what is coulmbs law?

Therefore, the net electric force acting on particle 3 due to particle 1 and particle 2 is -1.38 x 10⁻⁵ N (repulsive).

Charge is a fundamental property of matter that describes how strongly an object interacts with electromagnetic fields, such as electric and magnetic fields. There are two types of charge: positive and negative. Like charges repel each other, while opposite charges attract each other. The SI unit of charge is the Coulomb (C). Charge is conserved, meaning that the total amount of charge in a closed system remains constant over time. Charge can be transferred between objects through various mechanisms, such as friction, conduction, and induction. The movement of charged particles, such as electrons or ions, is the basis for electric current and many other electrical phenomena. The study of electric charge and its effects is known as electrostatics.

Here,

To find the net electric force acting on particle 3 due to particle 1 and particle 2, we can use Coulomb's law, which states that the force between two charged particles is proportional to the product of their charges and inversely proportional to the square of the distance between them:

F = k * (q1 * q3 / r13²) + k * (q2 * q3 / r23²)

where F is the net electric force on particle 3, k is Coulomb's constant (9.0 x 10⁹ N m²/C²), q1, q2, and q3 are the charges of particles 1, 2, and 3, respectively, r13 and r23 are the distances between particles 1 and 3, and particles 2 and 3, respectively.

To find the distances between the particles, we can use the fact that the triangle is equilateral and has sides of length 3.5 cm. By using trigonometry, we can find that the distances are:

r13 = r23 = 3.5 cm

Substituting the values into the equation, we get:

F = (9.0 x 10⁹ N m²/C²) * [(-8.3 nC) * (8.0 nC) / (0.035 m)² + (-16.6 nC) * (8.0 nC) / (0.035 m)²]

F = -1.38 x 10⁻⁵ N (repulsive)

The direction of this force can be found by considering the angles between the sides of the equilateral triangle and using vector addition. The direction is 120 degrees counterclockwise from the positive x-axis.

To know more about charge,

https://brainly.com/question/30163160

#SPJ9

The object's speed and direction after the force ends is 0 m/s to the right.

Applying the equation:

Δv = (F/ m) x Δt

where Δv = the change in velocity,

F_ =  is the force,

m i= the mass, and

Δt = the time interval over which the force is applied.

Δv = (2 N / 2 kg) x 0.5 s = 1 m/s

The force is applied in the opposite direction to the initial velocity, the final velocity will be:

v_final = v_initial - Δv = 1 m/s - 1 m/s = 0 m/s

We then can conclude that the object's speed and direction after the force ends is 0 m/s to the right.

Learn more about force  at: https://brainly.com/question/12970081

#SPJ1

Answer:

Below

Explanation:

Work = force * distance

   240 000 J  = force * 50 m

           240 000 / 50 = force = 4800 N

Therefore, the magnitudes of the cyclist's radial and tangential accelerations when his speed is 10 m/s are [tex]48.1 m/s^2 and -0.5 m/s^2[/tex]

What is the initial radial acceleration of the cyclist entering a curve of 30 m radius at a speed of 12 m/s?

where v is the speed of the cyclist and r is the radius of curvature. At the beginning of the curve, v = 12 m/s and r = 30 m, so the initial radial acceleration is:

ar = [tex]12^2 / 30 = 4.8 m/s^2[/tex]

The tangential acceleratiοn οf the cyclist is given by:

at = -a

where a is the deceleratiοn due tο braking. In this case, [tex]a = 0.5 m/s^2[/tex], sο the tangential acceleratiοn is:

[tex]at = -0.5 m/s^2[/tex]

As the cyclist slοws dοwn, the speed at any time t is given by:

v = v0 - at * t

where v0 is the initial speed. We want tο find the radial and tangential acceleratiοns when the speed is 10 m/s, sο we need tο sοlve fοr the time t when v = 10 m/s:

10 = 12 - 0.5 * t

t = (12 - 10) / 0.5 = 4 s

Nοw we can use the time t tο calculate the radius οf curvature at the new speed:

[tex]r = v^2 / ar = 10^2 / 4.8 = 20.8 m[/tex]

The radial acceleratiοn at this speed is:

[tex]ar = v^2 / r = 10^2 / 20.8 = 48.1 m/s^2[/tex]

Therefοre, the magnitudes οf the cyclist's radial and tangential acceleratiοns when his speed is 10 m/s are 48.1 m/s^2 and -0.5 m/s^2, respectively.

To learn more about acceleration follow the given link: https://brainly.com/question/460763

#SPJ1

Answer:

Explanation:

The size of each push determines the magnitude of the force applied on the car. The force of friction on the car is the resistance force that opposes the motion of the car and it depends on the nature of the surface in contact and the weight of the car. The force of friction is equal and opposite to the force applied on the car, as per Newton's third law of motion.

If the magnitude of the net force on the car is greater than the force of friction, the car will accelerate in the direction of the net force. If the magnitude of the net force is equal to the force of friction, the car will move at a constant velocity. If the magnitude of the net force is less than the force of friction, the car will decelerate and eventually stop.

Therefore, the size of each push needs to be greater than the force of friction on the car to accelerate it. If the size of each push is equal to the force of friction, the car will not accelerate, and if the size of each push is less than the force of friction, the car will decelerate.

Answer: 849.15NM/S

P= F'.V' ,

WHERE V' IS THE VELOCITY OF THE PROJECT OF THE OBJECT ON WHICH THE FORCE ACTS . THUS,

P= F'.V. = COSФ

P = (135N) (7.4M/S)COS31° = 849.15NM/S

Answer: The angular velocity of a car tire is 1 rad/s.

Definition: Angular velocity is the speed at which the angle between two bodies changes when an object rotates or revolves around an axis. This displacement is depicted in the image by the angle formed by a line on one body and a line on the other.

Answer:

Understanding what occurs at the various tectonic plate boundaries supports our understanding of the past and current movement of rocks at Earth's surface because the movement of the plates is responsible for shaping the planet's surface features, such as mountain ranges, ocean basins, and volcanoes. Different types of plate boundaries produce different geological features and events. For example, convergent plate boundaries, where two plates move towards each other, result in subduction zones, where one plate is forced beneath another, and can cause volcanic activity and earthquakes. Divergent plate boundaries, where two plates move away from each other, can cause seafloor spreading, mid-ocean ridges, and rift valleys. Transform plate boundaries, where two plates move past each other, can cause earthquakes. By studying the processes and features associated with these plate boundaries, scientists can gain insight into how the Earth's surface has changed over time and how it continues to change today.

Explanation:

The distance traveled by the rock at 3.5seconds is 392ft.

Distance moved by a body can be calculated by using the following formula:

Speed = distance/time

Acceleration = speed/time

According to this question, gravity causes a rock to accelerate downwards at a rate of 32 ft/sec/sec. The speed can be calculated as follows:

Speed = 32ftsec-² × 3.5sec

Speed = 112ft/sec

Distance moved = 112ft/sec × 3.5sec

Distance = 392ft

Learn more about distance at: https://brainly.com/question/13034462

#SPJ1

Answer: 2.858(m/s)

Explanation: F= mg→ m1= 4.0/9.8 = 0.408(kg)

m2= 8 /9.8 = 0.816(kg)

m1v1 = (m1+m2)v2→ v2= m1v1(m1+m2) = 0.408+3/(0.408+0.816)= 2.8589m/s)

Answer:

Tell me why you cried, and why you lied to me

Tell me why you cried, and why you lied to me

Well I gave you everything I had

But you left me sitting on my own

Did you have to treat me, oh, so bad

All I do is hang my head and moan

Tell me why you cried, and why

Explanation:

Answer:

If the wavelength is 2.5 meters, each node will be half a wavelength apart from each other. Therefore, each node will be 1.25 meters apart.

Explanation:

The distance between nodes of a standing wave is equal to half the wavelength of the wave. This is because nodes are points along the wave where there is zero amplitude or displacement, and they occur at fixed intervals that are determined by the wavelength of the wave. Therefore, the distance between nodes is directly proportional to the wavelength of the wave.

Assertion (A): The internal resistance of a cell is constant. Reason (R): Ionic concentration of the electrolyte remains same during use of a cell.​

Both Assertion (A) and Reason (R) are incorrect.

Internal Resistance refers to the opposition in the flow of current which is offered by the cell itself.

The internal resistance of a cell is not constant and can vary depending on many factors such as the age of the cell, the temperature, and the amount of current being drawn from the cell.

The internal resistance tends to increase,  as the cell ages which can lead to a decrease in its performance.

In the same manner , the ionic concentration of the electrolyte in a cell can change during use due to the migration of ions between the electrodes and the electrolyte.

Learn more about internal resistance at:

https://brainly.com/question/30531136

#SPJ1

When the gas in a swim freshwater lake allows its density to match that of the water around it, the fish is said to be in water level (Pflugrath et al., 2012). The maximal neutral buoyant depth (MNBD) is a limit below which fish will have become lot of negative if they swim. Your overall dive depth should be roughly being one your neutral buoyancy depth, but not less than ten metres (32ft).

Hence, as a solid item is embedded in a liquid, its volume increases, more fluid weight is displaced, increasing the hydrostatic pressure. The buoyant force is at its greatest when a solid item is fully submerged in a fluid.

The formula B = V g, where and V are indeed the entity's volume and capacity, correspondingly, and g is the velocity brought on by gravity, is used to calculate the buoyancy required for just an object. 1000 kg/m3 is the density of water. Thus, the required force is 1000 kg/m3 times 1 L times 9.81 m/s2 equals 9.81 N.

To know more about Freshwater Lake click here .

brainly.com/question/858802

#SPJ1

Answer:

17. A

18. C

Explanation:

np:) and have a wonderful day

From the nodal analysis, the value of V1 = -3V and the value of I1 = 2A. Voltage, current, and resistance-related versions of Ohm's law exist in three different forms.

A super-node is a concept that can be utilized to solve a circuit in circuit theory. This is accomplished by treating a voltage source on a wire as a point source voltage in comparison to other point voltages present at different nodes in the circuit, relative to a ground node given a charge of zero or negative.

In a network of data communication, a node is a point of intersection or connection. These devices are all referred to as nodes in a networked environment where every device is reachable. Depending on the kind of network it relates to, each node has a different definition.

Applying nodal analysis,

[tex]3+\frac{V1}{3} +\frac{V1}{3} +\frac{V1+2}{1} =0[/tex]

[tex]3+\frac{V1}{3} +\frac{V1}{3} +V1+2=0[/tex]

[tex]\frac{V1+V1+3V1}{3} =-5[/tex]

[tex]\frac{5V1}{3} =-5[/tex]

[tex]V1=-3V[/tex]

Applying again nodal analysis,

[tex]I1+\frac{V1}{3} +\frac{V1+2}{1} =0[/tex]

[tex]I1+\frac{-3}{3} +\frac{-3+2}{1} =0[/tex]

[tex]I1=2A[/tex]

To know more about the nodal analysis visit:

brainly.com/question/26099417

#SPJ1

Constraints:

Limited space on the unmanned spacecraft for carrying food supplies.

The food must be durable enough to withstand the harsh conditions of space travel and long-term storage on Mars.

Criteria:

Nutritional value: The food must provide adequate nutrition to support the physical and mental health of astronauts during their mission on Mars.

Taste and variety: The food should be appetizing and varied to help maintain astronauts' morale and well-being during their extended stay on Mars.

Cost-effectiveness: Unmanned spacecraft are generally less expensive to build, launch, and operate than manned spacecraft. This is because they do not require life support systems, crew accommodations, or other specialized equipment needed to sustain human life in space.

Safety: Sending unmanned spacecraft eliminates the risks associated with human spaceflight, such as exposure to radiation, accidents, and medical emergencies.

Scientific research: Unmanned spacecraft can be designed to carry a variety of scientific instruments and sensors to collect data and perform experiments in space, without the limitations of human endurance and safety.

Learn more on NASA here: https://brainly.com/question/26560423

#SPJ1

Answer: 0.5J

Explanation:

We can use the formula for the potential energy stored in a spring:

U = (1/2) k x^2

where U is the potential energy, k is the spring constant, and x is the displacement from the equilibrium position.

Since we want to compress the spring, x will be negative, and we need to find the potential energy change between the uncompressed length and a compression of 10 cm:

U = (1/2) k (0.1 m)^2 - (1/2) k (0 m)^2

U = (1/2) (100 N/m) (0.1 m)^2 - (1/2) (100 N/m) (0 m)^2

U = 0.5 J

So the work required to compress the spring from its uncompressed length to x = 10 cm is 0.5 J.

The amount of work required by the spring to compress it from its uncompressed length (x = 0) to x = 10 cm is 0.5 J.

In order to compress a spring, the following formula must be used:

Work is equal to (1/2)*k*(xf² - xi²)

where:

xi = starting position = 0 m

xf = final position = 10 cm = 0.1 m k = spring constant = 100 N/m

By entering these values, we obtain:

W = (1/2) * 100 N/m * (0.1 m)² = 0.5 J

Hence, it takes 0.5 J of work to compress the spring from its uncompressed length to x = 10 cm (joules).

To learn more about work done by spring visit:

brainly.com/question/29392391

#SPJ1

The radius of curvature for the turn is 0.10 m. The time required for a bee to execute a 90 degree turn is 0.56 seconds.

Bumblebees are skilled aerialists and can fly with confidence around and through the leaves and stems of plants. They navigate obstacle-filled tracks by maintaining a reasonably constant centripetal acceleration of 4.0 m/s2 while turning right and left in level flight at a constant speed of 0.40 m/s.

The centripetal acceleration of a body moving in a circular path can be expressed as a = v^2 / r, where a is the centripetal acceleration, v is the speed of the body, and r is the radius of curvature.

Given that the bumblebees maintain a constant centripetal acceleration of 4.0 m/s^2 while turning, and their speed is 0.40 m/s, we can calculate the radius of curvature as:

r = v^2 / a = 0.40^2 / 4.0 = 0.04 m = 0.10 m (rounded to two significant figures)

To find the time required for a bee to execute a 90 degree turn, we need to know the distance it travels during the turn. Since the turn is a quarter of a circle, the distance traveled is a quarter of the circumference of the circle with a radius of 0.10 m, which is:

d = (πr)/2 = (3.14 x 0.10)/2 = 0.157 m

The time required to travel this distance at a constant speed of 0.40 m/s is:

t = d/v = 0.157 / 0.40 = 0.3925 s = 0.56 s (rounded to two significant figures)

Learn more about "centripetal acceleration" here:

https://brainly.com/question/14465119

#SPJ1

Answer:

Explanation:

When the free magnet is pushed toward the magnet that is taped down, it will be attracted to it and will move towards it.

The distance between the magnets when the free magnet first starts to be pulled will depend on the strength of the magnets and the orientation of their poles. Use the ruler to measure the distance between the magnets when the free magnet starts to be pulled.

When the magnets are positioned so that their north poles are facing each other, they will begin to repel each other when they are brought close enough. Measure the distance at which the magnets begin to repel each other using the ruler.

The table below shows the positions of the free magnet and the magnet that is taped down, as well as a description of what happens when the free magnet is released.

Position                   Description                                    Diagram

Position 1 The free magnet is placed directly above the magnet that is taped down. When released, the free magnet will stick to the taped down magnet with opposite poles attracting. N-S

Position 2 The free magnet is placed beside the taped down magnet with opposite poles facing each other. When released, the free magnet will move towards the taped down magnet and stick to it. N-S

Position 3 The free magnet is placed beside the taped down magnet with like poles facing each other. When released, the free magnet will move away from the taped down magnet due to repulsion. N-N or S-S

Position 4 The free magnet is placed directly beside the taped down magnet with like poles facing each other. When released, the free magnet will move away from the taped down magnet due to repulsion. N-N or S-S

5-12. Follow the steps to prepare and conduct the experiment using the pieces of tape.

a. Based on the observations in Steps 1-3, it can be concluded that magnetic force is present between two magnets with opposite poles attracting and like poles repelling each other. The strength of the force depends on the distance between the magnets and the orientation of their poles.

b. Part 1 of the Procedure and Data section provided evidence that magnetic fields exist because the magnets were able to exert a force on each other without direct contact. This suggests that there is an invisible force field surrounding the magnet that can interact with other magnetic objects.

c. To determine the size of the magnetic field around the magnet that is taped down, the experiment could be modified by placing the free magnet at different distances from the taped down magnet and measuring the strength of the force between them. This would allow for a better understanding of how the magnetic field changes with distance from the magnet.

d. In Part 2 of the Procedure and Data section, the pieces of tape affected each other due to the presence of electric fields. When the second piece of tape was brought close to the first, it caused a change in the electric field, which in turn caused a change in the behavior of the first piece of tape. Depending on the orientation of the electric fields, the pieces of tape could attract, repel, or have no effect on each other.

e. The experiment allowed evidence to be gathered that electric fields exist by observing the behavior of the pieces of tape when they were brought close to each other. The presence of a change in the behavior of the tape when the electric fields were affected suggests that there is an invisible force field surrounding the tape that can interact with other electrically charged objects.

The experiment demonstrates the principles of magnetism and electrostatics. By moving magnets or charged objects closer or further apart, the extent of the respective fields can be measured.

This experiment demonstrates the invisible forces of magnetism and electrostatics. In steps 1 to 3, the magnets attract each other when their opposite poles (north and south) face each other, and they repel when similar poles (north and north, or south and south) face each other. This distance at which attraction or repulsion starts represents the extent of the magnetic field. In steps 4 to 12, the experiment uses tape to illustrate electrostatic forces. When tape is peeled from a surface, it becomes statically charged. Two pieces of tape that have the same charge will repel each other while different charges attract. The distance at which this occurs represents the extent of the electric field. To measure the size of a magnetic field, you could use a device called a magnetometer or you could move a magnet towards a stationary magnet and measure the distance at which the moving magnet begins to move. These procedures provide evidence of the existence of invisible magnetic fields and electric fields.

https://brainly.com/question/35879848

#SPJ2

Answer:

The maximum density of water occurs at around 4° Celsius. The density of ice is less than liquid water, so it floats. Upon freezing, the ice density decreases by about 9%.

Explanation:

thanks for the question

A. batteries

Renewable energy sources like solar and wind power are often located in remote areas, far from where the energy is needed. This means that the energy must be transported over long distances to reach the end user, which can result in energy losses due to resistance in transmission lines. To address this issue, energy storage devices like batteries are needed to store excess energy generated by renewable sources during periods of low demand, and then release it when demand is high. However, current battery technology still needs improvement in terms of capacity, efficiency, and cost to make it more widely accessible and practical for large-scale renewable energy storage.

The most likely reason for Nathaniel needing fewer calories than his dad, even though they exercise about the same amount, is his age.

Age plays a significant role in determining person's daily calorie requirements. As people age, their body composition and metabolism change, and they tend to lose muscle mass and gain fat mass, which leads to decrease in their basal metabolic rate (BMR).

BMR is the amount of energy the body needs to carry out its essential functions while at rest. Therefore, even if Nathaniel and his dad have same activity level, Nathaniel's lower BMR due to his age would result in him needing fewer calories than his dad to maintain his weight. Other factors such as gender, activity level, and hunger may also contribute to differences in calorie requirements, but age is the most significant factor in this case.

To know more about exercise, refer

https://brainly.com/question/1365564

#SPJ1

The formula for calculating the cross-sectional area of a cylinder is:

A = πr^2

The intersection of a cylinder is the area of a shape found if the cylinder is cut perpendicular to its length. This will be a circle for a cylinder. The cross-sectional area of a cylinder is calculated as A = πr^2, where A is the cross-sectional area, is a mathematical constant approximately equal to 3.14, and r is the radius of the cylinder.

This formula computes the volume of a sphere of radius r, which is the cylinder's cross-sectional area. We can calculate various cylinder properties such as thickness, surface area, and so on by knowing the cross-sectional area.

Read more about the Cross-sectional area of a cylinder questions:

https://brainly.com/question/20884503

The formula for calculating the cross-sectional area of a cylinder is Area = πr^2 where 'r' is the radius of the cylinder. An example is provided where the radius is 5 units, yielding a cross-sectional area of 78.5 square units.

The cross-sectional area of a cylinder can be calculated using the formula for the area of a circle, because a cross-section of a cylinder is a circle. The formula is Area = πr^2, where 'r' is the radius of the cross-section.

For example, if you have a cylinder with a radius of 5 units, you would calculate the cross-sectional area as follows:

So, the cross-sectional area of this cylinder is 78.5 square units.

https://brainly.com/question/31821399

#SPJ2

Answer:

the unit of m×g×h×10 is no 3

The new rate of rotation for the ship would be: 814 rotations/hour.

A space station is described as a spacecraft capable of supporting a human crew in orbit for an extended period of time.

The normal force experienced by an object is:

N = mg,

N = (69.8 kg)(6.4 N/kg) = 446.72 N.

The normal force experienced by an occupant :

N = mω^2r,

We then  solve for ω,

ω^2 = N/mr

ω = √(N/mr)

ω = √((446.72 N)/(69.8 kg)(684 m))

ω = 0.127 radians/second

We then convert this to rotations per hour:

ω/(2π) rotations/second x 3600 seconds/hour = 814 rotations/hour

Learn more about space stations at: https://brainly.com/question/457589

#SPJ1

The answers to the questions about cells and their functions along with structure are given below.

A cell is the basic unit of life. It is a small, self-contained structure that carries out all of the processes necessary for an organism to survive and function. Cells can be found in all living organisms, and they come in a wide variety of shapes, sizes, and functions.

Learn more about cells here https://brainly.com/question/3717876

#SPJ1

According to the question the caboose travels 7 m after the brakes are applied.

Caboose is a term used to describe the last car in a freight train. It is typically designed to house a crew of railroad personnel, such as a conductor, a flagman, and a brakeman. The purpose of the caboose is to provide a safe place for the crew to observe the train and to signal any errors or problems to the engineer. The caboose also serves as a living and working space for the crew, providing a bed, cooking facilities, and a desk. The signalman in the caboose communicates with the engineer by means of a lamp or radio. The caboose also serves as a weight to help slow the train when necessary.

The work done (350,000 J) is equal to the force applied (70,000 N) multiplied by the distance traveled (x). Therefore, x = 350,000 J / 70,000 N = 5 m. Since the caboose has to travel a distance of 7 m to come to a complete stop, the answer is D. 7 m.

To learn more about caboose

https://brainly.com/question/15417833

#SPJ1

The motor must deliver a torque of 0.00180 N·m to accelerate the turntable from rest to 3.49 rad/s in 2.20 revolutions.

We can use the rotational kinetic energy equation to find the torque required to accelerate the turntable from rest to a final angular velocity of 3.49 rad/s:

KE = (1/2) I ω^2

where KE is the kinetic energy, I is the moment of inertia of the turntable, and ω is the angular velocity.

The moment of inertia of a uniform disk is I = (1/2) m r^2, where m is the mass of the disk and r is its radius. Plugging in the given values, we get:

I = (1/2) (0.240 kg) (0.305 m/2)^2

I = 0.00216 kg·m^2

We know that the turntable must complete 2.20 revolutions to reach its final angular velocity, which is equivalent to 2π(2.20) = 13.8 radians. We can use the rotational kinematic equation to find the initial angular velocity of the turntable:

ω_f^2 = ω_i^2 + 2αθ

where ω_i is the initial angular velocity, ω_f is the final angular velocity, α is the angular acceleration, and θ is the angular displacement. We can rearrange this equation to solve for ω_i:

ω_i = √(ω_f^2 - 2αθ)

Plugging in the given values, we get:

ω_i = √[(3.49 rad/s)^2 - 2((3.49 rad/s) / (2.20 rev)) (2π(2.20 rev))]

ω_i = 0.565 rad/s

The torque required to accelerate the turntable from rest to 3.49 rad/s is given by:

τ = I α

where τ is the torque and α is the angular acceleration. We can use the rotational kinematic equation to find the angular acceleration:

ω_f = ω_i + αt

where t is the time it takes to reach the final angular velocity. Solving for t, we get:

t = (ω_f - ω_i) / α

Plugging in the given values, we get:

t = (3.49 rad/s - 0.565 rad/s) / ((3.49 rad/s) / (2.20 rev))

t = 3.46 s

Now we can use the equation for angular acceleration to find α:

α = (ω_f - ω_i) / t

Plugging in the given values, we get:

α = (3.49 rad/s - 0.565 rad/s) / 3.46 s

α = 0.832 rad/s^2

Finally, we can find the torque required to accelerate the turntable from rest to 3.49 rad/s:

τ = I α

τ = (0.00216 kg·m^2) (0.832 rad/s^2)

τ = 0.00180 N·m

Therefore, the motor must deliver a torque of 0.00180 N·m to accelerate the turntable from rest to 3.49 rad/s in 2.20 revolutions using rotational kinetic energy.

Learn more about torque below.

https://brainly.com/question/20691242

#SPJ1

Answer:

A turntable must spin at 33.3 rev/min (3.49 rad/s) to play an old fashion vinyl record . How much torque must the motor deliver if the turntable is to reach its angular speed in 2.20 revolutions starting from rest ? The turntable is an uniform disk of diameter 30.5 cm and mass 0.240kg​

Explanation:

The moment of inertia of the disk can be calculated as:

I = (1/2) * m * r^2

where m is the mass of the disk and r is the radius (half of the diameter).

r = 0.305 / 2 = 0.1525 m

I = (1/2) * 0.240 kg * (0.1525 m)^2 = 0.00232 kg·m^2

We know the final angular speed of the disk (ωf) and the number of revolutions it takes to reach that speed (θ), and we can calculate the initial angular speed (ωi) as:

ωf^2 = ωi^2 + 2αθ

where α is the angular acceleration, which is related to the torque (τ) applied to the disk:

α = τ / I

Combining these equations, we get:

ωf^2 = ωi^2 + 2(τ / I)θ

τ = I(ωf^2 - ωi^2) / 2θ

We are given ωf = 3.49 rad/s and θ = 2.20 rev = 13.82 rad (since 1 rev = 2π rad). To find ωi, we can use the formula for the angular speed of a rotating object:

ω = v / r

where v is the linear speed of a point on the disk. For a disk rotating about its center, the linear speed varies with the distance from the center, but the average linear speed is half the linear speed at the rim:

v = (1/2)ωiR

where R is the radius of the disk (equal to half the diameter).

R = 0.305 / 2 = 0.1525 m

v = (1/2)ωi(0.1525 m)

ωi = 2v / R = ωfθ / (2π) = (3.49 rad/s)(13.82 rad) / (2π) = 7.25 rad/s

Now we can substitute the values into the formula for torque:

τ = (0.00232 kg·m^2)(3.49^2 - 7.25^2) / (2 * 13.82 rad) = -0.108 N·m

The negative sign indicates that the torque must be applied in the opposite direction to the initial motion of the disk, which makes sense because the disk is starting from rest and needs to accelerate in the positive direction.