Question #4
4. Anthony walks to the pizza place for lunch. He walk 4 km
east, he realized he passed it and then walked 1 km west.
What distance did he cover? What was his displacement?

Answer:

Oscillation whose amplitude reduce with time are called damped oscillation. This happen because of the friction. In oscillation if its amplitude doesn't change with time then they are called Undamped oscillation

Damped and undamped vibration refer to two different types of vibrations. The main difference between damped and undamped vibration is that undamped vibration refer to vibrations where energy of the vibrating object does not get dissipated to surroundings over time, whereas damped vibration refers to vibrations where the vibrating object loses its energy to the surroundings.

Answer:

Explanation:

"fuse wire" typically refers to a thin, single-use wire that is used to protect an electrical circuit from overloading or short circuiting. The wire is designed to melt and break the circuit if the current flowing through it exceeds a certain level, which helps to prevent damage to the electrical equipment or a potential fire hazard. Once the fuse wire has melted, it must be replaced with a new one.

an "MCB" (miniature circuit breaker) is a type of switch that automatically trips and breaks the circuit when there is an overcurrent or short circuit.

Unlike a fuse wire, an MCB can be reset after it has tripped, making it more convenient for protecting electrical circuits. MCBs are typically more expensive than fuse wires, but they offer greater protection and are often used in modern electrical systems.

The voltage of the power source flowing through the given wire is determined as 2.67 x 10⁻⁵ V.

The voltage of the power source is determined from ohm's law as shown below;

V = IR

where;

But, I = Q/t

V = (Q/t)R

\(V = \frac{QR}{t} \\\\V = \frac{(1\times 10^{15} \times 1.602\times 10^{-19} \ C) \times \ 10 \ ohms}{1 \times 60\ s} \\\\V = 2.67 \times 10^{-5} \ V\)

Thus, the voltage of the power source flowing through the given wire is determined as 2.67 x 10⁻⁵ V.

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Answer:

prototype - a first model of something

obsolete - out of date

Unintended Consequence - outcomes of actions that weren't predicted and intended

Feedback - reactions to something from someone like a customer

Answer:

1.40 m/s

Explanation:

The potential energy of a compressed spring can be expressed as:

\(E_{ps}=\dfrac{1}{2}kx^2\)

From above;

k = spring constant

x = distance of the spring (compressed)

From the barrel, the kinetic energy (i.e. the final K.E) of the ball is calculated using the relation:

\(E_{kf}= \dfrac{1}{2}mv^2\)

where;

m = the ball mass

v = ball's speed

Equating both equations above, we have:

\(E_{ps}- F_fd=E_{kf\)

This can be re-written as:

\(\dfrac{1}{2}kx^2 - F_fd=\dfrac{1}{2}mv^2}\)

\(v^2 = (\dfrac{k}{m})x^2-\dfrac{2F_fd}{m}\)

\(v =\sqrt{ (\dfrac{k}{m})x^2-\dfrac{2F_fd}{m}}\)

replacing the values from the given information:

\(v =\sqrt{ (\dfrac{8.00\ N/m}{5.30\times10^{-3} \ kg})(5.00 \ cm \times \dfrac{10^{-2} \ m}{1 \ cm})^2-(\dfrac{2(0.032 \ N)(0.150 \ m)}{5.30\times \dfrac{10^{-3} \ kg}{1 \ g}})}\)

\(v = \sqrt{1.962264151}\)

v ≅ 1.40 m/s

The speed at which the projectile leaves the barrel of the cannon will be given as \(v=1.40\ \frac{m}{s}\)

Speed is defined as the movement of any object with respect to time. It is the ratio of distance and time.

Now it is given in the question:

Mass of ball m = 5.30 g

The deflection of spring = 5 cm

The force constant of spring  \(k= 8 \ \frac{N}{m^2}\)

The length of the barrel = is 15 cm

The frictional force of the barrel = 0.032 N

Now from the conservation of energy, we can write as

\(E_{spring}-E_{friction}=E_{ball}\)

\(\dfrac{1}{2} kx^2-F_fd=\dfrac{1}{2} mv^2\)

\(v=\sqrt{\dfrac{k}{m}(x^2) -\dfrac{2F_fd}{m} }\)

Now putting the values in the above formula:

\(v=\sqrt{\dfrac{8}{5.30\times 10^{-3}}(15\times10^{-2}) -\dfrac{2\times(0.0032)\times (0.015)}{5.30\times 10^{-3}} }\)

\(v=1.40\ \frac{m}{s}\)

Thus the speed at which the projectile leaves the barrel of the cannon will be given as \(v=1.40\ \frac{m}{s}\)

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Horizontal force will be there but angular force is zero because it is dependent on angle and angular velocity is constant.

\(\tau = rF\sin\theta\)

T= torque

r= radius

In mechanics, every action that tries to preserve, alter, or change a body's motion is referred to as a force. Isaac Newton's Principia Mathematica has three principles of motion that are usually used to explain the concept of force (1687).

Newton's first law states that in the absence of an external force, a body will continue to be in either its resting or evenly moving condition along a straight path. According to the second law, any time an outside force acts on a body, the body accelerates (changing velocity) in the force's direction.

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The Title of the interviews Questionnaire is : Community Members' Right to Safe and Healthy Living Questionnaire. The Questionnaire is attached.

A tool for research known as a questionnaire comprises a series of questions formulated to extract data from individuals or a collective of individuals. A systematic approach in acquiring data, which permits researchers to obtain uniform feedback and perspectives from respondents, is termed as structured data collection.

Questionnaires have multiple applications such as conducting surveys, holding interviews, performing assessments, and carrying out evaluations.

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Answer:

6.1 cm

61 N

35°

Explanation:

Given scale:  1 cm = 10 N

Parallelogram method (attachment 1)

When two vectors are represented by two adjacent sides of a parallelogram by direction and magnitude, the resultant of these vectors is represented (in magnitude and direction) by the diagonal of the parallelogram starting from the same point.

F₁ = 30 N = 3 cm

F₂ = 40 N = 4 cm

Draw a 3 cm horizontal line from the head of vector F₂ that is parallel to and the same length as vector F₁.

Draw a 4 cm line from the head of vector F₂ that is parallel to and the same length as vector F₁.

You have now constructed a parallelogram.

The diagonal of the parallelogram represents the resultant force vector.

Measure the length of the diagonal:

Measure the angle between the x-axis and the resultant force vector:

Polygon method (attachment 2)

If a number of vectors can be represented in magnitude and direction by the sides of a polygon taken in the same order, then their resultant is represented in magnitude and direction by the closing side of the polygon taken in the opposite order.

F₁ = 30 N = 3 cm

F₂ = 40 N = 4 cm

Draw a 3 cm horizontal line from the origin along the x-axis.  This is vector F₁.

Draw a 4 cm line at 60° to the x-axis from the head of F₁.  The is vector F₂.

Close the polygon by drawing a line that connects the tail of vector F₁ to the head of vector F₂.  This is the resultant force vector.

Measure the length of the closing side of the polygon:

Measure the angle between the x-axis and the resultant force vector.

Note: The resultant vector length, force and direction are the same for both methods.

Using parallelogram method for vector addition of two vectors with magnitude 40 Newton and 30 Newton at an angle of 60 degree the resultant vector is equal to 60.8 Newton and its length is equal to 6.08 cm.

The parallelogram rule says that on placing two vectors such that they have the same initial point, and complete into a parallelogram, then the sum of the vectors is the directed diagonal that starts at the same point as the vectors.

Polygon law of vector addition states that if a number of vectors can be represented in magnitude and direction by the sides of a polygon taken in the same order, then their resultant is represented in magnitude and direction by the closing side of the polygon taken in the opposite order.

Given:

Magnitude of first vector (a) = 30N

Magnitude of second vector (b) = 40N

Direction between two vectors= 60°

Using the law of parallelogram vector addition we get the value of resultant vector (R)-

\(R = \sqrt{(900+1600+1200)}\)

R = 60.8 newton

Now it is given that 1 cm in graph represents 10 newton.

Therefore, 60.8 newton will comprise a length = 60.8/10

60.8 newton will comprise a length = 6.08cm

The direction of the resultant vector is equal to 34.7° .

Here only two vectors are given therefore polygon law of vector addition becomes exactly like parallelogram vector addition.

Therefore,

\(R = \sqrt{(900+1600+1200)}\)

R = 60.8 newton

60.8 newton will comprise a length of 6.08cm.

Vector addition of two vectors with magnitude 40 Newton and 30 Newton at an angle of 60 degree the resultant vector is equal to 60.8 Newton and its length is equal to 6.08 cm.

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The approximate distance that the smoke travels up from the furnace is 9metres.

Distance is described as a numerical or occasionally qualitative measurement of how far apart objects or points are. In the field of physics or everyday usage, distance is usually referred to a physical length or an estimation based on other criteria.

Parameters given:

Velocity = 1.5

time = 6 seconds

We know that distance = speed x time

Hence, distance = 1.5 x 6 seconds

distance = 9 meters.

Distance is a scalar quantity that refers to how much ground an object has covered in the course of its motion while we can describe displacement as a vector quantity that refers to "how far out of place an object is"; it is the object's overall change in position.

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Voltage depends on the amount of resistance, current according to the Ohm's law, and, by definition, is the measurement of electrical pressure.

According to the Ohm's Law,  the current through a conductor between two points is directly proportional to the voltage across the two points.

Mathematically,

V ∝ I

V = IR

where, R is the resistance of the conductor and I is the current flowing in the conductor. So, the voltage depends on the amount of resistance and current.

Also, Voltage is the pressure from an electrical circuit's power source that pushes charged electrons (current) through a conducting loop, enabling them to do work such as illuminating a light.

Hence All of the above option in the given question are true.

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The force on the particle is 3619 N.

Force can be defined as the product of the mass of a body to its acceleration. The S.I unit of force is Newton (N)

To calculate the force on the particle, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, The force on the particle is 3619 N.

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Explanation:

Her cells will not work well when they have low levels of oxygen.

The diameter of the smaller end of the pipe is approximately 0.78 meters.

To determine the diameter of the smaller end of the pipe, we can use the principle of conservation of mass. According to this principle, the mass flow rate of water should remain constant throughout the pipe.

The mass flow rate is given by the equation:
Mass flow rate = density of water * cross-sectional area * velocity

Since the density of the water remains constant, we can write:
Cross-sectional area1 * velocity1 = Cross-sectional area2 * velocity2

Given that the velocity1 is 13 m/s, the diameter1 is 1.2 m, and the velocity2 is 30 m/s, we can solve for the diameter2 using the equation:
(pi * (diameter1/2)^2) * velocity1 = (pi * (diameter2/2)^2) * velocity2

Simplifying the equation:
(1.2/2)^2 * 13 = (diameter2/2)^2 * 30

Calculating the equation:
(0.6)^2 * 13 = (diameter2/2)^2 * 30

0.36 * 13 = (diameter2/2)^2 * 30

4.68 = (diameter2/2)^2 * 30

Dividing both sides by 30:
0.156 = (diameter2/2)^2

Taking the square root of both sides:
0.39 = diameter2/2

Multiplying both sides by 2:
0.78 = diameter2

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Answer:

Option C. 70 Ω

Explanation:

Data obtained from the question include:

Resistor (R) = 20 Ω

From diagram given ABOVE, we observed the following

1. R and R are in parallel connections.

2. 2R and 2R are in parallel connections.

3. 4R and 4R are in parallel connections.

Next, we shall determine the equivalent resistance in each case.

This is illustrated below:

1. Determination of the equivalent resistance for R and R parallel connections.

R = 20 Ω

Equivalent R = (R×R) /(R+R)

Equivalent R = (20 × 20) /(20 + 20)

Equivalent R = 400/40

Equivalent R = 10 Ω

2. Determination of the equivalent resistance for 2R and 2R parallel connections.

R = 20 Ω

2R = 2 × 20 = 40 Ω

Equivalent 2R = (2R×2R) /(2R+2R)

Equivalent 2R = (40 × 40) /(40 + 40)

Equivalent 2R = 1600/80

Equivalent 2R = 20 Ω

3. Determination of the equivalent resistance for 4R and 4R parallel connections.

R = 20 Ω

4R = 4 × 20 = 80 Ω

Equivalent 4R = (4R×4R) /(4R+4R)

Equivalent 4R = (80 × 80) /(80 + 80)

Equivalent 4R = 6400/160

Equivalent 4R = 40 Ω

Thus, the equivalence of R, 2R and 4R are now in series connections. We can obtain the equivalent resistance in the circuit as follow:

Equivalent of R = 10 Ω

Equivalent of 2R = 20 Ω

Equivalent of 4R = 40 Ω

Equivalent =?

Equivalent = Equivalent of (R + 2R + 4R)

Equivalent = 10 + 20 + 40

Equivalent = 70 Ω

Therefore, the equivalent resistance between point A and B is 70 Ω.

Answer:

d

Explanation:

Answer:

s = 14.3 ft

Explanation:

First we need to calculate the distances traveled by both the cars. We use third equation of motion for that:

2as = Vf² - Vi²

where,

a = acceleration

s = distance

Vf = Final Velocity

Vi = Initial velocity

FOR CAR A:

Vi = Va = (40 mph)(5280 ft/1 mile)(1 h/3600 s) = 58.66 ft/s

Vf = 0 ft/s

a = aA = - 22 ft/s²

s = sa = ?

Therefore,

2(- 22 ft/s²)(sa) = (58.66 ft/s)² - (0 ft/s)²

sa = 78.2 ft

FOR CAR B:

Vi = Vb = (45 mph)(5280 ft/1 mile)(1 h/3600 s) = 66 ft/s

Vf = 0 ft/s

a = aB = - 20 ft/s²

s = sb = ?

Therefore,

2(- 20 ft/s²)(sb) = (66 ft/s)² - (0 ft/s)²

sb = 108.9 ft

Since, the car A was initially 45 ft ahead of car B. Therefore,

sa = 45 ft + 78.2 ft = 123.2 ft

Now, the distance between the cars will be:

s = sa - sb

s = 123.2 ft - 108.9 ft

s = 14.3 ft

Answer:

The principle of simple machine states that "if there is no friction in a simple machine, work output and work input are found equal in that machine.

Explanation:

Answer:

Usually, the term refers to the six classical simple machines which were defined by Renaissance scientists:

Also, a simple machine uses a single applied force to do work against a single load force.

Answer:

and yes, sound travels at the speed of entity expressions is whhy you need math for a job in mc donalds :

293 x gj -2 = 23r = velocity of rocket ship is 2.74

Answer:

c

Explanation:

X-ray tube is an evacuated electron tube that creates X rays by accelerating electrons to a high velocity and causing them to collide with a target, the anode plate, using a high-voltage field.

Answer:

FALSE

Explanation:

Answer:

Its nymber 2

Explanation:

Answer:

45kw45_32+675&453try to get it done

Answer:

A: 9 kg

Explanation:

on edge! hope this helps!!~ ∩(︶▽︶)∩

Answer: 490

Explanation:

8.27 x 1013 meres is the orbital radius.

Jupiter's mass, 1.9 x 1027 kg, and the time interval, 16.9 days, are equal to 1.46 x 106 seconds. The radius is needed, thus r. Solution

The moon must be held in its orbit by a gravitational force equal to the centripetal force between Jupiter and the moon.

6.67 x 10⁻¹¹ N/m²kg

2 x 1.9 x 10/27 x 1.46 x 10'6 / 4 r = 6.85 x 102'7 G = 6.67 x 10'11 N/m2kg2 r = 8.27 x 10'7

The second-largest moon in Jupiter's orbit and the third-largest moon in the solar system is called Callisto. Of all the objects in our solar system, its surface has the most craters.

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Part (A)

The final speed of the car can be expressed as,

Plug in the known values,

The force acting on the car can be given as,

Substitute the known values,

The average speed of the car can be given as,

Substitute the known values,

The average mechanical output of the engine is,

Substitute the known values,

Thus, the average mechanical power output of engine is 82720 W.

Part (B)

The power generated by gasoline can be given as,

Substitute the known values,

The energy generated by gasoline can be given as,

Substituting known values,

The volume consumed by gasoline can be calculated as,

Thus, the volume of gasoline consumed is 0.08 L.

Apart from the two electrodes, several factors can affect the voltage in an electrical circuit. These factors such as wire gauge, component ratings, load requirements, and temperature considerations.

These factors include:

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If a 5kg mass starts from rest at xo = -1 and moves under the action of a variable force F(x) = √1-x² to point xf = 1. Then the total work done by the force is equal to π/2 + 1.

To calculate the total work done by the force in this scenario, we can use the formula for work:

Work = ∫F(x) dx

where F(x) is the force as a function of position and dx represents an infinitesimal displacement.

In this case, the force is given by F(x) = √(1 - x²), and we need to find the total work done as the object moves from xo = -1 to xf = 1.

Let's break down the calculation step by step:

Write the integral for work:

Work = ∫F(x) dx

Substitute the given force:

Work = ∫√(1 - x²) dx

Integrate with respect to x:

To integrate the square root of (1 - x²), we use the trigonometric substitution. Let's substitute x = sin(θ) and dx = cos(θ) dθ.

Work = ∫√(1 - sin²(θ)) cos(θ) dθ

Simplify the integrand:

Using the trigonometric identity sin²(θ) + cos²(θ) = 1, we can rewrite the integrand as cos²(θ).

Work = ∫cos²(θ) dθ

Apply the power-reducing formula:

The power-reducing formula states that cos²(θ) = (1 + cos(2θ)) / 2. We can use this formula to simplify the integrand further.

Work = ∫(1 + cos(2θ))/2 dθ

Integrate the terms separately:

Work = (1/2) ∫dθ + (1/2) ∫cos(2θ) dθ

The first integral, ∫dθ, is simply θ, and the second integral, ∫cos(2θ) dθ, can be calculated as sin(2θ)/2.

Work = (1/2) θ + (1/2) (sin(2θ)/2) + C

Evaluate the integral limits:

To find the total work done, we need to evaluate the integral at the upper and lower limits of integration.

At xf = 1, the angle θ is π/2, and at xo = -1, the angle θ is -π/2.

Work = (1/2) (π/2) + (1/2) (sin(2(π/2))/2) - [(1/2) (-π/2) + (1/2) (sin(2(-π/2))/2)]

Simplifying further:

Work = π/4 + (1/2) - (-π/4 + (1/2))

Work = π/4 + 1/2 + π/4 + 1/2

Work = π/2 + 1

Therefore, the total work done by the force is equal to π/2 + 1.

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Answer:6.5

Explanation: take 650 and divide it by 100

\(x = 100 + 650 \\ \sqrt22y1x \leqslant y3.y1y \geqslant y = - y..x1431} \)

Answer:

8s

Explanation:

period of pendulum = 2π*√(l/g)

l = length of pendulum

period for 1st pendulum = 4 sec

thats 2π*√(l/g) = 4

for 2nd pendulum

length = 4 l

substitute 4l in formula

2π*√4l/g = 2*4= 8s

Given the data from the question, the period of the pendulum 2 is 8 s

The period of pendulum 2 can be obtained as illustrated below:

T²₁ / L₁ = T²₂ / L₂

4² / L = T²₂ / 4L

Cancel out L

4² = T²₂ / 4

Cross multiply

T²₂ = 4² × 4

T²₂ = 64

Take the square root of both sides

T₂ = √64

T₂ = 8 s

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