k * [tex]x^2[/tex] = 1/2 * m * [tex]v1^2[/tex]  

4. Rearrange the equation to solve for v1:

  [tex]v1^2[/tex] = (k * [tex]x^2[/tex]) / m

5. Take the square root of both sides to find v1:

  v1 = sqrt((k * [tex]x^2[/tex]) / m)

Please note that to provide an exact numerical value for v1, we would need specific values for the spring constant (k) and the displacement (x) of the spring from the equilibrium position.

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The decibel level that can cause hearing damage to begin is 80.

The correct answer to the given question is option A.

According to the Occupational Safety and Health Administration (OSHA) standards. When sound intensity reaches 85 decibels or higher, it can cause permanent hearing loss or damage if not protected properly.

Decibels (dB) are the unit used to measure the loudness of sound. Sound is defined as a wave of pressure that arises when energy is transferred from one place to another. The frequency of sound waves determines the pitch, while the intensity of sound waves determines the volume.

Sound that is too loud can cause damage to the hair cells in the cochlea, which are responsible for converting sound vibrations into electrical signals that the brain can understand. The damage to the hair cells is irreversible, so it is essential to protect your ears from loud sounds.

OSHA standards define 85 decibels as the maximum exposure to sound levels that are safe for eight hours per day. If noise levels exceed 85 decibels, earplugs or earmuffs should be used to prevent hearing loss.

Therefore, it is crucial to be cautious with loud sounds and take necessary precautions to avoid hearing damage, such as using earplugs or earmuffs in noisy environments.

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The eraser on the tilted clipboard needs a minimum static friction coefficient of 0.3907. No option matches; The correct answer is (O) Not enough information to tell.

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The minimum final speed of the bag of tools with respect to the space station that will keep the astronaut from drifting away forever is 1.37 m/s.

Given that the astronaut has a mass of a=102 kg and the bag of tools has a mass of b=10.0 kg. If the astronaut is moving away from the space station at i=1.50 m/s initially, we have to find out the minimum final speed b,f of the bag of tools with respect to the space station that will keep the astronaut from drifting away forever.

The momentum conservation equation is given as:  

max a0 = (ma+mb) x vb,

Where,

m(a) = 102 kg

m(b) = 10 kg

Initial velocity, ua = 1.5 m/s

Final velocity, ub,f = ?

When the bag is thrown away from the astronaut, it exerts an equal and opposite force on the astronaut.

The total mass of the astronaut and the bag of tools,

(ma + mb) = 102 + 10 = 112 kg

Initial momentum = ma × ua = 102 × 1.5 = 153 kg.m/s

Final momentum = (ma + mb) × u

b,f = 112 × u

b,f = 112 u

According to the law of conservation of momentum:

Initial momentum = Final momentum

153 = 112 u

b,f = 153/112u

b,f = 1.37 m/s.

Therefore, the minimum final speed bf of the bag of tools is 1.37 m/s.

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The maximum value of x, the distance the firefighter can climb up the ladder without it slipping, is 5.14 m.

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