A 500-mm-long, 16-mm-diameter rod made of a homogenous,
isotropic material is observed to increase in length by 300 mm, and
to decrease in diameter by 2.4 mm when subjected to an axial 12-
kN load. Determine the modulus of elasticity and Poisson's ratio of
the material. [20 marks]

Answer:

666.7 W

Explanation:

Power = P = W/t = 4000 J/6 s = 666.7 W (watts)

Answer:

800

Explanation:

10^2 = 100
8 x 100  = 800

Answer: A step-down transformer changes the magnitude of the voltage in an alternating current (AC) electrical signal. It reduces the voltage of the AC signal by using a winding ratio between the primary (input) and secondary (output) coils that is less than 1:1.

Explanation: For example, if the winding ratio of a step-down transformer is 1:0.5, the output voltage of the secondary coil will be half the magnitude of the input voltage of the primary coil. In this case, the transformer would change the AC voltage from a higher value to a lower value.

The transformer does not change the frequency of the AC signal, which is determined by the source of the electrical power. The transformer also does not change the waveform of the AC signal, which is typically a sinusoidal wave.

Wind turbines, hydroelectric, and geothermal heat have been relied upon for decades to provide a renewable and clean energy source to people around the world. These alternative energy technologies provide optimal clean and renewable energy sources for many communities and countries striving for sustainable development.

Answer:

1.08 x 10^5 J

Explanation:

First, apply the formula V = IR , where V is the voltage, I is the current and R is the resistance.

R -> 20 ohm (Given)

I -> 3A (Given)

Hence, V = 3 x 20 = 60V (60 volts)

Next, apply the formula E = Pt , where E is the energy produced, P is the power and t is the time in seconds

Furthermore, since P = IV (power = current x voltage)

The formula can be re-expressed as E = VIt

t -> 10 minutes = 600 seconds (don't forget to convert time to seconds!)

Therefore, energy = (60 x 3 x 600) J

                              = 108000 J

                               = 1.08 x 10^5 J (in scientific notation)

Hea produced in the resistance = energy produced in the resistor

                                                      = 1.08 x 10^5 J

Answer:I have already did this the answer was bar graph!

Explanation:

Answer:

0.48 rad/s

Explanation:

We can use this equation to find the final velocity

[tex]w_f=w_0+at[/tex]

We are given

[tex]w_0=0.16[/tex]

[tex]t=8.0[/tex]

[tex]a=0.04[/tex]

Inserting those numbers into our equation gives us

[tex]w_f=0.16+0.04*8[/tex]

Lets solve for [tex]w_f[/tex].

[tex]w_f=0.16+0.32[/tex]

[tex]w_f=0.48[/tex]

Answer:

56.7m

Explanation:

horizontal velocity does not matter in this situation because it stays constant (no unbalanced force acting upon it)

a=9.81m/s^2              

t=3.4s

Vi=0m/s

d=Vi*t+1/2at^2

d=1/2at^2

d=1/2*9.81m/s^2*(3.4s)^2

d=4.905m/s^2*11.56s^2

d=56.7m

Answer:

Δp=-18799.5kg*m/s

Explanation:

Δv=Vf-Vi

Δv=2.9m/s-18m/s

Δv=-15.1m/s

m*Δv=Δp

1245kg*(-15.1m/s)=Δp

Δp=-18799.5kg*m/s

Extra:

Deriving mΔv=Δp

Δp=Pf-Pi

Δp=m*Vf-m*Vi

Δp=m(Vf-Vi)

Vf-Vi=Δv

Δp=m(Δv) or Δp=mΔv

The minimum force needed to move the whale along a horizontal ramp, given that the whale has a mass of 1.90×10⁵ Kg is 856520 N

We'll begin by listing out the given parameters from the question. This is shown below:

To obtain the force needed to move the whale, we shall first obtain the normal reaction. This is shown below:

N = mg

N = 1.90×10⁵ × 9.8

N = 1862000 N

Finally, we shall determine the force needed. Details below:

F = μN

F = μN

F = 0.460 × 1862000

F = 856520 N

Thus, we can conclude that the force needed is 856520 N

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The goal kick strikes a defender racing at 5 m/s away from a goalkeeper in the back. The ball was moving at a speed of 70 m/s if it weighed 500g and the player's mass was 70k.

The goalkeeper extends the amount of time he has to hold the ball by pulling his hands back. He lessens the force (rate of change of momentum) the football exerts on him by lengthening the time.

A vector quantity, momentum. A body's momentum is equal to P=m.v if it is travelling at a speed of v while having mass m. P=mv describes the magnitude of the momentum. Because momentum is a function of mass and velocity, its unit is the product of those two quantities.

By using conservation of momentum,

Initial momentum = Final momentum

(5 x 70) + (v x 0.5) = (5.5 x 70) + (0 x 0.5)

350 + 0.5v = 385 + 0

0.5v = 35

v = 70 m/s

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Beta decay is seen in the nuclear reaction: ⁹⁰₃₉Y → ⁹⁰₄₀Zr + ⁰₋₁e. Hence, option (A) is correct.

A proton can change into a neutron or vice versa inside the radioactive sample's nucleus through a process known as beta decay.

The radioactive sample's nucleus can approach the ideal neutron/proton ratio as closely as feasible through processes like beta decay and alpha decay. The nucleus releases a beta particle during this process, which can either be an electron or a positron.

As electron releases here, it is a Beta (β) decay.

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Louis de Broglie's principle of electrons states that (b) They behave as a wave and a particle.

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Two forces are said to be balanced when their strengths are equal but their directions of action are opposing.

The forces are balanced if the pullers are exerting equal force but going in the opposite direction on either side of the rope.

Forces that are balanced can cancel one another out. The thing stays in place whenever there is a balanced force.

To lift, turn, move, open, close, push, pull, and many other things requires forces. You apply force to a ball when you throw it in order for it to travel through the air. An object can be under the influence of multiple forces at once.

Therefore, Two forces are said to be balanced when their strengths are equal but their directions of action are opposing.

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If atmospheric pressure is 101.3 KPa and the absolute pressure at the bottom of the tank is 231.3 KPa, the specific gravity of the olive oil is 1.30

To calculate the specific gravity, deduct the absolute pressure at the bottom of the tank (231.3 KPa) from the atmospheric pressure (101.3 KPa). This will give you a ratio of 130KPa, then divide it by the atmospheric pressure which is the specific gravity of olive oil.

Use the formula below:

specific gravity = absolute pressure - atmospheric pressure / atmospheric pressure

Specific gravity = (231.3 KPa - 101.3 KPa) / (101.3 KPa) = 1.30

Therefore, the specific gravity of the olive oil is 1.30.

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(a) The magnitude of the car's normal force is 7,792.2 N.

(b) The mass of the car is 795.1 kg.

The weight of the car is calculated by applying Newton's second law of motion as shown below.

Mathematically, the formula for Newton's second law of motion is given as;

Ff = μW

where;

The weight of the car is calculated as follows;

W = Ff / μ

W = ( 6,000 N ) / ( 0.77 )

W = 7,792.2 N

Based on Newton's third law of motion, the weight of the car acting downwards is equal to normal force on the car, acting upward.

The mass of the car is calculated as follows;

W = mg

where;

m = W / g

m = ( 7792.2 ) / (9.8)

m = 795.1 kg

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Answer:

0.15 m/s²

Explanation:

Acceleration is rate of change of velocity-time function. We can find acceleration by finding the slope. The slope of graph can be found by:

[tex] \displaystyle{a = \dfrac{ \Delta v}{ \Delta t} \: \to \: \dfrac{v_f - v_i}{t_f- t_i}}[/tex]

Substitute in:

[tex] \displaystyle{a = \dfrac{5 - 2}{40 - 20}} \\ \\ \displaystyle{a = \dfrac{3}{20}} \\ \\ \displaystyle{a = 0.15 \: \text{m/s}^{2} }[/tex]

Therefore, the acceleration is 0.15 m/s²

Answer:

4.95 m

Explanation:

The rocket's initial kinetic energy is equal to the final gravitational potential energy, so we can set these equal to each other and solve for the additional height the rocket will rise:

KEinitial = KEfinal

1/2 * m * v^2 = m * g * h

Substituting the given values, we have:

1/2 * 9.5 kg * v^2 = 9.5 kg * 9.8 m/s^2 * h

Solving for h, we find that the additional height the rocket will rise is h = 2390 J / (9.5 kg * 9.8 m/s^2) = 4.95 m.

Acceleration = (change in speed) / (time for the change)

Change in speed = (10,000 m/s) - (5,000 m/s)

Change in speed = 5,000 m/s

Time for the change = 1 minute

Time for the change = 60 sec

Acceleration = (5,000 m/s) / (60 s)

Acceleration =  83-1/3 m/s²

The  average velocity of the airplane  between  Milwaukee and Chicago  is 1083.33 meter/second.

The rate at which a body's displacement changes in relation to time is known as its velocity. Velocity is a vector quantity with both magnitude and direction. SI unit of velocity is meter/second.

The total distance between  Milwaukee and Chicago = 130 kilometer

= 1,300,000 meter.

Time interval = 20 minute = 20×60 second = 1200 second.

The  average velocity of the airplane = total distance/time interval

= 1,300,000 meter / 1,200 second.

= 1083.33 meter/second.

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The magnitude of the average force exerted on the glove by the other boxer is 466.3 N.

The force that acts on a body is defined as an agent that causes a change in the position or the state of an object.

Force can be defined as a push or pull agent.

The impulse that acts on a body is the product of the force that acts on that body and the time in which it acts.

Hence, the  relationship between force and impulse is given below:

Force = Impulse/time

The force exerted on the glove by the other boxer is calculated using the formula above as follows:

Force = 194 / 0.416

Force = 466.3 N

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Answer:

total potential energy is 383.18.

Explanation:

It is because that when we hold something at the influence of gravity than work is done . Similarly we know that

Potential Energy is Equal to the product of m g and h.Here weight gives the product of mass and acceleration due to gravity.so

PE = mgh

= 112.7×3.4

=383.18 joule

Unit of energy is joule

The horizontal component of the cat's displacement, Dx = 0 m

The vertical component of the cat's displacement, Dy = 12 m

The horizontal component of a vector is the value of that vector acting in the horizontal direction.

The horizontal component of a vector is given as Dx.

Dx = Dcosθ

where;

D is the resultant of the vector

θ is the angle of the vector from the horizontal

The horizontal component of the cat's displacement is:

Dx = 12 * 0

Dx = 0 m

The vertical component of a vector is the value of that vector acting in the vertical direction.

The vertical component of a vector is given as Dy.

Dy = Dsinθ

where;

D is the resultant of the vector

θ is the angle of the vector from the horizontal

The vertical component of the cat's displacement is:

Dy = 12 * 1

Dy = 12 m

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The displacement, acceleration, energy and velocity of the simple harmonic motion of the mass attached to the spring are as follows;

A) x(t) = 0.05·sin(10·t + π/2)

B) The acceleration is; a(t) = -2.5 m/s²

C) The total energy is 0.0625 J

D) The velocity is ±√3/4 m/s

The restoring force of a body in simple harmonic motion is directly proportional to the displacement of the body from its mean or central position.

Mass of the block, m = 2 kg

The spring constant, k = 200 N/m

The extension of the spring = 5 cm

Time at which the spring is released, t = 0

A. The motion of the spring with the mass is a Simple Harmonic Motion

The angular velocity can be obtained using the formula;

ω = √(k/m)

Therefore;
ω = √(200/2) = 10

The angular velocity of the block on the spring is, ω = 10 rad/s

The period, T = The time to complete 2·π rad

Therefore; T = 2·π rad/(10 rad/s) = π/5 s

The amplitude, A, is the cistance of the mass from the at rest position, which is 5 cm = 0.05 m

The equation of the extension of the spring is therefore;

x(t) = 0.05·sin(10·t + c)

At t = 0, x(t) = 0.05, therefore;

sin(10 × 0 + c) = sin(c) = 1

c = π/2

The equation for the displacement as a function of time is therefore;

B. The acceleration when x(t) = A/2 is obtained as follows;

x(t) = 0.05·sin(10·t + π/2)

A/2 = 0.05·sin(10·t + π/2)

A = 0.05

0.05/2 = 0.05·sin(10·t + π/2)

sin(10·t + π/2) = 1/2

10·t + π/2 = π/6

t = -π/30

cos(10×(-π/30) + π/2) = ±√3/2

v(t) = x'(t) = 0.05 × 10 × cos(10·t + π/2)

a(t) = v'(t) = -5·sin(10·t + π/2)

a(t) = v'(t) = -5·sin(10·t + π/2) = -5 × 1/2 = -2.5

C. The energy in a pring = (1/2)·k·x²

When x = A/2, we get;

E = (1/2) × 200 × (0.05/2)² = 0.0625

D) The velocity when x = A/2 is; v(t) = x'(t) = 0.05 × 10 × cos(10·t + π/2)

v(t) = 0.5 × cos(10·t + π/2)

When x = A/2, sin(10·t + π/2) = 1/2, therefore;

cos(10·t + π/2) = ±√3/2

v(t) = 0.5 × ±√3/2 = ±√3/4

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If a longitudinal force exceeding 3000 N is applied. Young's modulus for that object equals DL = 0.0139m.

The greater the modulus, or the lesser elasticity strain that arises from the application of a given stress, the stronger that medium is. Young's modulus, sometimes referred to as mechanical performance, is a metric used to determine how stiff a material is. In other words, it is readily bent or stretched.

Young's modulus really measures a material's ability to withstand changes in length when compressed or under stress along its length. Divide the primary stresses by the strain to get Young's modulus, commonly known also as young's modulus.

Young's modulus Y= stress/strain

= (F/A) /(DL/L)

F=3000N,

A=0.54 cm²,

L=2.5cm,

Y=0.1 Gpa

0.1 * 10⁹ = (3000/(0.54* 10⁻⁴) (2.5 ⋆ 0.01/DL)

DL = 0.0139m

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Optimal Arousal theory focuses on finding the right level of stimulation.

William James (1842–1910), frequently referred to as the father of psychology in the United States, made significant contributions to early studies on motivation.

James proposed a number of instincts that help with survival as the driving forces behind conduct . An instinct is a species-specific pattern of behavior that is not taught, according to biology.

But there was a lot of disagreement over what exactly constitutes instinct among James's contemporaries. James postulated a number of unique human instincts, although many of his contemporaries had different lists.

Therefore, Optimal Arousal theory  focuses on finding the right level of stimulation.

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Altitude and Air

but mainly altitude, Air is just depending on the situation.

Air does not always influence an object's fall, but Altitude always influences it.

The perpendicular force that a surface applies to an item is known as the normal force. FN = m ⋅ g

The perpendicular force that a surface applies to an item is known as the normal force. For instance, if you place a book on a table, a gravitational force will cause it to fall. The table pulls on the book in order to counterbalance this force and keep it from dropping. The normal force, often known as the opposing force, is denoted by the symbols FN F N or  NN. "N" stands for the normal force unit (Newton).

A common illustration of Newton's third rule of motion is the normal force.

When one object applies force to another, the other applies a force in the opposite direction and of equal magnitude to the first object (action equals reaction).

Therefore, the force applied by the item to the surface is equal to the normal force. The calculations change according to the surface's slope.

The formula is as follows for an object laying on a flat surface:

FN = m ⋅ g

where

The mass of an object is m.

Gravitational acceleration is denoted by g.

The normal force (FN F N ) for an item on a flat surface is equal to its gravitational force, according to Newton's third law ( WW).

The formula is as follows for an object laying on a flat surface:

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