how long will be required for a car to go from a speed of 20.0 m/s to a speed of 25.0 m/s if the acceleration is 3.0 m/s2?

Her average speed was about 4.6 km/hr, and her average velocity was about 3.3 km/hr.

The entire distance travelled divided by the total time taken is the definition of average speed. In this case, the total distance travelled was 7.0 km, and the total time taken was 1.5 hours. Hence, the average speed can be determined as follows:

Average Speed = [tex]\frac{7.0 km }{ 1.5 \ hours }= 4.6 km/hr[/tex]

The displacement divided by the whole time travelled is the average velocity. In this case, the displacement was 3.0 km (from Mary's home to Sheila's home), and the total time taken was 1.5 hours.The average velocity can therefore be determined as follows:

Average Velocity = [tex]\frac{3.0 km }{1.5 \ hours} = 3.3 km/hr[/tex]

Therefore,Her average velocity was roughly 3.3 km/hr, and her average speed was roughly 4.6 km/hr.

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The answer is A. PE becomes part of American school curriculum.

Title IX, which forbids gender discrimination in sports, was enacted in 1972.

The YMCA opened its first gym in America in Boston in 1851.

The adjustable plate-loaded barbell was invented in the late 1940s by a man named George Snyder.

Physical Education (PE) has been a part of American school curriculums for well over a century, with the first school gymnasiums being built in the 1800s.

What is an american school curriculum?

The American school curriculum is the set of educational standards and guidelines used by schools in the United States to structure their academic programs. The curriculum typically includes courses in core academic subjects such as English, math, science, and social studies, as well as elective courses in areas such as the arts, foreign languages, and physical education.

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The initial velocity of the car is 26.9 m/s [S], and the final velocity is 0 m/s [S]. The time taken for the car to come to a stop is 2.61 s. Using the formula:

acceleration = (final velocity - initial velocity) / time

we can find the car's acceleration:

acceleration = (0 m/s - 26.9 m/s) / 2.61 s

acceleration = -10.305 m/s^2

The negative sign indicates that the car is decelerating, or slowing down.

To calculate the force acting on the car during the deceleration, we can use Newton's second law:

force = mass x acceleration

force = (1.18 × 10^3 kg) x (-10.305 m/s^2)

force = -12,166.1 N

The force acting on the car during deceleration is -12,166.1 N, or approximately 12.2 kN.

Answer:

- 0.33 m/s

Explanation:

An illustration is shown above,

In this case, since the two objects move in opposite directions before collision, then move together, the formula to be used is,

m1u1 - m2u2 = (m1 + m2)v

Where,

m1 = mass of the first object

u1 = initial velocity of the first object

v1 = final velocity of the first object

m2 = mass of the second object

u2 = initial velocity of the second object

v2 = final velocity of the second object

Therefore,

(4.0 • 3.0) - (8.0 • 2.0) = (4.0 + 8.0)v

12 - 16 = 12v

-4 = 12v

Divide both sides by 12,

-4 / 12 = 12v / 12

-1 / 3 = v

v = -0.33 m/s

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To solve this problem, we can use the conservation of mechanical energy principle. When the blocks are released from rest, the potential energy of the system is converted to kinetic energy. Since the surface is frictionless, the mechanical energy of the system is conserved.

Using the principle of mechanical energy conservation, we can write:

m1*g*h = (m1+m2)*v^2/2

where m1 is the mass of the first block, m2 is the mass of the second block, g is the acceleration due to gravity, h is the height that the second block falls, and v is the velocity of the system after the blocks have moved a distance x.

The displacement of the first block can be found by using the time it takes the system to reach this velocity. The time t can be found using the formula:

x = (1/2) * a * t^2

where a is the acceleration of the first block.

The acceleration of the first block is equal to the acceleration of the system, which can be found by using the equation:

m1*a = m2*g - m1*g

Substituting the value of a in the previous formula, we get:

x = (1/2) * (m2*g - m1*g) * t^2 / m1

Substituting the values we get:

x = (1/2) * (2.0 kg * 9.81 m/s^2 - 3.0 kg * 9.81 m/s^2) * (1.2 s)^2 / 3.0 kg

x ≈ 7.6 m

Therefore, the correct answer is D) 7.6 m.

Answer:  a stretch of 2

Explanation: because it 2 (x) - 3

Answer:

Explanation:

The torque is given by the formula:

τ = F × r × sin(θ)

where τ is the torque, F is the force applied, r is the distance between the force and the pivot point, and θ is the angle between the force and the lever arm.

In this case, the person's weight is the force being applied, and it can be calculated as:

F = m × g

where m is the mass of the person and g is the acceleration due to gravity (9.81 m/s^2).

F = 65 kg × 9.81 m/s^2 = 637.65 N

The distance between the person and the pivot point is 1.5 m, so r = 1.5 m.

The angle between the person's weight and the lever arm is 90 degrees, so sin(θ) = 1.

Therefore, the torque the person is exerting on the board is:

τ = F × r × sin(θ) = 637.65 N × 1.5 m × 1 = 956.475 N·m

So the person is exerting a torque of 956.475 N·m on the diving board with respect to the pivot point.

The magnitude of the total momentum of the two cars is 68,245.5  kg m/s.

To calculate the total momentum of the two cars, we need to first calculate the momentum of each car and then add them together.

The momentum of an object is given by the product of its mass and velocity. So, the momentum of each car can be calculated as:

p = m x v

where;

Since both cars have the same mass, their momenta will be equal if they have the same velocity. In this case, both cars are traveling at the same speed of 35.7 m/s.

The momentum of car 1 can be calculated by resolving its velocity into horizontal and vertical components:

vx1 = v1 cos(60°) = 0.5 x 35.7 = 17.85 m/s

vy1 = v1 sin(60°) = 0.866 x 35.7 = 30.97 m/s

The momentum of car 1 is then:

p₁ = m x v₁ = 1350 x √(vx₁² + vy₁²)

p₁ = 1350 x √(17.85² + 30.97²)

p₁ = 48,256.85  kg m/s

Similarly, the momentum of car 2 can be calculated by resolving its velocity into horizontal and vertical components:

vx2 = v2 cos(30°) = 0.866 x 35.7 = 30.97 m/s

vy2 = v2 sin(30°) = 0.5 x 35.7 = 17.85 m/s

The momentum of car 2 is then:

p₂ = m x v₂ = 1350 x √(vx₂² + vy₂²)

p₂ = 1350 x √(30.97² + 17.85²)

p₂ = 48,256.85  kg m/s

The total momentum of the two cars is the vector sum of their momenta, which can be calculated using the Pythagorean theorem:

ptotal = √(p₁² + p₂²)

= √((48,256.85  )² + (48,256.85²) = 68,245.5  kg m/s

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Answer:

Wavelength will decrease but frequency will stay the same.

Explanation:

The higher the frequency, the shorter the wavelength. The relationship between wavelength and frequency is called an inverse relationship, because as the frequency increases, the wavelength decreases.

However, the frequency usually remains the same because it is like a driven oscillation and maintains the frequency of the original source. If v changes and f remains the same, then the wavelength λ λ must change. Since v = f λ v = f λ , the higher the speed of a sound, the greater its wavelength for a given frequency.

Answer:

0.625 meters

Explanation:

We can use the work-energy that the work done on an object is equal to the change in its kinetic energy:

Work = ΔK = Kf - Ki

Where:

Work is the work done on the object

ΔK is the change in kinetic energy of the object

Kf is the final kinetic energy of the object

Ki is the initial kinetic energy of the object (which is zero since the object is at rest)

The work done on the object is equal to the force applied to the object multiplied by the distance over which the force is applied:

Work = F × d

Where:

F is the force applied to the object (50 N)

d is the distance over which the force is applied (unknown)

So we can write:

F × d = Kf - Ki

Substituting the given values:

50 N × d = 1/2 × 10 kg × (2.5 m/s)^2 - 0

Simplifying:

50 N × d = 31.25 J

Solving for d:

d = 31.25 J / 50 N = 0.625 m

Therefore, the object was moved a distance of 0.625 meters.

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Answer: When a disrupted part of the ecosystem is left alone so that nature can help restore itself what people are counting on happening is secondary succession

Explanation:

It takes 0.1311 seconds to hear the echo of the stone.

First we need to determine the time it takes for the sound wave to travel from the stone to the bottom of the mine shaft and back up to our ears.

Let's start by finding the time it takes for the sound wave to reach the bottom of the mine shaft. We can use the formula:

time = distance / speed

The distance is the depth of the mine shaft, which is 15 meters. The speed of sound is 343 m/s, as given in the problem. Therefore, the time it takes for the sound wave to reach the bottom of the mine shaft is:

time = 15 m / 343 m/s

time = 0.0437 s

Now, we need to find the time it takes for the sound wave to travel back up to our ears. Since the sound wave travels at the same speed, 343 m/s, the distance it needs to cover is twice the depth of the mine shaft, or 30 meters. Therefore, the time it takes for the sound wave to travel back up to our ears is:

time = 30 m / 343 m/s

time = 0.0874 s

Finally, to find the total time it takes to hear the echo, we add the time it takes for the sound wave to reach the bottom of the mine shaft to the time it takes to travel back up to our ears:

total time = 0.0437 s + 0.0874 s

total time = 0.1311 s

Therefore, it takes 0.1311 seconds to hear the echo of the stone.

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Explanation:

I'm sorry, but the statement you provided is incorrect. There is no such thing as Newton's 4th law. Newton's laws of motion consist of three laws, which are:

An object at rest tends to stay at rest, and an object in motion tends to stay in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

The acceleration of an object is directly proportional to the force applied to it and inversely proportional to its mass.

For every action, there is an equal and opposite reaction.

None of these laws state that action and reaction never start from the same point. However, it is true that the action and reaction forces act on different objects, not necessarily at the same point. This is because Newton's third law states that every action has an equal and opposite reaction, which means that when one object exerts a force on another object, the second object exerts an equal and opposite force back on the first object.

Answer:

Explanation:

Assuming negligible air resistance, the horizontal velocity of the shingle will remain constant and the vertical motion will be influenced by gravity.

We can use the kinematic equations of motion to determine the horizontal distance traveled by the shingle. The relevant equation is:

d = v * t

where d is the distance, v is the initial horizontal velocity, and t is the time of flight.

To find the time of flight, we can use the equation for the vertical displacement of an object under constant acceleration:

y = v0t + (1/2)at^2

where y is the vertical displacement, v0 is the initial vertical velocity (which is zero), a is the acceleration due to gravity (-9.8 m/s^2), and t is the time of flight. Solving for t, we get:

t = sqrt((2y)/a)

where sqrt means square root.

Substituting the given values, we have:

y = 9.4 m

a = -9.8 m/s^2

t = sqrt((2*9.4 m) / -9.8 m/s^2) = 1.45 s (using the positive root since time cannot be negative)

Now, we can use the horizontal velocity to find the distance traveled in this time:

d = v * t = 7.2 m/s * 1.45 s = 10.44 m

Therefore, the shingle moves a horizontal distance of 10.44 meters in this time.

A block of 0.5 kg is placed on top of another wooden block which weighs 1.0 kg. The coefficient of static friction between the two blocks is 0.35, whereas the coefficient of kinetic friction between the lower block and the level table is 0.20.

To calculate the maximum horizontal force that can be applied to the lower block, we need to determine the limiting frictional force between the two blocks.

Since the upper block is not moving, the force of static friction is acting on it. We can calculate this force as follows:

`F_static = friction coefficient * normal force`

where, normal force = weight of upper block = 0.5 kg * 9.81 m/s^2 = 4.905 N

`F_static = 0.35 * 4.905 = 1.718 N`

Therefore, the static frictional force acting on the upper block is 1.718 N.

Now, we need to find the maximum force that can be applied to the lower block before it starts moving. This force is equal to the force of static friction acting on the lower block.

Since the upper block is not moving, the force of static friction acting on the lower block is equal to the force of static friction acting on the upper block.

`F_static(lower block) = F_static(upper block) = 1.718 N`

This means that the maximum horizontal force that can be applied to the lower block is 1.718 N.

However, if the applied force exceeds this value, the lower block will start moving and the force of kinetic friction will be acting on it, which is equal to:

`F_kinetic = friction coefficient * normal force`

`F_kinetic = 0.20 * 4.905 = 0.981 N`

Hence, if the applied force exceeds 1.718 N, the lower block will start moving and the force of kinetic friction will act on it, which is 0.981 N.

Therefore, the maximum horizontal force that can be applied to the lower block is 1.718 N.

Answer:

Explanation:

To determine the maximum horizontal force that can be applied to the lower block without causing the blocks to move, we need to calculate the maximum static friction force between the two blocks. This force is given by:

F_friction = coefficient of static friction * normal force

where the normal force is the force perpendicular to the surface of contact between the blocks. Since the blocks are resting on a level table, the normal force acting on the lower block is equal to the weight of both blocks, which is:

N = (m1 + m2) * g

where m1 is the mass of the lower block, m2 is the mass of the upper block, and g is the acceleration due to gravity (9.81 m/s^2).

Plugging in the given values, we have:

N = (1.0 kg + 0.5 kg) * 9.81 m/s^2 = 14.715 N

The maximum static friction force is then:

F_friction = 0.35 * 14.715 N = 5.15025 N

Therefore, the maximum horizontal force that can be applied to the lower block without causing the blocks to move is 5.15025 N. If a greater force is applied, the blocks will start to move and the kinetic friction force will take effect, which is given by:

F_kinetic = coefficient of kinetic friction * normal force

where the coefficient of kinetic friction is 0.20 in this case.

Answer:

2) 42.6

3) 1500000 m

4) no he will not be late, it will take 3s

Explanation:

 #2:

Formula for average velocity:
 ⇒  [tex]v=\frac{d}{t}[/tex]

Substitute

 ⇒ [tex]\frac{2560}{60}[/tex]

⇒ [tex]42.6[/tex]

#3:

1st convert 60km to m/s (correct si unit must always come first)

to convert kilometer to meter, multiply by 1000 (prefix 'kilo' = 1000)

60 km x 1000 = 60000 m

use the formula for speed, distance, & time

60000 = d/25

to find displacement just multiply the speed and time together

60000 x 25

1500000m is the displacement

#4:

s = d/t

given are displacement and speed/velocity

d = 25m

v = 8.5 m/s

to find the time just divide displacement by speed

8.5 = 25/t

25/8.5

≈ 3 seconds

so he will not be late for class.

Answer:

It depends on how they are made.

Explanation:

Rubber balloons are not always spherical in shape. When filled with air, the inflation forms a balance between the balloon material, including its shape and thickness and its elasticity and the pressure of the air. That’s what determines its shape. Although a sphere is often the shape, it could be tubular, offset, and most other shapes.

So the change in energy of the box after being pulled by Liam over 19 m is 323 J.

Energy is capable of changing its forms. For instance, electrical energy transforms into thermal and light energy when a lightbulb is turned on. A automobile transforms the gasoline's molecular bonds' stored energy into a variety of other forms. Chemical energy is converted to light in the engine through a chemical reaction.

The work done on the box by Liam's force is:

work = force x distance x cos(theta)

where theta is the angle between the force and the direction of motion. Since the force is horizontal and the motion is also horizontal, theta is 0 degrees and cos(theta) is 1. Therefore, the work done on the box is:

work = 17 N x 19 m x 1 = 323 J

The change in energy of the box is equal to the work done on it, according to the work-energy principle. Therefore, the change in energy of the box is:

change in energy = work = 323 J

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The spring scale read just before the mass touches the lower spring is 80.36N, the spring constant for the lower spring is 2765N/m and at 2.9cm length the scale will read zero.

Given the mass of spring = 8.2kg

The force exerted for compressing of spring = 14N

The compression in spring = 2.4cm = 0.024m

(A.) Initially the spring scale reads only the weight of the mass = mg

W = 8.2 * 9.8 = 80.36N

(B) Let the value of spring constant = k

The net force exerted so that the scale reads(F') = 80.36N - 14 = 66.36N

We know that according to Hooke's law the force exerted on spring F = kx such that:

F' = kx then:

66.36 = k * 0.024

k = 66.36/0.024 = 2765N/m

(C) the compression where scale reads zero = x'

The scale reads zero when the restoring force equals to the weight of the mass then the scale reads zero such that:

x' = 80.36/2765 = 0.029m = 2.9cm

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Answer:

The period of a ticker-timer is the time interval between two consecutive dots made by the ticker.

If the frequency of the ticker-timer is 25 Hz, then it makes 25 dots in one second. Therefore, the period of the ticker-timer can be calculated as:

Period = 1/frequency = 1/25 Hz = 0.04 seconds

If the frequency of the ticker-timer is 50 Hz, then it makes 50 dots in one second. Therefore, the period of the ticker-timer can be calculated as:

Period = 1/frequency = 1/50 Hz = 0.02 seconds

So, the period of the ticker-timer is 0.04 seconds for a frequency of 25 Hz and 0.02 seconds for a frequency of 50 Hz

Explanation:

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The initial mass of the rocket was 106 kg.

We can use the principle of conservation of momentum to solve this problem.

The momentum of the rocket before takeoff is zero, since it is at rest, and the momentum after takeoff is the product of the mass of the rocket and its velocity.

However, during the takeoff, the rocket ejects a mass of fuel at a certain velocity, which creates a backward force (thrust) that propels the rocket forward.

This thrust can be calculated using the equation:

Thrust = (mass flow rate) x (exhaust velocity)

mass flow rate = (mass of fuel burned) / (burn time)

The mass of the rocket at any given time can be calculated using the equation:

mass = (initial mass) - (mass of fuel burned)

Using these equations, we can solve for the initial mass of the rocket:

Calculate the thrust:

Thrust = (118 kg / 10.0 s) x 1600 m/s = 1,888 N

Calculate the mass of the rocket at the end of the burn:

mass(end) = (initial mass) - (mass of fuel burned) = (initial mass) - 118 kg

Use the principle of conservation of momentum to find the initial mass:

momentum before = momentum after

0 = (mass(end) + 118 kg) x 110 m/s

mass(end) = -118 kg / 110 m/s = -1.07 kg/s

mass(end) = (initial mass) - 118 kg

(initial mass) = mass(end) + 118 kg

(initial mass) = (-1.07 kg/s x 10.0 s) + 118 kg

(initial mass) = 106 kg

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Based on the results of the experiment, it can be concluded that the rate of flow of heat through different materials of the same thickness is different.

Here is an experimental plan to test the rate of flow of heat through different materials of the same thickness:

Materials:

Three blocks of different materials (e.g., metal, plastic, and wood)

Thermometer

Heat source (e.g., hot plate)

Stopwatch

Insulating material (e.g., foam)

Procedure:

Cut three blocks of the same thickness from each of the three materials.

Measure the initial temperature of each block using a thermometer.

Place the three blocks on a heat source (e.g., hot plate) with the same amount of heat and start the stopwatch.

Measure the temperature of each block every 30 seconds using the thermometer.

Record the temperature of each block at each time interval.

After 5 minutes, turn off the heat source and measure the final temperature of each block.

Calculate the temperature difference between the initial and final temperatures for each block.

Calculate the rate of heat flow for each block by dividing the temperature difference by the time interval.

Repeat the experiment at least three times for each block and take an average of the results.

Place each block on an insulating material (e.g., foam) and repeat the experiment to compare the effect of insulation on the rate of heat flow.

Data analysis:

Plot a graph of the rate of heat flow (y-axis) versus time (x-axis) for each block.

Compare the slopes of the graphs to determine the rate of heat flow for each block.

Compare the rates of heat flow for the three blocks to test the statement that the rate of flow of heat through different materials of the same thickness is different.

Compare the rates of heat flow for each block with and without insulation to determine the effect of insulation on the rate of heat flow.

Conclusion:

The rate of heat flow depends on the thermal conductivity of the material, which is a measure of how well a material conducts heat. Materials with higher thermal conductivity will have a higher rate of heat flow, while materials with lower thermal conductivity will have a lower rate of heat flow.

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Answer:

Most likely the answer is D;

Explanation:

Because they formed from the same molecular cloud.

Bucky definitely will live shorter. And we can detect Bucky faster due it's enormous rate of burring fuel.

Both of the stars will have the same heavy elements.

The two stars, Bucky and Badger are formed in the same giant molecular cloud. Among them Bucky has five solar mass, which is five times the solar mass of Badger.

As a result of the higher solar mass of Bucky, its fuel will burn up very faster than Badger. So, Bucky will have shorter life. Also it will spin faster and become a protostar in short time.

Since, both the stars, Bucky and Badger are formed in the same giant molecular cloud, both of them will have the same heavy elements.

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Answer : 0.00885 farads or 8.85 microfarads

Explanation: To calculate the capacitance required, we can use the following formula:

C = 1 / [2 * pi * f * ((V^2 - Vlamp^2)/P)]

where:

C = capacitance in farads (F)

pi = 3.14159...

f = frequency in hertz (Hz)

V = voltage in volts (V)

P = power in watts (W)

Vlamp = voltage of the lamp in volts (V)

Using the given values, we have:

C = 1 / [2 * pi * 60 * ((230^2 - 100^2)/750)]

C = 1 / [2 * 3.14159 * 60 * ((230^2 - 100^2)/750)]

C = 1 / [113.09724]

C = 0.00885 farads (F)

Therefore, the capacitance required is approximately 0.00885 farads or 8.85 microfarads.

Answer:

Isaac Newton, the English physicist, mathematician, and astronomer, discovered the concept of gravity in the late 17th century. The story of his discovery of gravity is one of the most famous in scientific history.

The most well-known anecdote is that Newton was sitting under an apple tree when an apple fell from the tree and hit him on the head. This event, however, is likely to be a myth created to make the story more memorable. Nonetheless, it is true that Newton began to wonder why objects fall to the ground instead of flying off into space.

Newton's curiosity led him to conduct experiments to understand the behavior of falling objects. He reasoned that the same force that caused an apple to fall to the ground was responsible for holding the moon in orbit around the Earth.

Newton's breakthrough came when he realized that the force that causes objects to fall to the ground is the same force that governs the motion of the planets in the solar system. He described this force as "gravity" and formulated his famous law of universal gravitation, which states that every object in the universe attracts every other object with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them.

Newton's discovery of gravity was a major scientific achievement that revolutionized our understanding of the physical world. It laid the foundation for the development of classical mechanics, and the law of gravitation has since been used to explain a wide range of phenomena in physics, from the motion of planets to the behavior of subatomic particles.

In summary, Newton discovered gravity through a process of curiosity, experimentation, and mathematical reasoning. Although the apple falling on his head is unlikely to be true, his discovery has had a profound impact on our understanding of the universe.

Answer:

Isaac Newton did not "discover" gravity, as it was already known that objects were attracted to each other. However, he did discover the law of universal gravitation, which states that every particle in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of their separation distance.

Answer:

Explanation:

a. Since the electrostatic force is attractive, the charges must have opposite signs.

b. Let's assume that charge A is positive and charge B is negative. Then, the electrostatic force would be given by:

F = (k * |qA| * |qB|) / r^2

where k is Coulomb's constant, r is the distance between the charges, and |qA| and |qB| are the magnitudes of the charges. Since the force is attractive, |qA| > |qB|.

c. From the given information, we know that:

F = 23.2 N

r = 2.3 cm = 0.023 m

Let |qB| = q, then |qA| = 4q. Substituting these values into the equation for the electrostatic force, we get:

23.2 = (k * 4q * q) / (0.023)^2

Solving for q, we get:

q = 3.38 x 10^-7 C

Then, |qA| = 4q = 1.35 x 10^-6 C.

d. Charge A has a value of 1.35 x 10^-6 C and charge B has a value of -3.38 x 10^-7 C.

The tension in the swing's chain at the instant shown in the image is 441.6 N.

option D

At the bottom of the swing, the girl is traveling at a constant speed, so her acceleration is zero. Therefore, the net force acting on her is also zero.

Thus, we have:

0 = T - mg - mv²/r

where;

At the bottom of the swing, the radius is equal to the length of the chain, so we have:

r = L = 4.0 m

Substituting the values we have:

T = (32 kg)(9.8 m/s²) + (32 kg)(4 m/s)²/4.0 m

Solving for T, we get:

T = (32 kg)(9.8 m/s²) + (32 kg)(4 m/s)²/4.0 m

T = 441.6 N.

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Downslope at 0.64 m/s², m = 12.4 kg

Upslope at 0.76 m/s², m = 6.35 kg

In Physics, mass is the most basic property of matter, and it is one of the fundamental quantities. Mass is defined as the amount of matter present in a body. The SI unit of mass is the kilogram (kg). The formula of mass can be written as:

Part A)

The sum of forces on the left-hand mass

T - mgsin(angle) = ma

T - (2.6) (9.8) (sin 70) = 2.6(.64)

T = 25.6 N

m = left mass.........M = right mass

T - mg×sin70 = ma

Mg×sin16 - T = Ma

Mg×sin16 - mg×sin70 = a×(M+m)

M×g×sin16 - mg×sin70 = Ma + ma

M× (g×sin16 -a) = m× (a + gsin70)

M = m× (a + gsin70) / (g×sin16 -a)

a) a = 0.64

M = 10.98 Kg

b) M = 11.82 kg

For the right-hand mass, the sum of forces...

mgsin(angle) - T = ma

m (9.8) (sin 16) - 25.6 = m (.64)

2.7m - 25.6 = .64m

m = 12.4 kg

Part B)

For the left-hand mass

mgsin(70) - T = ma

(2.6) (9.8) (sin 70) - T = (2.6) (.76)

T = 21.97 N

Then for the right-hand mass

T - mgsin(16) = ma

21.97 - m (9.8) (sin 16) = m (.76)

21.97 - 2.7m = .76m

m = 6.35 kg

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The right-hand mass should be 3.3 kg to accelerate up the slope at 0.76 m/s². To solve this problem, we need to use the principles of Newton's laws of motion and trigonometry.

We know that the force of gravity acting on the mass is equal to its weight, which can be calculated using the formula Fg = mg, where Fg is the force of gravity, m is the mass, and g is the acceleration due to gravity (which is approximately 9.8 m/s²).

To find the force acting down the slope, we need to calculate the component of the weight that acts down the slope, which is given by Fg sin θ, where θ is the angle of the slope. Using the given angle of 52°, we can calculate the force acting down the slope for the left-hand mass as:

Fdown = Fg sin θ

Fdown = (2.5 kg)(9.8 m/s²) sin 52°

Fdown = 18.9 N

To find the required mass for the right-hand mass to accelerate at 0.64 m/s^2 down the slope, we can use Newton's second law of motion, which states that the force acting on an object is equal to its mass times its acceleration (F = ma). Therefore, we can calculate the required force for the right-hand mass as:

F = ma

F = (m)(0.64 m/s²)

Since the force acting down the slope is 18.9 N, we can set these two equations equal to each other and solve for the mass:

F = Fdown

(m)(0.64 m/s²) = 18.9 N

m = 29.5 kg

Therefore, the right-hand mass should be 29.5 kg to accelerate down the slope at 0.64 m/s².

To find the required mass for the right-hand mass to accelerate at 0.76 m/s² up the slope, we can use the same approach, but this time we need to use the component of the weight that acts up the slope, which is given by Fg cos θ, where θ is the angle of the slope. Using the given angle of 25°, we can calculate the force acting up the slope for the right-hand mass as:

Fup = Fg cos θ

Fup = (m)(9.8 m/s²) cos 25°

Setting this equal to the force required for the right-hand mass to accelerate up the slope, we get:

Fup = ma

(m)(0.76 m/s²) = (m)(9.8 m/s²) cos 25°

m = 3.3 kg

Therefore, the right-hand mass should be 3.3 kg to accelerate up the slope at 0.76 m/s².

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(a) The smallest vertical magnetic field B that would cause the rod to

slide is 0.145 Tesla for given  The coefficient of static friction

between the rod and rails is μs= 0.60

A magnetic field is a vector field that describes the magnetic influence on moving charges, currents, and magnetic materials. A moving charge in a magnetic field is subjected to a force that is perpendicular to both its own velocity and the magnetic field.

(a) using formula

 μs × m × g = I × L × B

μs= 0.60

M= 1.2 kg

I = current =  55.0 A

L = Length = 0.9 m

magnetic field (B) =  0.145 Tesla

(b) expression

force (f) = I × L × B × sinФ

(c)  given B = 0.145 Tesla

 μs × m × g= I × L × B × sinФ

Ф = 90°

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Answer: increases

Explanation: