a 25.0kg child jumps to the ground from a structure 1.00m high and comes to rest 0.500s after first contact with the ground. what average force is applied by the child in coming to rest

With a potential difference of 14 volts across it, the 10.0 ohm resistor dissipates 19.6 watts of electrical power.

Any equation connecting power to current, voltage, and resistance may be used to calculate the power wasted by each resistor.

The following formula must be used to determine the amount of electrical power a resistor dissipates in a parallel circuit:

P = V²/R

In this case, the resistance is 10.0 ohms and the potential difference is 14 volts.

These values are combined together to give us:

P = (14 V)²/ 10.0 Ω

P = 196 V²/ 10.0 Ω

P = 19.6 W

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The first billiard ball moves in the x-direction with a velocity of 50.0 cm/s after the collision, while the second ball stops. The first ball moves in the same direction as before the collision, indicating a conservation of direction.

The first ball was moving in the x-direction with a velocity of 30.0 cm/s and after the collision, it moved in a direction that is a combination of the x and y directions with a velocity of 50.0 cm/s. The second ball was moving in the y-direction with a velocity of 40.0 cm/s and stopped after the collision. Therefore, the final direction of the first ball can be found using trigonometry. Let's define θ as the angle between the x-axis and the direction of motion of the first ball after the collision. Then, we can use the following equation:

tan(θ) = (final velocity in the y-direction) / (final velocity in the x-direction)

tan(θ) = 0 / 50.0

θ = 0 degrees

Therefore, the first ball moves in the x-direction after the collision, with no change in direction.

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The initial ball advances in the final direction at an angle of 53.13 degrees above the x-axis. We must compute the angle the initial ball makes with the x-axis in order to determine its final orientation.

The issue includes a collision between two pool balls, the ultimate velocity and direction of the first ball needing to be calculated, and the initial velocities of the balls are known. The final velocity and angle of the first ball can be calculated using the laws of conservation of momentum and energy. Since the second ball stops after the collision, it is possible to solve for the first ball's end velocity in terms of the beginning velocities and masses by writing the momentum equations in the x- and y-directions.  We can determine the final direction of the first ball by solving for the angle.The initial ball advances in the final direction at an angle of 53.13 degrees above the x-axis.

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In the given scenario, a nonmetallic-sheathed cable is used to connect a wall-mounted oven. The insulated conductors are 10 AWG. Therefore, the size of the equipment grounding conductor in this cable is 10 AWG.

What is a nonmetallic-sheathed cable? A nonmetallic-sheathed cable is a cable used in houses and buildings for installing electrical outlets, switches, and other electrical devices. It contains 2 or more insulated conductors and a bare grounding conductor that is not a part of the circuit.

The bare grounding conductor is designed to reduce the risk of electrical shock and damage by providing a low resistance path to ground. In case of a short circuit or ground fault, the grounding conductor diverts the current to the ground wire, causing a fuse or circuit breaker to trip.

Ground fault circuit interrupters (GFCIs) are often used to protect against electric shock from a nonmetallic sheathed cable.

What is equipment grounding conductor?

An equipment grounding conductor is a conductor that is intended to carry ground-fault current from the point of a ground fault on the equipment back to the source. Grounding conductors are essential for ensuring safety and preventing damage to electrical equipment. In the given scenario, the size of the equipment grounding conductor in the nonmetallic-sheathed cable is 10 AWG.

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A polynomial in linear algebra that has the eigenvalues as roots and is invariant under matrix similarity is known as the characteristic polynomial of a square matrix.

Among its coefficients are the determinant and the trace of the matrix. The characteristic equation of the matrix A is det (A -  λI) = 0, and its roots (the values of  λ) are referred to as characteristic roots or eigenvalues. Also, it is well known that each square matrix has a unique equation.

The characteristic equation of the matrix A is det(A - λI) = 0. The roots of the characteristic equation are eigenvalues  λ of A. The equation (A- λ I)x = 0 has nonzero solutions that are associated eigenvectors of A.

At steady state, the response to a complex exponential (or sinusoid) at a specific frequency is the same complex exponential (or sinusoid), but its amplitude and phase depend on the system's frequency sensitivity at that frequency.

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The answer is B) 0.19 s, which is the approximate reaction time for someone to catch an object that has fallen 7 inches on a meter stick.

the interval of time between when a stimulus first appears or is presented and when a particular response to that stimulus actually occurs. There are various kinds, such as choice and easy reaction times. You can evaluate many psychological constructs using reaction time.

The time it takes for an object to fall a certain distance can be calculated using the formula:

d = 1/2 * g * t^2

Where:

d is the distance fallen (in meters)

g is the acceleration due to gravity (approximately 9.81 m/s^2)

t is the time taken (in seconds)

In this case, the distance fallen is 7 inches, which is equivalent to 0.1778 meters. We can use this value to solve for the time taken:

0.1778 = 1/2 * 9.81 * t^2

Simplifying this equation, we get:

t^2 = 0.0362

Taking the square root of both sides, we get:

t = 0.19 s (rounded to two decimal places)

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The speed v1 that will cause the vehicle to roll completely over to its right side is approximately 0.91 m/s.

To estimate the speed v1 that will cause the vehicle to roll completely over to its right side, we can follow these steps:

1. Identify the given parameters: mass (m) = 2300 kg, moment of inertia (Ig) = 900 kg m².

2. Recognize that the vehicle's kinetic energy will be converted into gravitational potential energy during the tipping process.

3. Calculate the initial kinetic energy (KE) of the vehicle: KE = 0.5 * m * v1²

4. Calculate the gravitational potential energy (PE) at the tipping point: PE = m * g * h, where g is the acceleration due to gravity (9.81 m/s²) and h is the height of the vehicle's center of mass above the ground.

5. Set KE equal to PE, and solve for v1: 0.5 * m * v1² = m * g * h

6. As we don't have the height (h) of the vehicle's center of mass, we can use the moment of inertia (Ig) to determine the relationship between v1 and h: Ig = m * h². From this, we can solve for h: h = sqrt(Ig/m)

7. Substitute the expression for h in the previous equation:

0.5 * m * v1² = [tex]m \times g \times \sqrt{\frac{Ig}{m} }[/tex]

8. Solve for v1: v1 = [tex]\sqrt{2 \times g \times {\sqrt{\frac{Ig}{m} }/ {m} }}[/tex]

9. Plug in the given values and calculate v1: v1 = sqrt((2 * 9.81 * sqrt(900/2300))/2300) = sqrt(0.830) ≈ 0.91 m/s

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When we draw loop within a wire that carries current uniformly across its circular cross-sectional area, the value of the integral in Ampere's law is proportional to the current encircled by the loop.

Ampere's law is an equation that represents the relationship between the current and the magnetic field produced by that current. It states that the magnetic field created by a current-carrying wire can be calculated by integrating the product of the magnetic field and the length of the wire around a closed path (Amperian loop).

An Amperian loop is a loop-like path used to calculate the magnetic field created by a current-carrying wire using Ampere's law.

An Amperian loop encircles the wire, and the magnetic field created by the current passing through the wire is perpendicular to the loop's surface.

The value of the integral in Ampere's law is proportional to the current encircled by the loop.

Therefore, if the Amperian loop encircles a section of wire that carries more current, the integral will be higher. If the Amperian loop encircles a section of wire that carries less current, the integral will be lower.

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The peak voltage of the generator is 25.07 V

To calculate the peak voltage of a generator that rotates its 250 turns, 0.100 m diameter coil at 3600 rpm in a 0.840 T field, you can use the equation for the induced emf in a generator, which is

E = NBAω.

Here, E is the induced emf, N is the number of turns in the coil, B is the magnetic field strength, A is the area of the coil, and ω is the angular velocity of the coil. To find the peak voltage, we need to multiply this induced emf by the square root of 2. Here's how to do it:

Number of turns N = 250, Diameter d = 0.100 m, Radius r = d/2 = 0.050 m, Angular velocity ω = 3600 rpm = 377 rad/s, Magnetic field strength B = 0.840 T,

Formula: E = NBAω

Peak voltage, Vmax = √2E

Using the above formula and substituting the given values, we have:

E = NBAωE = (250)(0.050²)(0.840)(377)

E = 125.25 V

Peak voltage, Vmax = √2E = √(2)(125.25) = 25.07 V

Therefore, the peak voltage of the generator is 25.07 V.

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Hello and regards obajimi57

Therefore, the acceleration that the 50 Newton unbalanced force gives to the 0.025 kg mass is 2000 m/s^2.

We are solving an exercise of Newton's second law.

Newton's second law states that the net force acting on an object is proportional to the object's mass and its acceleration. In mathematical terms, it is expressed as follows:

This equation indicates that if a net force acts on an object, the object's mass determines the amount of acceleration it will experience in response to that force. That is, the greater the mass, the more difficult it is to accelerate the object with the same force, and the greater the applied force, the faster the object will accelerate.

Newton's second law formula is expressed as:

Net force = mass x acceleration

where:

It tells us that an unbalanced force of 50 Newton acts on a mass of 0.025 kg, here we calculate the acceleration; so

a = F/m

a = 50 N/0.025 kg

a = 2000 m/s²

Therefore, the acceleration that the 50 Newton unbalanced force gives to the 0.025 kg mass is 2000 m/s^2.

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[tex]\Large\bold{SOLUTION}[/tex]

We can use Newton's second law of motion to solve this problem, which states that the net force acting on an object is equal to its mass times its acceleration. Mathematically, this can be expressed as:

where:

In this problem, we are given that an unbalanced force of 50 newtons acts on a 0.025 kg mass. So, we can plug these values into the equation above and solve for acceleration:

Therefore, the acceleration of the 0.025 kg mass due to the unbalanced force of 50 N is [tex]2000\: m/s^2[/tex].

[tex]\rule{200pt}{5pt}[/tex]

If pink noise is sent through a guitar amp and recorded by two microphones, the second lowest frequency that will be 180 degrees out of phase is determined by the distance between the two microphones.

Assuming the speed of sound in air is 1,126 ft/s, the frequency can be calculated using the formula f = v/2d, where f is the frequency, v is the speed of sound, and d is the distance between the microphones. Using the given information, the frequency can be calculated as:

f = 1,126 ft/s / 2(5.5 in x 12 in/in) = 76.11 Hz

Therefore, the second lowest frequency that will be 180 degrees out of phase is 76.11 Hz.

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When a force of 3 pounds compresses a 15-inch spring a total of 3 inches, the work done is 1.35 ft-lbs. The question is 4/3 ft-lbs work is done in compressing the spring 8 inches.

To solve this problem, we can use Hooke's law and the work-energy principle.

Hooke's law states that the force required to compress or extend a spring is proportional to the displacement.

Mathematically, this can be expressed as:

F = -kx

where F is the force, x is the displacement, and k is the spring constant.

The negative sign indicates that the force is opposite to the direction of displacement.

In this problem, we are given that a force of 3 pounds compresses a 15-inch spring a total of 3 inches. This means that the spring constant is given by:

k = F/x = 3/3 = 1 pound per inch

Using Hooke's law, we can find the force required to compress the spring 8 inches:F = -kx = -1(8) = -8 pounds

The negative sign indicates that the force is compressive, i.e. in the opposite direction of displacement.

To find the work done, we need to integrate the force over the displacement.

Since the force is not constant, we need to use calculus.

W = ∫ F dx = ∫ -kx dx = -kx²/2

where W is the work done, F is the force, and x is the displacement.

We can substitute the values we have:

k = 1 pound per inchx = 8 inches

W = -kx²/2 = -(1/12) × (8)² = -4/3 ft-lbs

Since the work done is negative, this means that the force is doing work against the spring, i.e. the spring is doing negative work.

To find the absolute value of the work done, we take the magnitude:

|W| = 4/3 ft-lbs

Therefore, the work done in compressing the spring 8 inches is 4/3 ft-lbs.

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A bird runs into the window of a building because it sees the reflection of the sky in the window. the sky does not appear distorted in this window. The window is acting as a plane mirror. It reflects an image with a left-right inversion but no distortion of the image.

A mirror is an object that reflects an image that falls upon it and a mirror typically comprises a smooth and polished surface, a backing material, and a frame. Mirrors can reflect light in two different ways, the first is to produce a picture of something that is facing the mirror. The second is to bounce light back into the room that is facing the mirror. A plane mirror is a flat mirror that generates a virtual image of the same size as the original object, with a left-right inversion but no distortion of the image. A plane mirror's surface is smooth and uniform, reflecting light in a way that makes it look like the mirror's surface has a depth, while in fact, it does not have a depth.

Because of this optical illusion, objects reflected in the mirror seem to be behind the mirror's surface. A lens is a piece of glass or other transparent material with curved sides for magnifying or focusing light rays, it has two surfaces with different radii of curvature. When a beam of light passes through a lens, it is refracted by the lens, causing the light to converge or diverge depending on the lens' shape. Reflection is the return of light waves, sound waves, or any other type of wave after they hit a surface. When waves bounce back, they change direction, but they do not change their speed, frequency, or wavelength, this happens when a wave strikes a surface that cannot absorb the energy of the wave.

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Two ice skaters, Paula and Ricardo, push off from each other. Ricardo weighs more than Paula i.e.(a) both skaters have momentums of equal magnitude.(b) Paula has greater speed after push-off.

(A) Provided that two skaters Ricardo and Paula are initially at rest, momentum must be conserved. Paula is heavier than Ricardo.

Assume Paula has a mass of m, and Ricardo has a mass of M.

Let V and v, respectively, be their final velocities.

Both are initially at rest.

Thus, Paula and Ricardo have no beginning impetus.

The end momentum of the system must match the starting momentum of the system in accordance with the law of conservation of momentum.

Final momentum equals initial momentum

0 = MV + mv

MV = -mv

They both therefore possess the same amount of momentum, albeit in different directions.

(B) If we compare Paula and Ricardo's respective momentum magnitudes, then:

MV = mv

M/m = v/V

Now that we are aware, M>m

so, M/m > 1

therefore:

v/V > 1

v > V

Paula is faster as a result.

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The radius of the chamber, given a centripetal force, is 5.09 m.

The centripetal force equation is given by:
F = m x v2/r
Where,
F = 560 N
m = 83 kg
v = 3.2 m/s

Solving for r, we get:
r = m x v2/F
r = 83 x 3.22/560
r = 5.09 m

Mass of the person (m) = 83 kg. Force experienced by person (F) = 560 N. Velocity of the outer wall (v) = 3.2 m/s. Let the radius of the chamber be (r)Here, the force on the person is acting towards the centre of the circular motion which is given by F = mv²/r.

The centripetal force F = mv²/r

Therefore, v² = Fr/mr = Fv²/mr = 560 x 3.2²/83r = 5.09 m

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The effective spring constant k of the two-spring system is: k = k1k2 / (k1 + k2).

Given that two massless springs are connected in series.
Spring 1 has a spring constant k1, and spring 2 has a spring constant k2.

A constant force of magnitude f is being applied to the right. When the two springs are connected in this way, they form a system equivalent to a single spring of spring constant k.

To determine the effective spring constant k of the two-spring system:
The displacement x1 of the mass m1 of the first spring with a spring constant k1 can be written ask1x1 = f ----(1)
The displacement x2 of the mass m2 of the second spring with a spring constant k2 can be written ask2x2 = k1x1 ----(2)
Total force on the mass m2 of the second spring F= f-k1x1----(3)
Since the system is equivalent to a single spring with a spring constant k, the total force F can be written askx= kx----(4)

Equating (3) and (4) gives, f - k1x1 = kx---(5)
Replacing x1 from (1), we get:f - k1(f/k1) = kxOr,f = kx --- (6)

From equations (5) and (6), we can find the effective spring constant k of the two-spring system by equating both equations, we get:kx = f - k1x1

Solving for k, we get: k = k1k2 / (k1 + k2)

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The pressure system that brings cloudy and stormy weather is a low-pressure system.

Low pressure systems are characterized by an area of low atmospheric pressure, which causes air to rise and create clouds. As the air rises, it cools, and moisture condenses, forming clouds and rain. This cycle repeats itself until the low-pressure system passes.

Low-pressure systems bring cloudy and stormy weather as they move through an area, as the air is unstable, and the clouds and rain form more quickly. Low-pressure systems can cause more severe weather when they are accompanied by strong winds.

When winds are strong, the pressure difference between the low pressure system and surrounding areas is greater, and the winds can help to push the system along, causing the formation of thunderstorms, heavy rains, and strong winds.

Low-pressure systems often form when warm air from the tropics meets cold air from the poles. This causes a pressure difference and the formation of low-pressure systems. Low-pressure systems can also be caused by the flow of air along the Earth's surface, and by the heating of the Earth's surface.

In summary, a low-pressure system is an area of low atmospheric pressure, which brings cloudy and stormy weather as the air rises and moisture condenses. Low-pressure systems can also bring more severe weather when accompanied by strong winds.

Low-pressure systems often form when warm air from the tropics meets cold air from the poles, from the flow of air along the Earth's surface, or from the heating of the Earth's surface.

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Answer: Smaller stars burn smoothly for billions of years.

These smaller stars become white dwarfs.

Metals in stars accelerate supernova status.

Larger stars explode as supernovae.

Supernovae leave a neutron star or black hole.

Explanation:

The new angular speed of the student is 0.592 rad/s.

We can use the conservation of angular momentum to solve this problem:

Initial angular momentum = final angular momentum

The initial angular momentum is given by:

L1 = I1ω1

where I1 is the moment of inertia of the student plus stool plus extended objects, and ω1 is the initial angular speed.

The final angular momentum is given by:

L2 = I2ω2

where I2 is the moment of inertia of the student plus stool plus objects with the objects pulled in, and ω2 is the final angular speed.

Since the moment of inertia changes when the objects are pulled in, we need to use the parallel axis theorem to calculate I2:

I2 = I1 + 2mr2

where m is the mass of each object (2.9 kg), and r is the distance from the rotation axis to the objects (0.26 m).

Plugging in the numbers, we get:

I2 = 3.4 kg m² + 2(2.9 kg)(0.26 m)²

I2 = 3.4 kg m² + 0.644 kg m²

I2 = 4.044 kg m²

Now we can solve for ω2:

L1 = L2

I1ω1 = I2ω2

(3.4 kg m² )(0.7 rad/s) = (4.044 kg m² )ω2

ω2 = (3.4 kg m² )(0.7 rad/s)/(4.044 kg m² )

ω2 = 0.592 rad/s

Therefore, the new angular speed of the student is 0.592 rad/s.

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Sir Issac Newton came up with a theory about (d). gravity in 1687 is the correct option.

Sir Isaac Newton FRS was an English mathematician, physicist, astronomer, alchemist, theologian, and author who was known in his day as a "natural philosopher." He lived from 25 December 1642 to 20 March 1726/27. He was a pivotal player in the Enlightenment, an intellectual movement. He founded classical mechanics in his 1687 work Philosophize Naturalis Principia Mathematica (Mathematical Foundations of Natural Philosophy).

Newton co-developed the concept of infinitesimal calculus with German mathematician Gottfried Wilhelm Leibniz, and he made important contributions to optics as well.

Before the theory of relativity took its place, Newton's Principia contained the laws of motion and the universal gravitation, which constituted the prevailing scientific perspective for centuries. Newton eliminated uncertainty about the heliocentricity of the Solar System by using his mathematical description of gravity to deduce Kepler's laws of planetary motion, account for tides, the trajectories of comets, the precession of the equinoxes, and other phenomena.

He showed that the same concepts could be used to explain the motion of objects on Earth and heavenly bodies. The geodetic observations of Maupertuis, La Condamine, and others later corroborated Newton's deduction that the Earth is an oblate spheroid, persuading the majority of European scientists that Newtonian mechanics is superior to earlier theories.

Therefore, the correct option is (d) gravity.

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The direction of the friction force is opposite to the direction of the velocity of a sliding object. This means that the friction force acts in the direction opposite to the motion of the object.

When an object slides on a surface, there is often a resistance to its motion called friction. Friction arises due to the interaction between the surfaces in contact and can slow down or stop the object's motion. The friction force always acts in a direction opposite to the direction of motion, or velocity, of the sliding object. This is because the friction force is caused by the irregularities in the surfaces, which push against each other as the object moves. The force of friction is proportional to the normal force pressing the surfaces together, and the coefficient of friction between the surfaces. Understanding the direction of the friction force is important in many practical applications, such as braking systems in vehicles.

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Use the law of cosines to get the analytical expression of a force that forms a 130° angle with ej x and has a 5N modulus. According to this law, the square of the power module is equal.

to the sum of the squares of the power module components in the directions of x, e, and y. The components in this case are Fx = 5cos(130°) and Fy = 5sin(130°) in the direction of x and y, respectively. Hence, the analytical expression of force is F = (5cos(130°))i + (5sin(130°))j, where I y j are the unitary vectors in the directions of x, e, and y, respectively. According to this law, the square of the power module is equal.This expression may be made simpler by using F = -2.09i + 4.56j en.

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The linear velocity of the ball at the bottom of the ramp is v = √(10gh/7).

We can use the principle of conservation of energy to solve this problem. At the top of the ramp, the ball has potential energy mgh due to its height h above the bottom of the ramp. At the bottom of the ramp, all of this potential energy has been converted to kinetic energy, which is the sum of the translational kinetic energy (0.5mv^2) and the rotational kinetic energy (0.5Iω^2) of the ball.

Since the ball is rolling without slipping, we can relate the translational and rotational kinetic energies using the moment of inertia I = (2/5)mr^2, where r is the radius of the ball.

Thus, we have,

mgh = 0.5mv^2 + 0.5(2/5)mr^2(v/r)^2

Simplifying and solving for v,

v = √(10gh/7)

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A magnetic field created by the electric current causes the compass needle to move. Option D is correct choice.

When a current flows through a wire, it creates a magnetic field around it. This magnetic field interacts with the magnetic field of the compass needle causing it to move. The direction of the needle's movement is perpendicular to the direction of the current flow, as determined by the right-hand rule. Therefore, placing a compass near a simple circuit will cause the needle to move, indicating the presence of a magnetic field created by the current in the circuit. Hence, option D is correct.

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The y-coordinate of the center of mass of the right-angled triangle with vertices at (0,0), (5.1,0), and (5.1,3.5) units and uniform thickness is 1.75 units.

The center of mаss is the point аt which the object is perfectly bаlаnced. The center of mаss of а triаngle is found in а strаightforwаrd mаnner.

To calculate the center of mass, we can use the formula:

ycm = (A1*y1 + A2*y2 + A3*y3) / (A1 + A2 + A3)

where A1, A2 and A3 are the areas of the three triangles created by the vertices, and y1, y2 and y3 are the y-coordinates of the vertices.

In this case, we have the areas of the three triangles created by the vertices:

A1 = 0.5 * 5.1 * 3.5 = 8.675

A2 = 0.5 * 5.1 * 3.5 = 8.675

A3 = 0.5 * 3.5 * 3.5 = 6.125

The y-coordinates of the vertices are

y1 = 0

y2 = 0

y3 = 3.5

Substituting these values into the formula, we get:

ycm = (8.675*0 + 8.675*0 + 6.125*3.5) / (8.675 + 8.675 + 6.125)

= 1.75 units

Thus, the y-coordinate of its center of mass is 1.75 units.

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The electron's speed force is 2.39 x 105 metres per second.

The electron is moving at a speed of around 2,200 kilometres per second, according to a computation. The Earth can be round in just over 18 seconds at that speed, which is less than 1% of the speed of light.

The following equation describes the force acting on a charged particle travelling in a magnetic field:

F = q v B

where F is the force, q is the particle's charge, v is its speed, and B is the intensity of the magnetic field.

v = F / (q B)

Substituting the values given, we get:

[tex]v = (8.9 x 10^-15 N) / (-1.602 x 10^-19 C)(0.23 T)[/tex]

[tex]v = -2.39 x 10^5 m/s[/tex]

The electron is travelling against the magnetic field, as seen by the electron's sign being negative.

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It takes approximately 7.7 seconds for the ball to reach you from your friend who is 60 meters away from you. This is calculated by using the formula v=u+at, where v is the final velocity, u is the initial velocity and t is the time taken for the ball to reach you.

Here, the final velocity is 0 m/s, the initial velocity is 17 m/s and the acceleration due to the grass is -1.0 m/s2. By substituting these values in the formula, we get t=v-u/a. After solving the equation, we get t=17-(-1)/1=7.7 seconds. This is the time taken for the ball to reach you from your friend who is 60 meters away.

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The value of the charge that experiences a force of 2.4 × 10–3 N in an electric field of 6.8 × 10–5 N/C is 3.5 x 101 c

The force (F) experienced by a charged particle in an electric field (E) is given by the equation:

F = qE

Where q is the charge of the particle.

In this problem, we are given the force (F) and the electric field (E), and we need to find the value of the charge (q).

Substituting the given values into the equation, we get:

2.4 × 10–3 N = q × 6.8 × 10–5 N/C

Solving for q, we get:

q = (2.4 × 10–3 N) / (6.8 × 10–5 N/C)

q = 3.529 × 10–2 C

Therefore, the value of the charge that experiences a force of 2.4 × 10–3 N in an electric field of 6.8 × 10–5 N/C is 3.529 × 10–2 C.

The closest answer option is (d) 3.5 x 101 c, which is approximately equal to 3.529 × 10–2 C.

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The rock is 20.71 m above the ground if  the gravitational potential energy of a 34.5-kg rock is 671 j relative to a value of zero on the ground.

The gravitational potential energy of a 34.5-kg rock is 671 J relative to a value of zero on the ground.

This means that the rock is 671 J higher than it would be if it were on the ground.

To calculate the height of the rock above the ground, we need to use the formula for gravitational potential energy: G(PE) = mgh,

where m is the mass of the rock (34.5 kg),

g is the acceleration due to gravity (9.81 m/s²), and

h is the height of the rock.

Therefore, the height of the rock above the ground can be calculated by rearranging the equation to get

h = G(PE)/(mg) = 671 j/(34.5 kg × 9.81 m/s²) = 20.71 m.

Therefore, the rock is 20.71 m above the ground.

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The capacitance of the homemade capacitor is approximately [tex]4.33 * 10^-^8[/tex]Farads.

Capacitance is the term used to describe a capacitor's capacity to hold charges. Pairs of opposing charges are held apart in capacitors to retain energy. A parallel plate capacitor has the most basic construction and is made up of two metal plates with a space in between them.

The capacitance of a parallel-plate capacitor is given by the formula:

C = εA/d

Where C is the capacitance, ε is the permittivity of free space, A is the area of each plate, and d is the distance between the plates.

In this case, the area of each plate is 35 cm * 35 cm = 1225 cm^2. However, we need to convert this to square meters to use the formula.

[tex]1 cm^2 = 1 * 10^-4 m^2[/tex]

Therefore, [tex]1225 cm^2 = 0.1225 m^2[/tex]

The distance between the plates is given as 0.25 mm. We need to convert this to meters as well:

[tex]1 mm = 1 * 10^-3 m[/tex]

Therefore, 0.25 mm = 0.00025 m

The permittivity of free space is approximately [tex]8.85 * 10^-^1^2 F/m.[/tex]

Now we can use the formula to calculate the capacitance:

[tex]C = εA/d = (8.85 * 10^-12 F/m) * 0.1225 m^2 / 0.00025 m[/tex]

[tex]C = 4.33 * 10^-^8 F[/tex]

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a) To find the moment of inertia of the system about an axis perpendicular to the rod and passing through the center of the rod, we can use the parallel axis theorem. The moment of inertia of the rod about an axis perpendicular to it and passing through its center is (1/12)ML^2, and the moment of inertia of each small block about an axis passing through its center and perpendicular to it is (1/12)ma^2, where a is the length of each block.

Using the parallel axis theorem, the moment of inertia of each block about an axis passing through one end of the rod is (1/12)ma^2 + (1/4)m(L/2)^2 = (1/12)m(a^2 + L^2/16), since the distance between the axis passing through the center of the rod and the axis passing through one end of the rod is L/4.

There are two blocks, one at each end of the rod, so their combined moment of inertia about an axis passing through one end of the rod is (2/12)m(a^2 + L^2/16) = (1/6)m(a^2 + L^2/16).

The moment of inertia of the rod about an axis passing through one end of the rod is (1/3)ML^2. Therefore, the moment of inertia of the entire system about an axis passing through one end of the rod is:

I = (1/6)m(a^2 + L^2/16) + (1/3)ML^2

b) To find the moment of inertia of the system about an axis perpendicular to the rod and passing through a point one-fourth of the length from one end, we can again use the parallel axis theorem.

The distance between the new axis and the axis passing through the center of the rod is L/4, and the distance between the new axis and the axis passing through one end of the rod is L/2 - L/4 = L/4.

The moment of inertia of the rod about the new axis is (1/12)ML^2 + (1/4)M(L/4)^2 = (7/192)ML^2.

The moment of inertia of each block about the new axis is (1/12)ma^2 + (1/4)m(L/4)^2 = (1/12)m(a^2 + L^2/16).

Again, there are two blocks, so their combined moment of inertia about the new axis is (2/12)m(a^2 + L^2/16) = (1/6)m(a^2 + L^2/16).

Therefore, the moment of inertia of the entire system about the new axis is:

I = (1/6)m(a^2 + L^2/16) + (7/192)ML^2

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