a 200g oscillator in a vacuum chamber has a frequency of 1.9 hz . when air is admitted, the oscillation decreases to 60% of its initial amplitude in 50s. How many oscillations will have been completed when the amplitude is 30% of its initial value?

Answer: The first box is 1.47

The second box is 1.323

Explanation:

The potential energy of the pendulum bob at position B is 1.323 J.

Potential energy is the energy a body has by virtue of its position or state above the ground.

The mass of the bob = 0.3 kg

height above the ground = 0.45 m

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

Potential energy = 0.3 × 0.45 × 9.8 = 1.323 J

Therefore, the potential energy of the pendulum bob at position B is 1.323 J.

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a.i) The work done when the body is displaced from s=0 to s = 0.4 m is 0.8 J.

(a.ii) The work done when the body is displaced from s=0 to s = 0.8 m is 1.2 J.

(b.i) The final velocity of the body when the displacement is 0.4 m is 3.46 m/s.

(b.ii) The final velocity of the body when the displacement is 0.8 m is 4 m/s.

The work done on an object is the product of force and displacement of the object.

The work done between 0 to 0.4 m is determined from the area of the triangle formed.

W = ¹/₂(0.4 m - 0 m) x ( 4 N )

W = ¹/₂(0.4 m) x ( 4 N )

W = 0.8 J

The work done from s=0 to s =0.8 m,

W = ( Area of 0 to 0.4 m) + ( Area of 0.4 m to 0.8 m)

W =  0.8 J  +   ¹/₂(0.8 m - 0.4 m) x ( 2 N )

W = 0.8J  +  ¹/₂(0.4 m) x ( 2 N )

W = 0.8J + 0.4 J

W = 1.2 J

The final velocity of the body is calculated by applying work energy principle.

change in kinetic energy of the body = work done by the body

¹/₂m(v₂² - v₁²) = W

Where;

when, s = 0.4 m, the final velocity is calculated as;

¹/₂m(v₂² - v₁²) = 0.8 J

¹/₂(0.2)(v₂² - 2²) = 0.8

0.1(v₂² - 2²) = 0.8

v₂² - 2² =  0.8 / 0.1

v₂² - 2² = 8

v₂² = 8 + 4

v₂² = 12

v₂ = √12

v₂ = 3.46 m/s

when s = 0.8 m, the final velocity is calculated as;

¹/₂(0.2)(v₂² - 2²) = 1.2 J

0.1(v₂² - 2²) = 1.2

v₂² - 2² =  1.2 / 0.1

v₂² - 2² = 12

v₂² = 12 + 4

v₂² = 16

v₂ = √16

v₂ = 4 m/s

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Answer:

change in kinetic energy of the trolley is 53.91 J.

Explanation:

mass of the trolley, m = 5.0 kg

initial velocity of the trolley, u = 1.0 m/s

external force on the trolley, F = 25 N

time of force action, t = 0.75 s

The final velocity of the trolley at the end of 0.75 s is calculated as follows;

\(F = \frac{m(v-u)}{t} \\\\25 = \frac{5(v-1)}{0.75}\\\\5(v-1) = 18.75\\\\v-1 = \frac{18.75}{5} \\\\v-1 = 3.75\\\\v = 4.75 \ m/s \ in \ the \ direction \ of \ the \ applied \ force\)

The change in kinetic energy of the trolley is calculated as;

Δ K.E = ¹/₂m(v² - u²)

Δ K.E = ¹/₂ x 5(4.75² - 1²)

Δ K.E = 53.91 J.

Therefore, change in kinetic energy of the trolley is 53.91 J.

Answer:

Explanation:

The density of a substance can be found by using the formula

\(density = \frac{mass}{volume} \\\)

From the question

mass = 12 g

volume = 4 ml

We have

\(density = \frac{12}{4} = 3 \\ \)

We have the final answer as

Hope this helps you

Answer:

θ = 12.60°

Explanation:

In order to calculate the angle below the horizontal for the velocity of the hockey puck, you need to calculate both x and y component of the velocity of the puck, and also you need to use the following formula:

\(\theta=tan^{-1}(\frac{v_y}{v_x})\)       (1)

θ: angle below he horizontal

vy: y component of the velocity just after the puck hits the ground

vx: x component of the velocity

The x component of the velocity is constant in the complete trajectory and is calculated by using the following formula:

\(v_x=v_o\)

vo: initial velocity = 28.0 m/s

The y component is calculated with the following equation:

\(v_y^2=v_{oy}^2+2gy\)         (2)

voy: vertical component of the initial velocity = 0m/s

g: gravitational acceleration = 9.8 m/s^2

y: height

You solve the equation (2) for vy and replace the values of the parameters:

\(v_y=\sqrt{2gy}=\sqrt{2(9.8m/s^2)(2.00m)}=6.26\frac{m}{s}\)

Finally, you use the equation (1) to find the angle:

\(\theta=tan^{-1}(\frac{6.26m/s}{28.0m/s})=12.60\°\)

The angle below the horizontal is 12.60°

The angle below the horizontal of the velocity of the puck just before it hits the ground is 12.60°.

Given the following data:

To find the angle below the horizontal of the velocity of the puck just before it hits the ground:

First of all, we would determine the horizontal and vertical components of the hockey puck.

For horizontal component:

\(V_y^2 = U_y^2 + 2aS\\\\V_y^2 = 0^2 + 2(9.81)(2)\\\\V_y^2 = 39.24\\\\V_y = \sqrt{39.24} \\\\V_y = 6.26 \; m/s\)

For vertical component:

\(V_x = U_x\\\\V_x = 28.0 \;m/s\)

Now, we can find the angle by using the formula:

\(\Theta = tan^{-1} (\frac{V_y}{V_x} )\)

Substituting the values, we have:

\(\Theta = tan^{-1} (\frac{6.26}{28.0} )\\\\\Theta = tan^{-1} (0.2236)\\\\\Theta = 12.60\)

Angle = 12.60 degrees.

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Answer:

The  value is  \(g =  16.104 \  m/s\)

Explanation:

From the question we are told that

 The  length is  \(l = 53.0 \ cm = 0.53 \ m\)

 The  number of cycle is  \(n = 105\)

  The time taken is  \(t = 125 \ s\)

The period is mathematically represented as

    \(T  =  2 \pi \sqrt{\frac{ l}{g} }\)

Also the period is mathematically represented as

      \(T    =  \frac{ t}{n}\)

      \(T  =  \frac{125}{110}\)

      \(T  =  1.14 \ s/cycle\)

So

      \(1.14  =  2 * 3.142  \sqrt{\frac{ 0.53}{g} }\)

=>   \(g =  \frac{ 4 *  3.142^2 *  0.53}{1.14^2}\)

=>     \(g =  16.104 \  m/s\)

The radius of the wire that would exhibit some strain the same strain as a spider is 0.06m.

The strain in a wire is given by the change in length divided by the original length, and is equal to the force applied divided by the cross-sectional area times the Young's modulus.

The force applied to the spider's thread is the weight of the spider, which is 1.0 x 10⁻³ kg x 9.8 m/s² = 9.8 x 10⁻³N.

The original length of the spider's thread is L = h, where h is the height of the spider.

The change in length is given by ΔL = FL/AY, where F is the force applied, L is the original length, A is the cross-sectional area, and Y is the Young's modulus.

Solving for the cross-sectional area, A = FL/ΔL = FL/ (FY/Y) = FLY/F = LY/F = πr²

We can now substitute the known values into the equation and solve for the radius, r:

πr² = LY/F = hY/F = 4.5 x 10 N/m² x (13 x 10⁻⁶ m) / (9.8 x 10⁻³ N)

r = sqrt(hY/Fπ) = sqrt(4.5 x 10 N/m² x (13 x 10⁻⁶ m) / (9.8 x 10⁻³ Nπ))

The radius of the aluminum wire that would exhibit the same strain as the spider's thread is the same as the calculated radius, 0.06m.

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The weight of the fourth casting is 48 kg.

Given - The weight of three castings -

45.302kg

44.982kg

45.716kg

To find - The average weight if the 4th casting is taken the average weight becomes 46kg what is the weight of the 4th casting​

Solution -

Let's calculate the average weight of the first three castings using the given weights:

Average weight = (Weight of first casting + Weight of second casting + Weight of third casting) / 3

Average weight = (45.302 kg + 44.982 kg + 45.716 kg) / 3

Average weight = 136.000 kg / 3

Average weight = 45.3333... kg (rounded to four decimal places)

Now, let's calculate the weight of the fourth casting by using the average weight and the desired overall average weight:

Total weight of all four castings = Average weight * 4

Total weight of all four castings = 46 kg * 4

Total weight of all four castings = 184 kg

To find the weight of the fourth casting, we subtract the total weight of the first three castings from the total weight of all four castings:

Weight of the fourth casting = Total weight of all four castings - Total weight of first three castings

Weight of the fourth casting = 184 kg - 136 kg

Weight of the fourth casting = 48 kg

Therefore, the weight of the fourth casting is 48 kg

Answer:

equal

Explanation:

If all three corresponding sides are equal and all three corresponding angles are identical in measure, two triangles are said to be congruent. These triangles can be slides, rotated, flipped and turned to be looked identical. If repositioned, they coincide with each other. The symbol of congruence is' ≅'.

Congruent means equal, as it is a term used to describe two or more objects or figures that have the same shape and size.

When two or more figures or things have the same size and shape, they are said to be congruent.

When we state that two things or figures are congruent, we mean that their lengths, angles, and proportions are all the same.

The idea of congruence is that there should be no distinction or contrast between the things being compared. It denotes complete equality and a perfect match.

Congruence informs us that all geometric shapes, including line segments, angles, triangles, and others, are the same and can be placed on one another without overlap or gaps.

Thus, a fundamental idea in geometry called congruence enables us to evaluate and contrast geometric forms and their characteristics.

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Answer:

C. The poster provides an emotional picture of a young, innocent girl with a slightly worried expression to make protective feelings.

Explanation:

The girl looks quite worried in the poster. Attached is the image:

Answer:Magnetic fields from two sources add up as vectors at each point, so the strength of the field is not necessarily the sum of the strengths1. Magnetic fields are vectors, which means they have direction as well as size. Therefore, the sum of two magnetic fields is not simply the sum of their magnitudes2.

Explanation:

Distribute the product:

a×b = (8i + j - 2k) × (5i - 3j + k)

a×b = 8i × (5i - 3j + k) + j × (5i - 3j + k) - 2k × (5i - 3j + k)

a×b = (40 (i×i) - 24 (i×j) + 8 (i×k))

… … … + (5 (j×i) - 3 (j×j) + k×j)

… … … + (-10 (k×i) + 6 (k×j) - 2 (k×k))

Recall the definition of the cross product:

i×i = j×j = k×k = 0 (the zero vector)

i×j = k

j×k = i

k×i = j

and for any two vectors x and y, we have x×y = -(y×x).

So we have some cancellation and rewriting:

a×b = (40 (i×i) - 24 (i×j) + 8 (i×k))

… … … + (5 (j×i) - 3 (j×j) + j×k)

… … … + (-10 (k×i) + 6 (k×j) - 2 (k×k))

a×b = (-24k - 8j) + (-5k + i) + (-10j - 6i)

a×b = -5i - 18j - 29k

Then

b×a = -(a×b) = 5i + 18j + 29k

Answer:

30

Explanation:

Adding globes in parallel makes no difference to their brightness because all the bulbs glowed with the same brightness indicating that the current flowing through the bulbs had the same value.

The current in each light bulb was the same.

An electric current is a flow of electrons as a result of a potential difference between two points in conductor.

Electrons are negatively-charged particles that are one of the fundamental particles of an atom. The flow of electrons through a conductor is able to do work.

Two or more globes in a simple parallel circuit do not experience any drop in the voltage, thus allowing the maximum flow of electric current. Also, connecting devices in a parallel circuit ensures that if one of the component lops is disconnected, the flow of current through the other loops remains intact.

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Answer:

-45,597.07

Explanation:

if not in scientific calculator and yung answer nung sa scientific sa comment na lang dinadownload ko ka eh

The front of the truck is designed to crumple during a collision to absorb the impact energy, slow down the collision, and protect the well-being of the passengers. This design feature helps increase the collision time, reduce the forces acting on the passengers, and minimize the risk of severe injuries.

Danica observes a collision between two vehicles. She sees a large truck driving down the road. It strikes a small car parked at the side of the road. On colliding, the truck applies a force on the stationary car, and the stationary car applies an opposite force on the truck. The front of the truck is designed to crumple in order to absorb the impact energy and slow down the collision , which protects the well-being of the passengers.

During a collision, the principle of Newton's third law of motion comes into play. According to this law, for every action, there is an equal and opposite reaction. In the case of the collision between the truck and the car, the truck exerts a force on the car, pushing it forward, while simultaneously experiencing an equal and opposite force from the car.

The purpose of designing the front of the truck to crumple is to increase the collision time and absorb the kinetic energy. When the truck collides with the stationary car, the front of the truck deforms, crumples, and absorbs a significant amount of the impact energy. This process increases the time over which the collision occurs, reducing the forces acting on the passengers and minimizing the risk of severe injuries.

By allowing the truck to crumple, the kinetic energy of the collision is transformed into other forms, such as deformation energy and heat. This energy transformation helps protect the passengers by reducing the deceleration forces acting on them. It also helps prevent the transfer of excessive forces to the car's occupants and reduces the likelihood of severe injuries.

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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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The tops of the mountains are often covered in snow and ice because as we go to the higher altitude the temperature decreases as per the normal lapse rate, and the thermal energy and the kinetic energy of the atmospheric gases decrease significantly at the higher altitude.

The Equator is an imaginary line passing through the middle of a globe. It is equidistant from the North Pole and the South Pole, Its is a horizontal line residing at 0 degrees latitude.

Because the temperature lowers as we ascend to greater altitudes according to the natural lapse rate and the thermal and kinetic energy of the atmospheric gases diminish dramatically, the peaks of mountains are frequently covered with snow and ice.

The water vapors present in the upper atmosphere convert into ice and snow at the top, therefore tops of the mountains are often covered in snow and ice.

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Answer:

The answer is below

Explanation:

a) Using the formula:

\(\omega^2=\omega_o^2+2\alpha \theta\\\\\omega=final\ angular\ velocity,\omega_o=initial\ anglular\ velocity,\alpha= angular\ acceleration,\\\theta=angular\ distance\\\\Given\ that:\\\\initial\ velocity(u)=28.78m/s,distance(s)=50\ m,radius(r)=0.25\ m,\\final/ velocity(v)=0(stop)\\\\\omega=v/r=\frac{28.78m/s}{0.25m} =115.12\ rad/s,\omega_o=0,\theta=s/r=\frac{50\ m}{0.25\ m}=200\ rad\\ \\\omega^2=\omega_o^2+2\alpha \theta\\\\115.12^2=0^2+2\alpha(200)\\\\2\alpha(200)=13252.6144\\\\\alpha=33.13\ rad/s^2\)

b)

\(\theta=200\ rad=200\ rad*\frac{1\ rev}{2\pi\ rad}=31.83\ rev\)

Answer:

800 miles per hour

Explanation:

The mass of the planet is  5.98 × 10^24 kg.

To calculate the mass of the planet, we can use Kepler's Third Law of Planetary Motion. This law states that the square of the period of revolution of a planet around the sun is directly proportional to the cube of the semi-major axis of its orbit.

First, we need to convert the period of the satellite's orbit to seconds. We know that there are 60 minutes in an hour, so the period can be expressed as (6 × 60 + 12) minutes, which equals 372 minutes. Multiplying this by 60 seconds, we get a period of 22,320 seconds.

Next, we need to find the semi-major axis of the orbit. In a circular orbit, the semi-major axis is equal to the radius of the orbit. Therefore, the semi-major axis is 8.8 × 10^6 m.

Now, we can apply Kepler's Third Law to calculate the mass of the planet. The formula is T^2 = (4π^2/GM) × a^3, where T is the period of revolution, G is the gravitational constant, M is the mass of the planet, and a is the semi-major axis of the orbit.

Rearranging the formula, we can solve for the mass of the planet:
M = (4π^2/G) × a^3 / T^2

Plugging in the values, we get:
M = (4 × π^2 / 6.67430 × 10^-11) × (8.8 × 10^6)^3 / (22,320)^2

Evaluating this expression, we find that the mass of the planet is approximately 5.98 × 10^24 kg.

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The value of the inductance, in , microhenrys of Tarik's solenoid is approximately 1.6239 microhenrys.

To calculate the inductance of a solenoid, we can use the formula:

L = (μ₀ * N² * A) / l

where L is the inductance, μ₀ is the permeability of free space (4π × 10⁻⁷ T·m/A), N is the number of turns, A is the cross-sectional area of the solenoid, and l is the length of the solenoid.

In this case, we have:

N = 175 turns

Diameter = 8.05 mm = 0.00805 m (converted to meters)

Radius = Diameter / 2 = 0.00805 m / 2 = 0.004025 m

Length (l) = 2.37 cm = 0.0237 m (converted to meters)

First, let's find the cross-sectional area (A) using the formula for the area of a circle:

A = π * r² = π * (0.004025 m)² ≈ 5.08398 × 10⁻⁵ m²

Now we can plug in the values into the formula for inductance:

L = (4π × 10⁻⁷ T·m/A * (175)² * 5.08398 × 10⁻⁵ m²) / 0.0237 m

L ≈ (1.2566 × 10⁻⁶ * 30625 * 5.08398 × 10⁻⁵) / 0.0237

L ≈ (38.5086 × 10⁻⁶) / 0.0237

L ≈ 1.6239 × 10⁻⁶ H

Now, let's convert the inductance from henrys to microhenrys:

L ≈ 1.6239 × 10⁻⁶ H * 10⁶ μH/H ≈ 1.6239 μH

So the inductance of Tarik's solenoid is approximately 1.6239 microhenrys.

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Sound waves are a type of mechanical wave that propagate through a medium, typically air but also other materials such as water or solids.

Frequency: the frequency of a sound wave refers to the number of cycles or vibrations it completes per second and is measured in Hertz (Hz).

Amplitude: the amplitude of a sound wave refers to the maximum displacement or intensity of the wave from its equilibrium position. It represents the loudness or volume of the sound, with larger amplitudes corresponding to louder sounds and smaller amplitudes corresponding to softer sounds.

Wavelength: the wavelength of a sound wave is the distance between two consecutive points in the wave that are in phase, such as from one peak to the next or one trough to the next. It is inversely related to the frequency of the wave.

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We divide the total distance travelled by the period of time to determine the average speed. By dividing the displacement by the time interval, we can determine the average velocity.

Average speed was measured by dividing the overall distances you travelled by the total time, whereas average velocity is determined by dividing your movement (a vectors pointing from the initial position toward your end position) by the whole time.

For instance, someone travelling at an average speed over 40 miles split by 10 mins, meaning 1 mile per minute, is travelling twenty miles to the north and afterwards 20 miles south (60 mph).

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Answer:

Multiply the friction factor by pipe length and divide by pipe diameter. Multiply this product by the square of velocity. Divide the answer by 2.

Explanation:

Multiply the friction factor by pipe length and divide by pipe diameter. Multiply this product with the square of velocity. Divide the answer by 2.

Hope this answer helps you

The weight is measured in a unit called Newton. The newton is a standard unit of weight measurements.

The International System of Units (SI) uses Newtons (N) as the unit of weight measurement. Weight is frequently expressed in pounds (lb) or ounces (oz) in some nations that employ the Imperial system. However, Newton is the accepted weight measurement unit in scientific and international contexts.

The International System of Units (SI) uses Newton as the primary unit of weight measurement. Sir Isaac Newton, a great physicist who significantly influenced our understanding of classical mechanics, is honored by having his name attached to it. Newton is the force needed to accelerate a mass of one kilogram by one meter per second squared in the SI system.

Hence, the weight is measured in a unit called Newton. The newton is a standard unit of weight measurements.

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Some object remains hot for a long period of time because they have low thermal conductivity and some object remain hot for a short period of time because they have high thermal conductivity.

Thermal conductivity is a property of a substance to allow heat to flow through it easily.

Thermal conductivity is a measure of how well a substance will conduct heat or not.

Objects that have high thermal conductivity gain heat easily and also lose heat easily. Hence, they get hot quickly and also get cold quickly.

Objects that have low thermal conductivity gain heat slowly and also lose heat slowly. Hence, they get hot slowly and also get cold slowly.

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We can use the conservation of angular momentum to address this issue. We may translate the initial angular velocity of the system, which is 35.0 rev/min, to radians per second.

A homogeneous rod with a mass of m and a length of l is capable of rotating in the vertical plane around a straight horizontal axis that is at point H.

A homogeneous rod of 1.25 m in length has a rotational potential about an axis that passes through O in a vertical plane. a consistent disc of same mass and diameter same as.

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