5. average A body sets off from rest with a constant acceleration of 8.0 m/s? What distance will it have covered after 3.0 s? 6.
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The pendulum will be moving at approximately 0.754 m/s when it passes through the lowest point of its swing.

To determine the speed of the pendulum when it passes through the lowest point of its swing, we can use the principle of conservation of mechanical energy.

At the highest point (2.9 cm above the resting position), the pendulum has gravitational potential energy. As it swings down, this potential energy is converted into kinetic energy, given by the equation:

Potential Energy (PE) = Kinetic Energy (KE)

The highest point's potential energy is given by:

PE = mgh

Where:

m = pendulum mass (4.0 kg).

g = acceleration due to gravity (9.8 m/s^2)

h = height above the resting position (2.9 cm = 0.029 m)

Substituting the values, we have:

PE = 4.0 kg * 9.8 m/s^2 * 0.029 m = 1.1356 J

Since energy is conserved, this potential energy will be completely converted into kinetic energy at the lowest point. Thus, the kinetic energy is also 1.1356 J:

KE = 1.1356 J

The following equation gives the kinetic energy:

KE = (1/2)mv^2

Where:

m = pendulum mass (4.0 kg).

v = velocity of the pendulum at the lowest point

Rearranging the equation to solve for v:

v^2 = (2KE) / m

v^2 = (2 * 1.1356 J) / 4.0 kg

v^2 = 0.5678 m^2/s^2

Taking the square root of both sides results in the following:

v ≈ 0.754 m/s

Therefore, the pendulum will be moving at approximately 0.754 m/s when it passes through the lowest point of its swing.

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Answer:

a. i) The pressure drop per unit length is 52,151.89 Pa

ii) The atmospheric pressure ≈ 19.175 × The pressure drop along 10 cm length of aorta

b i) The power required for the heart to push blood along a 10 cm length of aorta, is 2.6075945 Watts

ii) The basal metabolic rate ≈ 38.35 × The power to push the blood along a 10 cm length of aorta

c. i) Please find attached the drawing for the velocity profile created with Microsoft Excel

ii) The velocity at the center is approximately 2.04 m/s

Explanation:

The given diameter of the aorta, D = 2.5 cm = 0.025 m

The maximum flow rate, Q = 500 cm³/s = 0.0005 m³/s

Assumptions;

The blood flow is laminar

The blood is a Newtonian fluid

The viscosity of water ≈ 0.01 poise = 1 cp

a. i) The pressure drop per unit length of pipe ΔP/L is given by the Hagen Poiseuille equation as follows;

\(Q = \dfrac{\pi \cdot R^4}{8 \cdot \mu} \cdot \left(\dfrac{\Delta p}{L} \right)\)

Where;

Q = The flow rate = A·v

A = The cross sectional area

R = The radius = D/2

Δp/L = The pressure drop per unit length of the pipe

Therefore, we have;

\(\dfrac{\Delta p}{L} = \dfrac{Q\cdot 8 \cdot \mu }{\pi \cdot R^4} = \dfrac{0.0005 \times 8 \times 1}{\pi \times 0.0125^4 } = 52151.89\)

The pressure drop per unit length ΔP/L = 52,151.89 Pa

ii) The pressure, ΔP, drop along 10 cm (0.1 m) length of aorta = ΔP/L × x;

∴ ΔP = 52,151.89 Pa × 0.1 m = 5,215.189 Pa

Given that the atmospheric pressure, \(P_{atm}\) = 10⁵ Pa, we have;

\(P_{atm}\)/ΔP = 10⁵/5,215.189 ≈ 19.175

Therefore, the atmospheric pressure is approximately 19.175 times the pressure drop along 10 cm length of aorta

b. i) The power, P = Q × ΔP

Therefore, the power required for the heart to push blood along a 10 cm length of aorta, is P₁₀ = 0.0005 m³/s × 5,215.189 Pa = 2.6075945 Watts

ii) Therefore compared to the basal metabolic rate of, 'P', 100 W, we have;

P/P₁₀ = 100 W/2.6075945 Watts = 38.349521 ≈ 38.35

The basal metabolic rate is approximately 38.35 times more powerful than the power to push the blood along a 10 cm length

c. i) The velocity profile across the aorta is given as follows;

\(v_m = \dfrac{1}{4 \cdot \mu} \cdot \dfrac{\Delta P}{L} \cdot R^2\)

Where;

\(v_m\) = The velocity at the center

We get;

\(v_m = \dfrac{1}{4 \times 1} \times 52,151.89 \times 0.0125^2 \approx 2 .04\)

The velocity at the center, \(v_m\) ≈ 2.04 m/s

ii) The velocity profile, v(r), is given by the following formula;

\(v(r) = v_m \cdot \left[1 - \dfrac{r^2}{R^2} \right]\)

Therefore, we have;

\(v(r) = 2.04 - \dfrac{2.04 \cdot r^2}{0.0125^2} \right] = 2.04 - 163\cdot r^2\)

The velocity profile of the pipe is created with Microsoft Excel

Answer:

PE = 137.2931 J

Explanation:

PE = 137.2931 J

The kinetic energy of the flywheel after 1 minute of rotation, given that it has a mass of 50 and radius of 40 cm is 32.4 KJ (Option D)

We'll begin by obtaining the velocity of the flywheel. This is shown below:

v = at

v = 0.6 × 60

v = 36 m/s

Finally, we shall determine the kinetic energy of the flywheel. Details below:

KE = ½mv²

KE = ½ × 50 × 36²

KE = 25 × 1296

KE = 32400 J

Divide by 1000 to express in KJ

KE = 32400 / 1000

KE = 32.4 KJ

Thus, the kinetic energy is 32.4 KJ (Option D)

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The current required for a uniform bar to be in rotational equilibrium when it is at an angle of 30.0° above the horizontal and carrying a current I in a magnetic field B is zero, as the torque acting on the bar is zero at this angle.

To find the current I in the bar for it to be in rotational equilibrium when it is at an angle of 30.0° above the horizontal, we need to use the torque equation for a uniform bar carrying a current I in a magnetic field B:

τ = 1/2 IBL² sinθ

where τ is the torque, I is the current, B is the magnetic field, L is the length of the bar, and θ is the angle of the bar relative to the magnetic field.

Since we want the bar to be in rotational equilibrium, the torque must be zero, so we can set the torque equation equal to zero:

0 = 1/2 IBL² sin30°

Solving for I, we get:

I = 0 / (1/2 B L² sin30°)

I = 0

Therefore, the current required for the bar to be in rotational equilibrium when it is at an angle of 30.0° above the horizontal is zero. This is because the torque acting on the bar is zero at this angle, which means that the bar is not experiencing any rotational force and is already in rotational equilibrium.

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Answer:

True. The two laws of thermal radiation state; 1) "Each square meter of a hotter object

Explanation:

Answer:

A Impulse = – 25 Ns

B. Time = 5 s

Explanation:

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

Mass (M) = 5 Kg

Initial velocity (u) = 8 m/s

Final velocity (v) = 3 m/s

Impulse (I) =?

Time (t) =?

A. Determination of the Impulse.

Mass (M) = 5 Kg

Initial velocity (u) = 8 m/s

Final velocity (v) = 3 m/s

Impulse (I) =?

I = Ft = M(v – u)

I = M(v – u)

I = 5 (3 – 8)

I = 5 × – 5

I = – 25 Ns

NOTE: the negative sign indicates that the net force is acting in the negative direction.

B. Determination of the time.

Impulse (I) = 25 Ns

Force (F) = 5 N

Time (t) =?

I = Ft

25 = 5 × t

Divide both side by 5

t = 25 / 5

t = 5 s

Thus, it will take 5 s for the box to slide through the 15 m long ramp.

Answer:

Magdeburg hemispheres are two half-spheres of equal size. Placing them together traps air between them. This air is merely trapped, and not compressed, so the pressure inside is the same as the pressure of the atmosphere outside the spheres. The spheres thus pull apart with nearly no resistance.

The Magdeburg hemispheres are a pair of large copper hemispheres, with mating rims. They were used to demonstrate the power of atmospheric pressure. When the rims were sealed with grease and the air was pumped out, the sphere contained a vacuum and could not be pulled apart by teams of horses.

Answer:

d. convention

Explanation:

hope this helped

Taking into account the definition of kinetic energy, the velocity of the object with a kinetic energy of 250 J and a mass of 32 kg is 3.95 m/s².

Kinetic energy is the energy possessed by a body or system due to its movement.

Kinetic energy is defined as the amount of work necessary to accelerate a body of a certain mass and in a position of rest, until it reaches a certain speed. Once the final speed is reached, the amount of kinetic energy accumulated will remain constant, that is, it will not vary, unless another force acts on the body again.

Kinetic energy is represented by the following expression:

Ec = 1/2×m×v²

Where:

In this case, you know:

Replacing in the definition of kinetic energy:

250 J = 1/2× 32 kg×v²

Solving:

250 J÷ (1/2× 32 kg) = v²

15.625 J÷kg = v²

√15.625 J÷kg = v

3.95 m/s² = v

Finally, the velocity of the object is 3.95 m/s².

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Explanation:

You want  N/m

 N = 66 * 9.81

 m = 2.3 x 10^-2 m

66* 9.81 / 2.3 x 10^-2  = 28150 =  28 000 N/m    to two S D

Answer:

Sleep-wake homeostasis. This technical term describes something most of us know implicitly from experience: the longer you’re awake, the more you feel a need to sleep. This is because of the homeostatic sleep drive, the body’s self-regulating system in which pressure to sleep builds up based on how long you’ve been awake. This same drive causes you to sleep longer or more deeply after a period of insufficient sleep.

Explanation:

huh

Answer:

Bob's angular speed is the same as that of lily

Explanation:

Because for a carousel the angular speed remains the same since velocity at center and edge are the same

A. The average speed you can use to pull the safe is 1.02 m/s

B. The time needed to pull the safe up is 17.65 s

First, we shall obtain the force. This is shown below:

F = mg

F = 60 × 9.8

F = 588 N

Finally, we shall obtain the average speed. Details below:

Power = force × average speed

600 = 588 × average speed

Divide both sides by 588

Average speed = 600 / 588

Average speed = 1.02 m/s

The time needed to pull the safe up can be obtained as follow:

Time = Total distance / average speed

Time = 18 / 1.02

Time = 17.65 s

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Complete question:

You know you can provide 600 W

of power to move large objects. You need to move a 60-kg

safe up to a storage loft, 18 m

above the floor.

Part A

With what average speed can you pull the safe straight up?

Part B

What is the time needed to pull the safe up?

Answer:

The two main types of bonds formed between atoms are ionic bonds and covalent bonds.

Explanation:

Hope this helped <3

In a case whereby the lowest pitch that the average human can hear has a frequency of 28.0 Hz sound with this frequency travels through air with a speed of 331M/S  the wave length is

Frequency refers to the number of vibrations measured each second. A wave is a collection of vibrations known as energy. The top node is referred to as the trough, and the bottom node as the crest.

λ = wave velocity/frequency

λ = 331 m/s / 28 Hz

λ = 11.82 m

As a result, the lowest pitch that a typical person can hear is at a frequency of 29 Hz. The wavelength of sound at this frequency is 11.82 m as it moves through air at a speed of 331 m/s.

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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

Answer:

Direction and magnitude

Answer:

I = 0.25 [amp]

Explanation:

To solve this problem we must use ohm's law which tells us that the voltage is equal to the product of the current by the resistance.

V = I*R

where:

V = voltage [Volt]

I = amperage or current [amp]

R = resistance [ohm]

Since all resistors are connected in series, the total resistance will be equal to the arithmetic sum of all resistors.

Rt = 2 + 8 + 14

Rt = 24 [ohm]

Now clearing I for amperage

I = V/Rt

I = 6/24

I = 0.25 [amp]

Answer: 0.25

Explanation:

The change in momentum is given as:

where the momentum is defined as:

The average acceleration of the motorcycle over the given distance is approximately 9.39 m/s².

To calculate the average acceleration of the motorcycle, we can use the formula:

Average acceleration = (final velocity - initial velocity) / time

First, let's convert the final velocity from km/h to m/s since the distance is given in meters. We know that 1 km/h is equal to 0.2778 m/s.

Converting the final velocity:

Final velocity = 78 km/h * 0.2778 m/s = 21.67 m/s

Since the motorcycle starts from rest (initial velocity is zero), the formula becomes:

Average acceleration = (21.67 m/s - 0 m/s) / time

To find the time taken to reach this velocity, we need to use the formula for average speed:

Average speed = total distance/time

Rearranging the formula:

time = total distance / average speed

Plugging in the values:

time = 50 m / 21.67 m/s ≈ 2.31 seconds

Now we can calculate the average acceleration:

Average acceleration = (21.67 m/s - 0 m/s) / 2.31 s ≈ 9.39 m/s²

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Compression reinforcement should be added to make this a tension-controlled section. The same process should be repeated for the second case, but with an assumed εr = 0.0035.

In this case, the task is to design two rectangular beam sections that can resist a factored design moment of Mu=270 kip-ft. The goal is to select b and d (based on integer values of b and h) and the tension steel area As (choose bar sizes that satisfy steel requirement). Both cases should have a section with b approximately equal d/2 and use fc = 5,000 psi and fy = 60,000 psi. Based on practicality, it is desired that b and h both be integers. Starting with an assumed Et is similar to assuming a as the starting point as in the example discussed in the class.

To start the design, one should assume that εr = 0.0050b and check that the ultimate moment capacity (M) computed using ACI procedures exceeds the factored design moment. If necessary, compression reinforcement should be added to make this a tension-controlled section. The same process should be repeated for the second case, but with an assumed εr = 0.0035.

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Answer:

It should be 125 CM

Explanation:

Volume is Length•Width•Height

A cube is equal on all lengths so, 5•5•5

Answer:

125cm cubed

Explanation:

just search volume calculator lol

Answer:

I belive that the answer is the A

Crest describes the high point of a transverse wave. Therefore, the correct option is option A.

Transverse waves are those which oscillate in directions that are opposite to the wave's forward motion. Electromagnetic radiation, seismic waves, or water surface ripples are all examples of transverse waves.

A simple transverse wave can be represented by a sine or cosine curve because any point's amplitude—that are, its distance from the axis—is proportional to the sine (or cosine) associated with that angle. Crest describes the high point of a transverse wave.

Therefore, the correct option is option A.

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Answer:

Explanation: The moon of the Earth is much lighter in mass than the planet itself. In addition to being smaller than Earth, the Moon is also only approximately 60% as dense. A human weighs less on the Moon because there is less gravitational attraction there than there is on Earth.

Moon has lesser mass as conpared to earth, therefore gravitational force exerted by moon on any object is lesser than that of gravitational force exerted by earth on the same object, hence we can say that astronauts weight less on moon, i.e approximately 1/6 th of their weight on earth.