why do you think a force is generated when a spring is stretched or compressed

The imaging properties of lenses and mirrors discussed in this write-up are based on the paraxial ray approximation,  which stipulates that the light rays involved make only small angles with the optic axis.

The mirror is a glass with one side coated with silver lining which help to  produces an image by reflection on only one surface. Whereas , the lens is a transparent substance that produces images by refraction

A paraxial ray is a ray that makes a small angle towards the optical axis of the system . When light rays make small angles with the optic axis, it is known as paraxial ray approximation.

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Answer:

The size of an object is directly proportional to the gravity

Explanation:

The size of an object has significant impact on the gravity exerted by such a body.

The more massive a body is, the larger the gravity it exerts.

The reason for this is because of the newton's law of universal gravitation.

The statement that belongs to the region marked X is a PN Junction

A PN Junction can be defined as a point where the negative side and positive side of an electronic component.

A PN Junction in the case of the venn diagram is the similarity between a PNP transistor and an NPN transistor.

In conclusion, The statement that belongs to the region marked X is a PN junction

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The magnitude of the ball's total displacement is approximately 94.7 cm. The direction of the displacement is approximately 195° counterclockwise from the horizontal x-axis.

To find the magnitude and direction of the ball's total displacement, we need to sum up the individual displacement vectors.

Given displacement vectors:

V₁: 83.0 cm at 90.0°

V₂: 57.0 cm at 149°

V₃: 61.0 cm at 223°

To find the total displacement, we can break down the vectors into their x and y components and then add them up.

For V₁:

V₁x = 83.0 cm * cos(90.0°) = 0 cm

V₁y = 83.0 cm * sin(90.0°) = 83.0 cm

For V₂:

V₂x = 57.0 cm * cos(149°)

V₂y = 57.0 cm * sin(149°)

For V₃:

V₃x = 61.0 cm * cos(223°)

V₃y = 61.0 cm * sin(223°)

Now we can calculate the sum of the x and y components:

Total displacement in the x-direction:

ΣVx = V₁x + V₂x + V₃x

Total displacement in the y-direction:

ΣVy = V₁y + V₂y + V₃y

To find the magnitude and direction of the total displacement, we can use the Pythagorean theorem and trigonometry:

Magnitude of displacement:

|ΣV| = sqrt((ΣVx)² + (ΣVy)²)

Direction of displacement:

θ = atan(ΣVy / ΣVx)

By substituting the given values and performing the calculations, we get:

V₁x = 0 cm

V₁y = 83.0 cm

V₂x ≈ -31.9 cm

V₂y ≈ 47.0 cm

V₃x ≈ -34.1 cm

V₃y ≈ -39.9 cm

ΣVx = V₁x + V₂x + V₃x

ΣVy = V₁y + V₂y + V₃y

|ΣV| = sqrt((ΣVx)² + (ΣVy)²)

θ ≈ atan(ΣVy / ΣVx)

By substituting the values and performing the calculations, we find:

ΣVx ≈ -65.9 cm

ΣVy ≈ 90.1 cm

|ΣV| ≈ 94.7 cm

θ ≈ 195°

Therefore, the magnitude of the ball's total displacement is approximately 94.7 cm, and the direction of the displacement is approximately 195° counterclockwise from the horizontal x-axis.

The ball's total displacement is approximately 94.7 cm in magnitude, and its direction is approximately 195° counterclockwise from the horizontal x-axis.

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.Explanation:

.......................................................

The average fluid velocity (in m/s) is 3.636 m/s.

The volume of fluid moving past a spot in a given amount of time is measured as the flow rate. Circular and noncircular pipelines both experience fluid flow in daily life.

From the question we have given:

The diameter of the pipe (l) is  3.00 cm or 0.0300 m.

The magnetic field (B) is  0.550 T.

The hall voltage (E) is  60.0 mv or 60 x 10⁻³ v.

  \(v = \frac{E}{Bl}\)

The average fluid velocity can be calculated using the equation E = Blv.

In this instance, the width really corresponds to the diameter:

\(v = \frac{60 \;*\; 10^{-3} \;V}{0.0165\; m} \\\)

\(v = 3.636 \;m/s\)

Thus, the average fluid velocity is 3.636 m/s.

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a. During the upward acceleration, the net force acting on the man is the force due to gravity (weight) plus the force exerted by the elevator (normal force), which can be expressed as:

Fnet = ma

Fnet = (72 kg)(1.30 m/s^2) = 93.6 N

The normal force exerted by the scale is equal in magnitude to the force due to gravity, so:

Fnormal = mg

Fnormal = (72 kg)(9.81 m/s^2) = 706.32 N

The scale reading is the magnitude of the normal force, which is:

scale reading = Fnormal = 706.32 N

b. During the constant velocity motion, the elevator is not accelerating, so the net force acting on the man is zero. Therefore, the normal force exerted by the scale is equal in magnitude to the force due to gravity:

Fnormal = mg

Fnormal = (72 kg)(9.81 m/s^2) = 706.32 N

The scale reading is the magnitude of the normal force, which is:

scale reading = Fnormal = 706.32 N

c. During the upward deceleration, the net force acting on the man is the force due to gravity (weight) minus the force exerted by the elevator (normal force), which can be expressed as:

Fnet = ma

Fnet = (72 kg)(-0.500 m/s^2) = -36 N

The normal force exerted by the scale is now less than the force due to gravity, so:

Fnormal = mg - Fnet

Fnormal = (72 kg)(9.81 m/s^2) - (-36 N)

Fnormal = 760.32 N

The scale reading is the magnitude of the normal force, which is:

scale reading = Fnormal = 760.32 N

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Charged particles are fundamental to the behavior of electric currents, electric circuits, and resistance. An electric current is the flow of charged particles, typically electrons, through a conductor.

The flow of charged particles generates an electric field that induces a potential difference, or voltage, across the conductor.Electric circuits are constructed by connecting conductors and electrical components, such as resistors, capacitors, and inductors, in a specific configuration. The arrangement of the components determines how the current flows through the circuit.

The flow of current through the circuit depends on the resistance offered by the components in the circuit and the potential difference across the circuit.Resistance is the property of a conductor that opposes the flow of current. The resistance of a conductor is proportional to the number of charged particles in the conductor, the length of the conductor, and the cross-sectional area of the conductor. The resistance can also be affected by the temperature of the conductor and its material properties.

In summary, charged particles are responsible for generating electric currents that flow through electrical circuits. The behavior of the currents is determined by the arrangement of the components in the circuit and the resistance offered by the conductors and components. Resistance is a fundamental property of a conductor that opposes the flow of charged particles and can be affected by various factors.

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The wavelength of the laser is 0.4464 mm.

The equation for the diffraction grating is given as:

dsinθ = mλ

where d is the distance between the slits (in meters), θ is the angle between the central maximum and the mth bright fringe (in radians), m is the order of the bright fringe, and λ is the wavelength of the light (in meters).

The equation to calculate the wavelength of a laser is λ = d × sin θ/m, where d is the distance between two adjacent slits on the diffraction grating (in this case, 1000 slits/mm, which is equivalent to 1 mm), θ is the angle of the fringe relative to the central axis (in this case, 26 degrees), and m is the order of the fringe (in this case, m=1). Therefore, plugging in the values:

λ = 1 mm × sin 26°/1 = 0.4464 mm

The wavelength of the laser is 0.4464 mm.

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Thermogenesis has been studied the plants in the genus arum, including skunk cabbage and the corpse flower. In these plants, these hypotheses have been provided to explain the reason behind thermogenesis

Thermogenesis, which takes place in specialised tissues such brown adipose tissue and skeletal muscle, is described as the disposal of energy through the generation of heat.

All metabolic activities involved in keeping the organism in a live condition require mandatory thermogenesis, which takes place in all organs. It also includes the energy used when food is consumed, digested, and processed (thermic effect of food, or TEF).

Thus, the reason behind thermogenesis are:

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the dimensions of the rectangle with the maximum area are approximately a height of 6.464 and a width of 8.944, and the maximum area is approximately 35.355.

The rectangle is constructed with its base on the x-axis and two of its vertices on the parabola y = 25 - x^2. To find the dimensions of the rectangle with the maximum area, we need to determine the length and width of the rectangle.

Let's consider a point (x, y) on the parabola. Since the base of the rectangle lies on the x-axis, the height of the rectangle is given by the y-coordinate of this point. Therefore, the height of the rectangle is y = 25 - x^2.

To determine the width of the rectangle, we need to find the x-coordinates of the two vertices of the rectangle on the parabola. The x-coordinate of the first vertex is the same as the x-coordinate of the point (x, y). The x-coordinate of the second vertex can be found by taking the negative value of the x-coordinate of the point (x, y). Therefore, the width of the rectangle is 2x.

The area of the rectangle is given by the product of its length and width, which is (25 - x^2) * 2x.

To find the dimensions of the rectangle with the maximum area, we need to find the value of x that maximizes the area. To do this, we can take the derivative of the area function with respect to x and set it equal to zero. This will give us critical points, which we can then test to find the maximum.

Taking the derivative of the area function, we get:

d/dx [(25 - x^2) * 2x] = 0
50x - 4x^3 = 0
2x(25 - 2x^2) = 0

From this equation, we can see that there are two critical points: x = 0 and x = √(25/2).

Next, we can test these critical points to find the maximum. Plugging in x = 0, we get an area of 0. Plugging in x = √(25/2), we get an area of (25 - (√(25/2))^2) * 2√(25/2) = 25√2.

Therefore, the dimensions of the rectangle with the maximum area are a height of 25 - (√(25/2))^2 and a width of 2√(25/2), and the maximum area is 25√2.

In summary, the dimensions of the rectangle with the maximum area are approximately a height of 6.464 and a width of 8.944, and the maximum area is approximately 35.355.

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In summary, the dimensions of the rectangle with the maximum area are a width of 2√5 units and a height of 20 units. The area of the rectangle is 5√5 square units.

To find the dimensions of the rectangle with the maximum area, we need to consider that the base of the rectangle is on the x-axis and two of its vertices are on the parabola y = 25 - x^2.

Step 1: Let's consider a point (x, y) on the parabola.

The x-coordinate of this point will be the width of the rectangle, and the y-coordinate will be the height of the rectangle.

Step 2: The area of the rectangle is given by the formula A = width * height.

Step 3: Substituting the coordinates of the point (x, y) into the area formula, we get A = x * y.

Step 4: Substituting y = 25 - x^2 into the area formula, we get A = x * (25 - x^2).

Step 5: To find the maximum area, we take the derivative of A with respect to x and set it equal to zero.

Step 6: Solving the derivative equation, we find the critical point x = ±√5.

Step 7: Plugging these x-values into the area formula, we find two possible areas: A = 5√5 and A = -5√5.

However, since area cannot be negative, the maximum area is A = 5√5.

Therefore, the dimensions of the rectangle with the maximum area are a width of 2√5 units and a height of 25 - 5 units.

The area of the rectangle is 5√5 square units.

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Answer:

\(a = \frac{v_{f} - v_{i}}{t} \\ = \frac{77 - 5}{8} = \frac{72}{8} \\ \boxed{a = 9 \: m. {sec}^{ - 2} }\)

As the current decreases, the voltage across the rod should also decrease.

The voltage across a rod, or any conductor, is directly proportional to the current passing through it, according to Ohm's Law. Ohm's Law states that the voltage (V) across a conductor is equal to the product of the current (I) flowing through it and the resistance (R) of the conductor, represented by the equation V = I * R.

If we assume that the resistance of the rod remains constant, then as the current decreases, the voltage across the rod must also decrease.

This relationship can be understood by considering the nature of resistance. Resistance is a measure of how much a conductor opposes the flow of current. When the current is higher, more energy is required to overcome the resistance, resulting in a higher voltage drop across the conductor.

Conversely, as the current decreases, there is less opposition to the flow of current, requiring less energy and resulting in a lower voltage drop. Therefore, as the current passing through the rod decreases, the voltage across the rod should also decrease.

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When they were falling, their acceleration is equal to the gravity acceleration.

When they started stopping, the time required to stop is 1.5 seconds, that is, 3 times less than the time accelerating.

Since the change in velocity when falling and when stopping is the same (same magnitude but opposite signal), the acceleration when stopping will be 3 times more than the acceleration when falling (because the change in velocity is the same and the time is 3 times less).

So we have:

Therefore the acceleration is 29.4 m/s².

The instantaneous acceleration at t=3.1s is approximately 71.24 m/s², and the average acceleration over the first 3 seconds is 53.8 m/s² .

The instantaneous acceleration at t=3.1s can be found by taking the derivative of the position function, x(t), with respect to time, t, and evaluating it at t=3.1s.

Given position function:

x(t) = (4.2 m/s³)t³- (4.0 m/s²)t² + (65 m/s)t - 7.0 m

To find the instantaneous acceleration, we need to calculate the second derivative of x(t) with respect to t. Let's denote the second derivative as a(t):

a(t) = d^2x(t)/dt^2

Taking the derivative of x(t) with respect to t, we get:

dx(t)/dt = v(t) = (4.2 m/s^3)(3t^2) - (4.0 m/s^2)(2t) + (65 m/s)

Now, taking the derivative of v(t) with respect to t, we obtain the acceleration function:

dv(t)/dt = a(t) = (4.2 m/s³)(6t) - (4.0 m/s²)

Substituting t=3.1s into the acceleration function, we can find the instantaneous acceleration at t=3.1s

a(3.1) = (4.2 m/s³)(6(3.1)) - (4.0 m/s²)

Now, let's calculate the values:

a(3.1) = 75.24 m/s² - 4.0 m/s²

a(3.1) ≈ 71.24 m/s²

Therefore, the instantaneous acceleration at t=3.1s is approximately 71.24 m/s².

Now, let's find the average acceleration over the first 3 seconds. The average acceleration is given by the change in velocity divided by the change in time.

To calculate the average acceleration, we need to find the velocity at t=3s and t=0s.

v(3) = (4.2 m/s³)(3(3)²) - (4.0 m/s²)(2(3)) + (65 m/s)

    = (4.2 m/s³)(27) - (4.0 m/s²)(6) + 65 m/s

    = 113.4 m/s - 24 m/s + 65 m/s

    = 154.4 m/s

v(0) = (4.2 m/s³)(0³) - (4.0 m/s²)(0²) + (65 m/s)(0) - 7.0 m

    = 0 m/s - 0 m/s + 0 m/s - 7.0 m

    = -7.0 m

The change in velocity is v(3) - v(0):

Δv = v(3) - v(0)

   = 154.4 m/s - (-7.0 m)

   = 154.4 m/s + 7.0 m

   = 161.4 m/s

The change in time is 3s - 0s:

Δt = 3s - 0s

   = 3s

Now, we can calculate the average acceleration:

average acceleration = Δv/Δt

                   = 161.4 m/s / 3s

                   = 53.8 m/s²

Therefore, the average acceleration over the first 3 seconds is 53.8 m/s².

The instantaneous acceleration at t=3.1s is approximately 71.24 m/s², and the average acceleration over the first 3 seconds is 53.8 m/s².

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The coefficient of static friction between the book and the tabletop is 0.13.

The coefficient of static friction between the book and the tabletop can be calculated using the formula:

μs = Fs / N

Where μs is the coefficient of static friction, Fs is the force of static friction, and N is the normal force.

In this case, the force of static friction is the force required to start the book sliding, which is 2.16 N. The normal force is the weight of the book, which is 1.70 kg × 9.8 m/s2 = 16.66 N.

Plugging in the values into the formula, we get:

μs = 2.16 N / 16.66 N
μs = 0.13

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The speed of the wave is 16 m/s. And the right option is B. 16 m/s.

Speed is the rate of change of displacement.

To calculate the speed of the wave, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

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Answer:

The time it takes for the jet to reach landing speed is approximately 0.136 hours which is approximately 489 seconds

The landing speed is approximately 466.365 km/hr

Explanation:

The given parameters are;

The initial cruising speed of the jet = Mach 0.79 = 844 km/hr

The rate of speed reduction in the last 89 km = -2780 km/hr²

The distance it  takes the jet to reduce its speed for landing = 89 km

Given the above information,  we make use of the following equation of motion;

s = u·t - 1/2·a·t²

v² = u² - 2·a·s

Where;

s = The distance over which the acceleration (deceleration) is applied = 89 km

u = The initial velocity = 844 km/hr

t = The time taken for the accelerating/decelerating motion

v = The final velocity (landing speed)

Substituting the values gives;

v² = 844² - 2·(2780)·89 = 217496

v = √217496 = 466.365 km/hr

v ≈ 466.365 km/hr

Therefore, the landing speed, v  ≈ 466.365 km/hr

The time it takes is given by the equation, v = u - a·t

Therefore;

t = (u - v)/a = (844 - 466.365)/2780 ≈ 0.136 hours

The time it takes for the jet to reach landing speed ≈ 0.136 hours

From, s = u·t - 1/2·a·t², we have

89 = 844·t - 1/2 × 2780 × t²

89 = 844·t - 1390 × t²

1390 × t² - 844·t + 89 = 0

Solving with an online application gives;

t = 211/695 + (√(27187/2))/695 = 0.4715 hours or t = 211/695 - (√(27187/2))/695 = 0.136 hours

We note that the second time is for the time it will take the jet to get back to 89 km after reaching a speed of 0

Therefore, the correct time is t = 0.136 hours

The time it takes for the jet to reach landing speed ≈ 0.136 hours

Answer:

0.64

Explanation:

v = d/t

v= 16/25

v= 0.64

8000 Joules is the amount of work required to haul up the equipment.

To calculate the work required to haul up the equipment, we need to consider two components: the work done against gravity and the work done against the weight of the rope.

The force due to gravity is given by the weight of the equipment, which is 100 N. The distance over which the force is applied is the height the equipment is being hauled, which is 40 meters. The work done against gravity can be calculated using the formula:

Work = Force × Distance

Work against gravity = 100 N × 40 m = 4000 N·m or 4000 J (Joules)

The weight of the rope can be calculated by multiplying the weight per meter (0.8 N/m) by the length of the rope (40 m):

Weight of the rope = 0.8 N/m × 40 m = 32 N

Since the rope is being hauled up, the work done against the weight of the rope is the same as the work done against gravity. Therefore, the work against the weight of the rope is also 4000 J.

The total work required to haul up the equipment is the sum of the work against gravity and the work against the weight of the rope:

Total work = Work against gravity + Work against rope weight

Total work = 4000 J + 4000 J

Total work = 8000 J

Therefore, it will take 8000 Joules of work to haul up the equipme

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Answer:

positive acceleration.

Explanation:

As its slowing down gradually, its positive acceleration. When the ball slows down, its acceleration vector is in the opposite direction of its motion. Therefore positive acceleration.