A 66 kg student traveling in a car with a constant velocity has a kinetic energy of 1.1 104 J. What is the speedometer reading of the car in km/h?

The average angular speed in each direction of the rotating head is 9.42 rad/s.

The average linear speed in each direction of the bristles against the teeth is 5.09 cm/s.

The approximate speed of the bristles against the teeth when brushing by hand with an ordinary toothbrush is 1.26 cm/s.

Part A: The formula ω = Δθ/Δt can be used to determine the rotating head's average angular speed in each direction.

Where Δθ denotes the angular displacement, Δt denotes the rotational time, and ω denotes the angular speed.

In this instance,

Δt = 1/(7600/2) s/rotation, and Δθ= 70.0 degrees = 70.0 x (π/180) radians.

Thus, ω = (70.0 x (π/180)) / (1/(7600/2)) = 9.42 rad/s is the average angular speed in each direction.

Part B: The following equation can be used to determine the average linear speed of the bristles against the teeth:

v = rω

where r is the head's radius (0.55 cm), v is the linear speed, and ω is the angular speed.

The average linear speed is therefore v = 0.55 x 9.42 = 5.09 cm/s in each direction (rounded to two significant figures)

Part C: Although it is challenging to measure precisely, it is possible to estimate the speed of the bristles against the teeth when brushing by hand with a regular toothbrush. The average linear speed can be estimated using the formula v = rΔθ/Δt if we suppose that the bristles rotate through an average displacement of 45 degrees five times each second.

Where Δθ = 45 degrees, Δt = 1/5 s, and r = the radius of the bristles (estimated as 0.2 cm).

So, the average linear speed is approximately:

v = 0.2 x (45 x (π/180)) / (1/5) = 1.26 cm/s (rounded to two significant figures).

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The spring constant of the spring is 200 N/m.

option C.

The spring constant of the spring is calculated  by applying the following formula as shown below;

.

Mathematically, the formula for energy stored in a spring is given as;

U = ¹/₂kx²

where;

k = ( 2U ) / ( x² )

k = ( 2 x 1 J ) / ( 0.1 m )²

k = 200 N/m

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At that point in its motion, the ball changes direction without changing its speed, is the a true statement.

Instantaneous acceleration refers to the rate of change of an object's velocity at a specific point in time. It measures the change in an object's velocity over an infinitesimal amount of time and is the derivative of velocity with respect to time.

This statement is true because when the acceleration vector is perpendicular to the velocity vector, it means the ball is changing direction without changing its speed. The direction of the acceleration vector determines the change in direction, and the magnitude of the acceleration vector determines the rate of change in speed. If the acceleration vector is perpendicular to the velocity vector, it means that the direction is changing, but the speed is not changing.

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The block has a density of 16309.2 kg/m3.

The density of a material is an indicator of how heavy it is in relation to its size. If an object is submerged in water, it will float if its density is lower than that of the water, and sink if it has a higher density. A differentiating characteristic that is unrelated to a substance's volume is its density.

We must apply Archimedes' principle, which states that the weight of the fluid that is displaced by an object when it is immersed in a fluid equals the buoyant force acting on the item.

Let's start by determining the block's weight:

mass = density * volume

    = density_block * length * width * height

weight_block = mass * g

= density_block * length * width * height * g

where g is the acceleration due to gravity (9.81 m/s²).

Next, let's find the weight of the displaced fluid:

volume_submerged = length * width * depth_submerged

weight_fluid = density_fluid * volume_submerged * g

Since the block is floating freely, the weight of the displaced fluid must be equal to the weight of the block:

density_block = density_fluid * volume_submerged / (length * width * height)

Plugging in the given values, we get:

density_block = 1354.6 kg/m³ * (0.8 m * 0.6 m * 150.45 m) / (1 m * 0.8 m * 0.6 m)

= 16309.2 kg/m³.

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The pike's acceleration during the strike is 30m/s² and the pike moves 0.049 meters.

An object's rate of change in velocity (speed and direction) over a predetermined amount of time is known as acceleration.

a. The following acceleration formula can be used to determine the pike's rate of acceleration during the strike:

a = Δv / Δt

where v denotes the velocity change and t the time change.

When we enter the values provided, we get:

acceleration = (4.2 m/s - 0 m/s) / 0.14 s = 30m/s²

The pike's acceleration during the hit is 30m/s².

b. The formula for distance based on initial velocity, final velocity, acceleration, and time can be used to calculate the distance the pike travels during the strike:

Distance = (1/2) * Acceleration * Time * Initial Velocity * Time

Given that the pike's initial speed is 0 m/s, the distance can be computed as follows:

Distance = 0 m/s * 0.14 s + (1/2) * 30 m/s * 0.14 s

=0.049 m.

Due to this hit, the pike moves 0.049 meters.

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The particle cannot accelerate toward the speed of light if no acceleration is applied. The correct answer is e) none of these.

The particle encounters a force of 10 N in the opposite direction of the initial force, creating an unbalanced force. This means that the particle experiences an acceleration of 10 N in the opposite direction, decelerating from its initial velocity.

However, since the acceleration caused by the second force is equal to the acceleration caused by the first force, the particle does not come to a rapid halt, but rather its velocity gradually decreases until it comes to a stop. This means that the correct answer to the question is b) decelerates gradually to a halt.

In order for the particle to theoretically tend to the speed of light, it must experience a constant acceleration in any direction.

Since the two forces are in opposite directions and of equal magnitude, the resultant force is zero, meaning that the particle experiences no acceleration and therefore its speed remains the same.

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The velocity of the object is (2.0 s) = 0+∫ = −3.2 m/s − 5 m/s = −8.2 m/s

Velocity is a vector quantity that measures the rate of change of an object's position. It is the speed of an object in a given direction and is usually represented by a vector with both magnitude (the speed) and direction. Velocity is the rate at which an object's position changes over time, or the derivative of an object's position with respect to time.

The velocity of the object at time t = 2.0 s can be calculated using the equation for velocity, =0+∫.
We can calculate the velocity at t = 2.0 s by first calculating the integral of the acceleration equation.
∫ = −(10/)sin(+3/2)
Substituting in t = 2.0 s, we get
∫ = −(10/)sin(2+3/2) = −(10/)sin(5/2) = −5 m/s
We then substitute this value into the equation for velocity and substitute in the initial velocity of the object at t = 0 s, 0 = −3.2 m/s, to get:
(2.0 s) = 0+∫ = −3.2 m/s − 5 m/s = −8.2 m/s

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The required electric field strengths are calculated to be E₁ = E₃ = 112.88 × 10³ N/C, E₂ = 0.

Length of the two glass rods is given as, L = 17 cm = 0.17 m

Charge on them = 16 nc = 16 × 10⁻⁹ C

Distance between the rods is given as 4 cm = 0.04 m.

Electric charge due to a single glass rod can be given by,

E = Q/ (2π ε₀ r L) ----(1)

(1) can be used to determine E₁, E₂, E₃ because the points lie within the two rods hence the net electric field produced will be equal to the difference in electric fields produced.

E₁ = Q/ (2π ε₀ r L) × [1/0.01 - 1/0.03]

⇒ (16 × 10⁻⁹)/(2× 3.14× 8.85 × 10⁻¹² × 0.17) × (66.67)

⇒  (16× 66.67 × 10³)/(9.45) = 112.88 × 10³ N/C

Let us find E₂,

E₂ = Q/ (2π ε₀ r L) × [1/0.02 - 1/0.02] = 0

And E₁ = E₃.

Thus, E₁ = E₃ = 112.88 × 10³ N/C, E₂ = 0.

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The spring constant of the spring is 5.1N/m.

The formula for calculating the period of oscillation is expressed as:

[tex]T = 2\pi \sqrt{\dfrac{m}{k}}[/tex]

,where m is the mass of the spring and k is the spring constant.

Making the spring constant "k" the subject of the formula will give;

[tex]k = 4\pi^2\dfrac{m}{T^2}[/tex]

Get the period of oscillation "T"

[tex]T = \dfrac{1}{f}[/tex]

frequency "f" is the number of oscillations completed in one second.

If a student with a stopwatch finds that 8 oscillations take 12.0 s, the number of oscillations in one sec will be 12/8 = 1.5 oscillations.

Period T = 1/1.5 = 0.67 seconds

Get the required spring constant,

   [tex]k = 4\pi^2\dfrac{0.240}{(0.67)^2}\\k = 21.06[/tex]

Hence the spring constant of the spring is 21.06 N/m.

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The center of mass of a right-circular cone with a base radius r, height h, and a non-uniform mass density varies as the square of the distance from apex (tip of the cone) is:

ρ(x, y, z) = k * (√(x^2 + y^2 + z^2))^2

where k is a constant of proportionality.

To find the center of mass of a right-circular cone with a base radius "r" and height "h", and a non-uniform mass density that varies as the square of the distance from the apex, we need to use the following formula:

Let "m" be the total mass of the cone, then the center of mass can be found using the following formulas for the x, y, and z-coordinates:

x-coordinate:

x_cm = (1/m) * ∫∫∫_V x * ρ(x, y, z) * dV

y-coordinate:

y_cm = (1/m) * ∫∫∫_V y * ρ(x, y, z) * dV

z-coordinate:

z_cm = (1/m) * ∫∫∫_V z * ρ(x, y, z) * dV

where V is the volume of the cone, ρ(x, y, z) is the mass density function, and the integration is performed over the entire volume of the cone.

Since the mass density varies as the square of the distance from the apex, we have:

ρ(x, y, z) = k * (√(x^2 + y^2 + z^2))^2

where k is a constant of proportionality.

Substituting this into the above equations, we can find the center of mass of the cone.

The final result will depend on the specific values of r, h, and k, and the integration may be challenging to perform analytically. But numerical integration methods can be used to approximate the center of mass with good accuracy.

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Rapid deformation rates, cooler temperatures, the existence of a high stress concentration degree of stress, radiation damage, and corrosion can all result in brittle fracture (including hydrogen embrittlement).

When temperatures exceed 90 degrees, you are in "hot" terrain from just a strictly thermometric perspective.

The average body temperature is between 36 and 37 degrees Celsius, however this varies based on age, exercise levels, time of day, and measuring method. Colds, the flu, and COVID-19 are examples of viral respiratory illnesses that can raise a person's temperature.

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Answer:

The deepest part of earth or oceans. They are most commonly found in oceans however

Explanation:

Between the plates, there is a 14 x 10^6 V/m electric field. The plates have a charge density of 2.32 x 10-17 C/m^2 C. The net charge on the membrane piece is 0 C, and the charge on each side of the membrane is 3 x 10-8 C in magnitude.

Part A:

Part B:

Part C:

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The magnitude of the resultant would be 40 N, the location of the resultant is 0 m.

Resultant is a term used to refer to the combined effect of two or more forces acting on an object. It is the vector sum of the individual forces acting on the object, and can be determined by adding the individual vectors of the forces together.

The magnitude of the resultant of the distributed load can be calculated by summing the forces at each point and then resolving them into components. The location of the resultant can then be determined by calculating the moment of the distributed load.

For example, if the load is distributed over a distance of 4 m and has a magnitude of 10 N/m,
the magnitude of the resultant would be 40 N.
This can be calculated by summing the forces at the start and end points (40 N = 10 N + 10 N + 10 N + 10 N).
The location of the resultant can then be determined by calculating the moment of the distributed load.
This is done by finding the sum of the moments at each point and then dividing by the total force (location = moment / force).
In this case, the moment at each point is 0 Nm, so the location of the resultant is 0 m.

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Complete Question is attached Below:

The electric field is zero, because a Gaussian sphere concentric with the sphere with X on its surface encloses zero net charge. The correct claim is (D).

The electric field at point X is the vector sum of the electric fields from the sphere and the shell. However, since the total charge on both the sphere and the shell is evenly distributed, the electric field from the sphere will be exactly canceled by the electric field from the shell at any point inside the sphere. Therefore, the net electric field at point X will be zero.

This can be proven by using a Gaussian surface, which is a hypothetical sphere drawn around point X. Since the electric field is spherically symmetric, we can choose the Gaussian surface to be a spherical shell centered at X.

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Answer:

Explanation:

jajs poza

Answer:

see below

Explanation:

we have ,

We know,

Work = mgh

Work = 1.5kg * 10m/s² * 0.2m

Work= 3J

and we are done!

The charge of the two capacitors will be equal when they are connected. Similarly their electrical potential will be equal. The charge distribution to attain equilibrium is making them equally charged.

The capacitance of a device is its ability to store charge.  Such devices are called capacitors. The capacitance of a capacitor is dependent on the electrical potential and charge as well as their size and shape.

According to the law of conservation of electrical charges, the charge lost by one body is equal to the charge gained by the other body. Hence, when two differently charged capacitors when connected each other, the start charge transfer until they attain equal charges.

Therefore, the measurement that is equal for the capacitors here connected by the wire is charge.

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Charge will be equal on both conductors after connecting with wire.

Electric charge is the physical property of matter that causes that matter to experience a force when placed in an electromagnetic field. Electric charge can be positive or negative.

Given,

Two conductors of different sizes and different initial charges are connected with a wire,

Connecting with a wire will start flow of charge until charges on both conductors become equal.

Hence, charge will then be equal for both conductors.

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The momenta of the two dynamic carts that start out at rest and then explode would be altered drastically.

Dynamic carts are shopping carts that are programmed to track data about customer purchases and preferences. This data is used to provide personalized product recommendations and discounts to customers. Dynamic carts are powered by advanced algorithms that analyze customer purchasing behavior and analyze it in real-time.

When the carts explode, the energy released from the explosion will create an equal and opposite reaction, pushing each cart in the opposite direction. This means that the momentum of each cart will be altered depending on the amount of energy released from the explosion. The total momentum of the system will remain the same, since the momentum of the first cart will be equal and opposite to that of the second cart.

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The path travelled by a projectile is known as its trajectory. The distance at which the two objects pass each other is 16.9 m.

Any object which is thrown into space and the only force acting on it is the force of gravity. The motion of a projectile is known as the projectile motion.

The height covered by the projectile from ground is:

h = ut - 1/2 gt²

h = 5t - 1/2 × 9.8 × t²

h = 5t - 4.9t²   (1)

When projectile is thrown downward, u = 0

65 - h = 1/2 gt²

65 - (5t - 4.9t² ) = 4.9t²

65 = 5t

t = 65/5 = 13 s

h = 65t - 4.9t²

= 65 × 13 - 4.9 × 169

= 16.9 m

Thus the distance at which the two objects pass each other is  16.9 m.

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Refrigerant migration into the compressor crankcase will not usually occur if the temperature where the compressor is located is kept well above the refrigerant's saturation temperature.

Refrigerant migration occurs when the refrigerant vapor in the system condenses into a liquid and migrates into the compressor crankcase oil. If the temperature around the compressor is kept well above the saturation temperature, the refrigerant remains in a vapor state and does not condense, thereby reducing the likelihood of refrigerant migration into the compressor crankcase.

It is important to maintain the proper temperature in the compressor area to prevent refrigerant migration as it can cause several issues such as decreased compressor efficiency, reduced system performance, and increased oil degradation.

Additionally, the presence of refrigerant in the oil can cause oil degradation and system contamination, which can ultimately lead to compressor failure. Therefore, it is important to keep the temperature in the compressor area well above the refrigerant's saturation temperature to prevent refrigerant migration and ensure the longevity and proper operation of the refrigeration system.

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Answer:

Look below

Explanation:

Part A:

The initial angular velocity of the rotor can be found using the formula:

ω = v/r

where ω is the angular velocity, v is the linear velocity, and r is the radius of the cylinder. Since the rotor is rotating at 9000 rpm, we can convert this to radians per second:

ωi = (9000 rpm) x (2π/60 s) = 942.48 rad/s

The final angular velocity is zero. The frictional torque acting on the rotor is given by:

τ = Iα

where τ is the torque, I is the moment of inertia, and α is the angular acceleration. The moment of inertia for a solid cylinder is:

I = (1/2)mr^2

Substituting in the given values and solving for α, we get:

α = τ/I = (1.73 m⋅N) / [(1/2)(3.72 kg)(0.0760 m)^2] = 371.7 rad/s^2

The final angular velocity is zero, so we can use the formula:

ωf^2 = ωi^2 + 2αθ

where θ is the angle of rotation. Solving for θ, we get:

θ = (ωf^2 - ωi^2) / (2α) = (0 - (942.48 rad/s)^2) / (2 x 371.7 rad/s^2) = 6.76 revolutions

Therefore, the rotor will turn approximately 6.76 revolutions before coming to rest.

Part B:

The time it takes for the rotor to come to rest can be found using the formula:

ωf = ωi + αt

where ωf is the final angular velocity, ωi is the initial angular velocity, and α is the angular acceleration. Solving for t, we get:

t = (ωf - ωi) / α = (0 - 942.48 rad/s) / 371.7 rad/s^2 = 2.535 s

Therefore, it will take approximately 2.535 seconds for the rotor to come to rest.

The potential at location B must be 452 V + 339 V = 791 V.

Potential is the capacity to become or develop into something, either tangible or intangible. It is an opportunity that, when acted on, can bring about a desired outcome. Potential exists both within individuals and within organizations, and can be realized through purposeful effort, ambition, and hard work.

When a particle is released from rest at location A with a potential of 452 V and arrives at location B with a velocity vB, the work done on the particle in moving it from location A to location B is equal to the difference in potentials between the two locations, or (791 V - 452 V) = 339 V.
This means that the potential at location B must be 452 V + 339 V = 791 V.

When the particle is released from rest from location C with a potential of 791 V and arrives at location B with twice the speed it had previously, or 2vB,
the work done on the particle in moving it from location C to location B is equal to the difference in potentials between the two locations, or (791 V - 791 V) = 0 V.
This means that the potential at location B must be 791 V + 0 V = 791 V, which is the same as the potential at location C.

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The electron gains more kinetic energy than the proton when accelerated through a potential difference of 1 V.

The relationship between the kinetic energies of the electron and proton can be determined using the formula for the kinetic energy of a particle:

[tex]KE = (1/2)mv^2[/tex]

[tex]V = (q/m)d[/tex]

where V is the potential difference, q is the charge, m is its mass, and d is the distance .

For the electron, [tex]V = 1 V[/tex]and[tex]q/m = -1.6 x 10^-19 C/kg[/tex], so its final velocity is:

[tex]v_e = sqrt((2qV)/m) = sqrt((2*(-1.6 x 10^-19)*1)/9.11 x 10^-31) = 5.93 x 10^6 m/s[/tex]

For the proton, [tex]V = -1 V and q/m = 1.6 x 10^-19 C/kg,[/tex] so its final velocity is:

[tex]v_p = sqrt((2qV)/m) = sqrt((2*(1.6 x 10^-19)*(-1))/1.67 x 10^-27) = 7.16 x 10^5 m/s[/tex]

Substituting these values into the formula for kinetic energy, we get:

[tex]KE_e = (1/2)9.11 x 10^-31(5.93 x 10^6)^2 = 1.63 x 10^-17 J[/tex][tex]KE_p = (1/2)1.67 x 10^-27(7.16 x 10^5)^2 = 0.84 x 10^-17 J[/tex]

Therefore, we have:

[tex]KE_e > KE_p[/tex] , This is because the electron has a much smaller mass than the proton, so it experiences a much larger acceleration and gains more velocity and kinetic energy.

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Answer:

The swimmer's velocity relative to the river bank is 0.35 m/s east.

Explanation:

This can be determined by adding the velocities together in the direction of the current. The velocity of the swimmer relative to still water (0.15m/s) and the velocity of the river (0.20m/s) must be added together in the eastward direction, resulting in a total velocity of 0.35m/s east.

The energy transfers and transformations involved in the falling of a rock off a cliff into seawater occur in the following order: potential energy, kinetic energy, and finally thermal energy.

The energy transfers and transformations involved in the falling of a rock off a cliff into seawater can be ranked as follows:

In summary, the energy transfers and transformations involved in the falling of a rock off a cliff into seawater occur in the following order: potential energy, kinetic energy, and finally thermal energy.

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a. The gauge pressure at this depth is 250 kPa.

b. The net force due to the water outside and the air inside the bell on a circular glass window 30.0 cm in diameter is 7.5 kN.

What do you mean by pressure?

Pressure is a measure of the force applied over a given area and is usually expressed in units such as pascals (Pa) or pounds per square inch (psi). It is a fundamental physical quantity found in all areas of physics, including fluid dynamics, thermodynamics, and mechanics.

a. The pressure at a certain depth in a body of water is given by the equation P = ρgh, where ρ is the density of water, g is the acceleration due to gravity, and h is the depth of the water. In this case, the gauge pressure at a depth of 150 m is equal to 250 kPa.

b. The net force on the glass window can be calculated by using the formula F = Pπr2, where P is the pressure, π is the mathematical constant, and r is the radius of the window. In this case, the net force on the window is 7.5 kN, which can be calculated as 7.5kN = 250kPa × (0.15m)2 × 3.14.

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The total distance covered by the subway train is 1796.5 m. The result is obtained by using the equations in uniformly accelerated straight motion.

A uniformly accelerated straight motion is a motion with acceleration or deceleration in a straight line. The equations apply in horizontal dimension are

v₁ = v₀ + at

v₁² = v₀² + 2ax

x = v₀t + ½ at²

Where

A subway train starts from rest at a station.

Find the total distance covered!

When it accelerates, the distance is

x₁ = v₀t + ½ a₁t₁²

x₁ = 0 + ½ (1.60)(14.0)²

x₁ = 0 + 0.8(196)

x₁ = 156.8 m

The final speed after 14 s is

v₁ = v₀ + at

v₁ = 0 + (1.6)(14.0)

v₁ = 22.4 m/s

The speed later will be constant for t₂ = 70.0 s.

When it moves with a constant speed (22.4 m/s), the distance is

x₂ = v₁t₂

x₂ = 22.4(70)

x₂ = 1568 m

When it slows down until it stops (v₂ = 0), the distance is

v₂² = v₁² - 2a₂x₃

0 = 22.4² - 2(3.5)x₃

22.4² = 2(3.5)x₃

501.76 = 7x₃

x₃ = 71.68 m

The total distance covered will be

x = x₁ + x₂ + x₃

x = 156.8 m + 1568 m + 71.68 m

x = 1796.48

x = 1796.5 m

Hence, the subway train traveled for a total distance of 1796.5 m.

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Spring force P on the cable if the spring is compressed 0.025 m when the mechanism is in the position shown is 0.198 kN.

When the mechanism is in the position indicated, the force P on the cable is 0.198 kN if the spring is compressed 0.025 m in 40 kg

When a spring mechanism is adjusted by a length away from its balance length, it exerts a force on items fastened to its end that is continuously coordinated towards its harmonic position. F = - kx. The term "spring steady" refers to the proportional constant k. It is a percentage of the solidity of the spring. The following power is negative (moving towards the left) if x is positive (uprooting to the right), and vice versa. As a result, the spring force often works to restore mass to its harmonious position. The force P on the cable is therefore 0.198 kN. when, the mechanism is in the position shown.

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