The new angular speed of the merry-go-round after the man walks to a point 1.0 m from the center is approximately 1.80 rad/s.
Let's denote the initial angular speed of the merry-go-round as ω₁, and the new angular speed after the man walks to a point 1.0 m from the center as ω₂.
Given:
Initial angular speed ω₁ = 0.30 rad/s
Mass of the man m = 80.0 kg
Initial distance of the man from the axis of rotation r₁ = 2.0 m
New distance of the man from the axis of rotation r₂ = 1.0 m
Mass of the merry-go-round (cylinder) M = 6.50 * 10² kg
Radius of the merry-go-round (cylinder) R = 2.00 m
The conservation of angular momentum can be applied in this scenario, where the initial angular momentum of the system is equal to the final angular momentum of the system.
The initial angular momentum of the system is given by:
Initial angular momentum L₁ = Moment of inertia of the man about the axis of rotation x initial angular speed of the merry-go-round
The moment of inertia of the man about the axis of rotation can be calculated using the formula for the moment of inertia of a point mass rotating about an axis at a distance r from the axis of rotation:
Moment of inertia of the man about the axis of rotation I₁ = m x r₁²
The final angular momentum of the system is given by:
Final angular momentum L₂ = Moment of inertia of the man about the new axis of rotation x new angular speed of the merry-go-round
The moment of inertia of the man about the new axis of rotation can be calculated using the same formula as above, but with the new distance r₂:
Moment of inertia of the man about the new axis of rotation I₂ = m x r₂²
Setting the initial and final angular momenta equal to each other, we can solve for the new angular speed ω₂:
L₁ = L₂
I₁ * ω₁ = I₁ * ω₂
Substituting the expressions for I₁, I₂, and the given values:
m * r₁² * ω₁ = m * r₂² * ω₂
Simplifying:
r₁² * ω₁ = r₂² * ω₂
Plugging in the given values for r₁, r₂, and ω₁, and solving for ω₂:
2.0² * 0.30 = 1.0² * ω₂
[tex]\omega_2 = \frac{(2.0^2*0.30)}{1.0^2}[/tex]
ω₂ ≈ 1.80 rad/s.
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a crane is moving a honda from a point on the ground to the top of a building. if the honda weighs 1400 kg and it lifts the car with a constant velocity of 6.0 m/s, what is the power the crane exerts during this lift?
The power exerted by the crane during the lift is 82,404 watts.
To calculate the power exerted by the crane while lifting a 1400 kg Honda at a constant velocity of 6.0 m/s, follow these steps:
1. First, calculate the gravitational force acting on the Honda using the equation F = m * g, where F is the force, m is the mass of the Honda (1400 kg), and g is the acceleration due to gravity (approximately 9.81 m/s²).
F = 1400 kg * 9.81 m/s²
F = 13734 N
2. Next, calculate the work done by the crane to lift the Honda at a constant velocity. Work is given by the equation:
W = F * d, where W is the work done, F is the force calculated in step 1, and d is the distance traveled (which can be calculated as the velocity multiplied by time).
However, since the crane is lifting at a constant velocity, the work done equals the force applied.
W = F
W = 13734 J
3. Finally, calculate the power exerted by the crane. Power is given by the equation P = W / t, where P is the power, W is the work done (calculated in step 2), and t is the time taken to lift the Honda.
Since the Honda is lifted at a constant velocity of 6.0 m/s, the power can be calculated as P = F * v, where F is the force and v is the velocity.
P = 13734 N * 6.0 m/s
P = 82404 W
Therefore, the power exerted by the crane is 82,404 watts.
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a weight lifter lifts a 420-n set of weights from ground level to a position over his head, a vertical distance of 1.75 m. how much work does the weight lifter do, assuming he moves the weights at constant speed?
The work done by a weightlifter to lift a 420 N set of weights from ground level to a position over his head is 735 j.
To calculate the work done by a weightlifter who lifts a 420 N set of weights from ground level to a position over his head, a vertical distance of 1.75 m, assuming he moves the weights at a constant speed:
Use the formula given below:
W = F × d
where,
W = work done by the weightlifter
F = force applied
d = distance moved by the weightlifter
From the given data, the force applied by the weightlifter is 420 N, and the distance moved is 1.75 m.
W = 420 N × 1.75 m = 735 J
Therefore, the work done by the weightlifter is 735 J.
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A 5 kg cannonball is shot out of a cannon and has an acceleration of 8 m/s^2 at the point where it exits the cannon. What force, in N, was applied to the cannonball? (only enter the number)
The force, in N, applied to the cannonball can be calculated using Newton's Second Law of Motion, which states that the force applied to an object is equal to its mass times its acceleration:
Force = mass x acceleration
Plugging in the given values, we get:
Force = 5 kg x 8 m/s^2 = 40 N
Therefore, the force applied to the cannonball was 40 N.
4. A student is thinking about how the results of this activity apply to driving a
car and says:
The puck slid a bigger distance before stopping when it was moving faster.
That means that if I'm driving my car 40 mph instead of 20 mph, I should hit
my brakes twice as far from a stop sign to stop my car in time.
Do you agree with this statement? Explain your reasoning using evidence from
your computational model.
Based on the statement made by the student, The student's statement that the puck slid a bigger distance before stopping when it was moving faster is correct.
What is the distance about?The above is because the kinetic energy of an object in motion is proportional to its mass and the square of its velocity. When an object is moving faster, it has more kinetic energy, and it takes more work to stop it. In the case of the puck, the frictional force acting on it was not strong enough to overcome the kinetic energy of the puck when it was moving faster, resulting in a longer sliding distance before it came to a stop.
However, the student's conclusion that they should hit their brakes twice as far from a stop sign when driving at 40 mph instead of 20 mph to stop their car in time is not necessarily accurate. While it is true that a car moving at a higher speed has more kinetic energy and requires more work to stop, the distance required to stop the car depends on several factors, such as the mass of the car, the efficiency of the brakes, and the condition of the road surface.
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the body position sense that orients us with respect to gravity and the immediate environment is a function of
The body position sense that orients us with respect to gravity and the immediate environment is a function of the vestibular system, which is located in the inner ear.
This system provides the brain with information about head position, acceleration, and movement, which in turn allows us to maintain balance and a sense of spatial orientation. Additionally, information from the eyes, muscles, and joints also contribute to body position sense, allowing us to integrate multiple sensory inputs and make accurate judgments about our position and movement in space. Overall, body position sense is a complex sensory and neural process that involves multiple inputs and processing centers in the brain.
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how fast will the ball passes its equilibrium position each time? assume that friction may be neglected
If we know the mass of the ball, the spring constant, and the maximum displacement (or amplitude) of the ball from its equilibrium position, we can calculate the speed at which the ball passes through its equilibrium position each time.
The speed at which the ball passes its equilibrium position each time depends on the amplitude and period of its motion.
Assuming the ball is executing simple harmonic motion, the time period (T) of the motion can be calculated using the formula:
T = 2π√(m/k)
where m is the mass of the ball and k is the spring constant.
Once we know the time period of the motion, we can calculate the speed at which the ball passes through its equilibrium position using the formula:
v = A/T
where A is the amplitude of the motion.
If the amplitude of the motion is not given, we can assume that it is equal to the maximum displacement of the ball from its equilibrium position. For a mass-spring system, this maximum displacement is equal to the amplitude of the oscillation.
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consider a conducting bar that is free to slide along conducting rails in an upward magnetic field as shown in the diagram below. if we connect the rails to the battery shown, which way will the bar be pushed?
The direction of the induced electric field is given by Lenz's law, which states that the direction of the induced field is such that it opposes the change in magnetic flux that is inducing it.
The movement of the bar upward in the field is what in this instance is responsible for the shift in magnetic flux. The induced electric field will induce a current in the bar that flows in a direction that produces a magnetic field that opposes the upward field in order to counteract this shift in flux.
We can calculate the direction of the current flow in the bar using the right-hand rule for current. Our fingertips will curl in the direction of the magnetic field created by the current if we point our thumb in the direction of the induced current.
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a bird grabs a clam, carries it in its beak to a considerable height, and then drops it on a rock below, breaking the clam shell. which is the correct energy conversion when the clam is dropped?
When the bird drops the clam from a height, the potential energy of the clam is converted into kinetic energy. As the clam falls, it gains kinetic energy and loses potential energy.
An object's kinetic energy is the type of energy it has as a result of motion. It is described as the effort required to move a mass-determined body from rest to the indicated velocity. The body holds onto the kinetic energy it acquired during its acceleration until its speed changes.When the clam hits the rock, the kinetic energy is converted into other forms of energy, such as sound and heat, and the clam shell breaks.
Therefore, the correct energy conversion when the clam is dropped is from potential energy to kinetic energy, followed by a conversion of kinetic energy into other forms of energy.
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a 50 kg ice skater spins about a vertical axis through her body with her arms horizontally outstretched, making 2.5 turns each second. the distance from one hand to the other is 1.50 m . biometric measurements indicate that each hand typically makes up about 1.25 % of body weight.what horizontal force must her wrist exert on her hand?
The horizontal force that her wrist must exert on her hand is 2,128 N.
How we determine horizontal force?Consider the rotational motion of the ice skater and the forces acting on her body.
The centripetal force required to keep the ice skater moving in a circle is provided by the tension force in her arms.
We can use the following equation to find the tension force:
F = mω²r
where F is the tension force, m is the mass of the ice skater, ω is the angular velocity (in radians per second), and r is the radius of the circle formed by the outstretched arms (i.e., half the distance between the hands).
First, let's calculate the radius:
r = 1.50 m / 2
= 0.75 m
Next, let's calculate the angular velocity:
ω = 2.5 turns/s x 2π radians/turn = 15.7 radians/s
Now, let's calculate the mass of the ice skater's hands:
m_hands = 0.0125 x 50 kg = 0.625 kg
Finally, let's use the equation above to find the tension force:
F = mω²r = (50 kg + 2 x 0.625 kg) x (15.7 radians/s)² x 0.75 m
= 2,128 N
Therefore, the horizontal force that her wrist must exert on her hand is 2,128 N.
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a train is moving at a speed of 132kmph. if the length of the train is 110 meters, how long will it take to cross a railway platform 165m long?
It will take 7.50 seconds to cross a railway platform 165m long, when a train is moving at a speed of 132kmph. if the length of the train is 110 meters.
At the point when a train crosses a stage, the all out distance it covers is the amount of the length of the train and the length of the stage. The time it takes to cover this distance relies upon the speed of the train, which is given in km/h. We can change this over completely to m/s by duplicating by 1000/3600.
For this situation, the speed of the train is 132 km/h, which is around 36.67 m/s. The complete distance the train should cover is the length of the train in addition to the length of the stage, which is 110 m + 165 m = 275 m.
To ascertain the time it takes to cover this distance, we can utilize the equation: time = distance/speed. Subbing the given qualities, we get:
time = 275 m/36.67 m/s
≈ 7.50 s
Accordingly, it will require around 7.50 seconds for the train to cross the 165 m long stage, accepting that there is no postponement because of some other factors like speed increase or deceleration.
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pls help me with this question I need it by Monday thanks Q1 and 2
1) current
2) in series
3) voltage
4) In parallel
How are ammeters and voltmeters connected?Ammeters are connected in series with the component or part of the circuit being measured, so that the entire current flows through the ammeter. This means that the ammeter must have a very low resistance, so that it does not significantly alter the current being measured. Typically, ammeters have a built-in shunt resistor to achieve this low resistance.
On the other hand, voltmeters are connected in parallel with the component or part of the circuit being measured, so that they measure the voltage across the component or part. This means that the voltmeter must have a very high resistance, so that it does not draw significant current from the circuit and alter the voltage being measured. Typically, voltmeters have a built-in series resistor to achieve this high resistance.
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a 90-kg (including any equipment) skydiver drops out of a plane. using an air density of 1.0 kg/m3, a frontal surface area of 1.0 m2, and a drag coefficient of 0.8, what will the skydiver's terminal velocity be?
The terminal velocity of a 90-kg (including any equipment) skydiver who jumps out of a plane can be found using the given data: air density of 1.0 kg/m3, a frontal surface area of 1.0 m2, and a drag coefficient of 0.8.What is terminal velocity.
Terminal velocity is the maximum velocity that a falling object can reach when air resistance is equal to the gravitational force acting on it. This is the point at which an object can no longer accelerate because the opposing forces are balanced. Terminal velocity can be computed using the formula: v = √(2mg/ρACd)where: v is the terminal velocity m is the mass of the objectρ is the air density A is the frontal surface area Cd is the drag coefficient of the object g is the acceleration due to gravity(9.81 m/s²)Substituting the provided values: v = √(2(90 kg)(9.81 m/s²)/(1.0 kg/m³)(1.0 m²)(0.8)) = 72.22 m/s Therefore, the skydiver's terminal velocity is 72.22 m/s.
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when measuring your angles of incidence and angles of refraction, how should you always make sure to measure them?
When measuring angles of incidence and angles of refraction, always make sure to measure them from the normal line, which is perpendicular to the surface at the point of contact. This ensures accurate measurements and proper calculations in refraction scenarios.
When measuring angles of incidence and angles of refraction, it is essential to ensure that you always measure them using the correct tools or instruments.What is an angle?An angle is a measure of rotation, expressed in degrees, that two lines or sides create around a common point called the vertex. Two rays or lines originate from a single point and diverge in different directions to form an angle.Measuring anglesTo measure angles, you'll need a protractor, a device that's specifically built for this task. Place the protractor on the angle's vertex so that the base lines of the protractor are parallel to the lines or sides of the angle you're measuring.Angle of incidenceThe angle of incidence is the angle between the incident ray and the normal line to a surface, such as the surface of an optical lens, mirror, or prism. The angle of incidence is denoted by the Greek letter “θ” (theta).Angle of refractionThe angle of refraction is the angle between the refracted ray and the normal line to a surface, such as the surface of an optical lens, mirror, or prism. The angle of refraction is denoted by the Greek letter “θ” (theta).Therefore, when measuring angles of incidence and angles of refraction, it is essential to ensure that you always measure them using the correct tools or instruments. The angle measurement process is done using a protractor.
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a helicopter, starting from rest, accelerates straight up from the roof of a hospital. the lifting force does work in raising the helicopter. an 840-kg helicopter rises from rest to a speed of 9.5 m/s in a time of 4.0 s. during this time it climbs to a height of 7.7 m. what is the average power generated by the lifting force?
The average power generated by the lifting force is equal to the total work done by the lifting force divided by the time taken.
The total work done by the lifting force is equal to the mass of the helicopter times the change in its gravitational potential energy.The change in its gravitational potential energy is equal to its mass times the gravitational acceleration times its change in height.
Therefore, the average power generated by the lifting force is equal to the mass of the helicopter times the gravitational acceleration times the change in height, divided by the time taken. In this case, the average power is equal to 840 kg times 9.81 m/s2 times 7.7 m, divided by 4.0 s, which is equal to 203 kW. Therefore, the average power generated by the lifting force is 203 kW.
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a lighter block and a heavier block sit on a frictionless surface. please answer the following questions about the final momenta and kinetic energies of the blocks for the given situations. both blocks are initially at rest. the same force f then pushes to the right on each block for 1 meter. which block has the larger final kinetic energy after the force acts?
The heavier block has the larger final kinetic energy after the force acts.
Here's the step-by-step explanation:
1. Both the lighter and heavier blocks are initially at rest, so their initial momenta and kinetic energies are both zero.
2. The same force F is applied to each block for a distance of 1 meter.
3. Since force and distance are the same for both blocks, they will both gain the same amount of work done on them (W = F × d).
4. Work done on an object is equal to the change in its kinetic energy (W = ΔKE).
5. As both blocks have the same amount of work done on them, they will both have the same increase in kinetic energy.
6. However, the heavier block initially had a higher mass, so its final kinetic energy will be larger than the lighter block's final kinetic energy. This is because kinetic energy is directly proportional to mass (KE = 0.5 × m × v^2).
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constant force is applied to an object, causing the object to accelerate at 5.50 m/s2 . what will the acceleration be if
The acceleration will be,
a) 11.00 m/s²
b) 2.75 m/s²
c) 5.50 m/s²
d) 22.00 m/s²
According to Newton's second law, the acceleration of an object is directly proportional to the force applied and inversely proportional to its mass. Therefore,
If the force is doubled, the acceleration will also double, resulting in an acceleration of 11.00 m/s².
If the object's mass is doubled, the acceleration will be halved, resulting in an acceleration of 2.75 m/s².
If both the force and the object's mass are doubled, the acceleration will remain the same, at 5.50 m/s².
If the force is doubled and the object's mass is halved, the acceleration will be quadrupled, resulting in an acceleration of 22.00 m/s².
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--The complete question is, A constant force is applied to an object, causing the object to accelerate at 5.50 m/s2 . What will the acceleration be if
a) The force is doubled?
b) The object's mass is doubled?
c) The force and the object's mass are both doubled?
d) The force is doubled and the object's mass is halved?--
the measured nodal voltages are: find voltage and the current . 6.864 0.624 (within three significant digits) what is the power for the voltage and current source in watts?
The power for the voltage source is -6.5744 W and the power for the current source is 0.02424 W (both to three significant digits).
To find the voltage Vab, we can use the voltage divider rule, which states that the voltage across a resistor in a series circuit is proportional to its resistance. In this case, Vab is the voltage across R2 and R3 in series, so:
Vab = Vo * (R2 + R3) / (R1 + R2 + R3)
= 9.84 * (9 + 6) / (10 + 9 + 6)
= 4.608 V
To find the current Ij, we can use Kirchhoff's current law, which states that the total current flowing into a junction is equal to the total current flowing out of the junction. In this case, the current flowing into node b is equal to the current flowing out of node b, so:
Ij = (Vc - Vab) / R3
= (4.296 - 4.608) / 6
= -0.052 A
Note that the negative sign indicates that the current is flowing in the opposite direction of the assumed direction.
To find the power for the voltage and current source, we can use the formulas P = V * I and P = I^2 * R, respectively. For the voltage source, the power is:
Pvg = Va * (Vc - Va) / R1
= 16 * (4.296 - 16) / 10
= -6.5744 W
Note that the negative sign indicates that the power is being dissipated, rather than generated.
For the current source, the power is:
Pig = Ij^2 * R2 = (-0.052)^2 * 9 = 0.02424 W
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Complete question:
m mo Vs( R1 = 10 kN2 R2 =9 k12 R3 = 6 kN2 The measured nodal voltages are: Va = 16 V Vo = 9.84 V Vc = 4.296 V Find voltage Vab and the current 11. Vab = mA Ij = (within three significant digits) What is the power for the voltage and current source in watts? Pvg = Pig = (within three significant digits)
a pendulum oscillates with a frequency of 1.5 hz . what is its length? express your answer to two significant figures and include the appropriate units.
The length of the pendulum is approximately 1.04 m, rounded to two significant figures.
The period (T) of a pendulum is given by T = [tex]2π√(L/g)[/tex], where L is the length of the pendulum and g is the acceleration due to gravity (approximately 9.81 [tex]m/s^2[/tex]). The frequency (f) of the pendulum is simply the inverse of the period, so f = 1/T.
Given that the frequency of the pendulum is 1.5 Hz, we can calculate the period as follows: f = 1/T 1.5 Hz = 1/T T = 1/1.5 s T = 0.667 s Now, we can use the period formula to find the length of the pendulum: T = 2π√(L/g) 0.667 s =[tex]2π√[/tex]([tex]L/9.81 m/s^2[/tex]) 0.667 s/([tex]2π[/tex]) = [tex]√(L/9.81 m/s^2[/tex]) 0.106 [tex]s^2/m =[/tex] [tex]L/9.81 m/s^2 L[/tex]= 1.04 m
Therefore, the length of the pendulum is approximately 1.04 m, rounded to two significant figures. It's important to note that the length of a pendulum affects its period and, consequently, its frequency.
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consider two stars, one at a distance of 10,000 light years from the galactic center and one at a distance of 26,000 light years from the galactic center. which stars has a higher rotational velocity?
The star located 10,000 light-years away from the galactic center would have a higher rotational velocity than the star located 26,000 light-years away.
The galaxy's rotational speed is not constant across its radius. The Milky Way, like most galaxies, has a dark matter halo that encloses the visible matter. The circular velocity profile of the Milky Way, which is almost flat beyond the Sun's location, offers a measure of the total mass distribution. The orbital velocities of material at various radii around the galactic center, such as gas and stars, can be measured to determine this profile.
Galactic rotation is characterized by Kepler's third law, which states that for a galaxy with a spherically symmetric mass distribution, the rotation speed is proportional to the square root of the distance to the center. As a result, a star that is closer to the galactic center would have a higher rotational speed than one that is farther away.
Since we have two stars, one located 10,000 light-years from the galactic center and the other located 26,000 light-years from the galactic center, we can quickly determine which star has the higher rotational velocity using Kepler's third law. The star closer to the galactic center, which is located 10,000 light-years away, would have a higher rotational velocity than the star located 26,000 light-years away from the galactic center.
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during a process, 5 kj of heat is added to a closed system, and the system does 2 kj of work on the surroundings. what is the change of the internal energy of the system? here, neglect change in the bulk energy
The change in the internal energy of the system can be calculated using the first law of thermodynamics, which states that the change in the internal energy of a system is equal to th added to the system minus the work done by the system on the surroundings.
The formula for this is:ΔU = Q - W where ΔU is the change in internal energy, Q is the heat added to the system, and W is the work done by the system on the surroundings. In this case, 5 kJ of heat is added to the system, and the system does 2 kJ of work on the surroundings. Therefore, the change in internal energy is:ΔU = Q - WΔU = 5 kJ - 2 kJΔU = 3 kJSo, the change in the internal energy of the system is 3 kJ.
The change in internal energy of the system can be calculated using the first law of thermodynamics: ΔU = Q - W, where ΔU is the change in internal energy, Q is the heat added to the system, and W is the work done by the system. In this case, Q = 5 kJ and W = 2 kJ.
So, ΔU = 5 kJ - 2 kJ = 3 kJ.
The change in the internal energy of the system is 3 kJ, considering we neglect the change in the bulk energy.
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even though the electricity that powers them is generated primarily from burning fossil fuels, electric cars are still more efficient than gas-powered vehicles because:
Even though the electricity that powers them is generated primarily from burning fossil fuels, electric cars are still more efficient than gas-powered vehicles because they convert a higher percentage of their stored energy into kinetic energy, the energy of motion.
In comparison, gas-powered vehicles lose a significant amount of energy to heat and other forms of inefficiency through the combustion process.
Additionally, electric vehicles have regenerative braking, which captures some of the energy lost during braking and uses it to recharge the battery. This makes electric cars more energy-efficient and less polluting, even when powered by fossil fuels.
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what current is required in a loop of wire with radius 0.035 m to generate a magnetic field of strength 24e-6 t at the center of the loop?
To generate a magnetic field of strength 24e-6 T at the center of the loop, a current of approximately 4.4 A is required in a loop of wire with a radius of 0.035 m.
The magnetic field generated by a current-carrying loop of wire depends on the current and the geometry of the loop. The magnetic field strength at the center of the loop is given by the formula B = μ₀I/(2r), where B is the magnetic field strength, μ₀ is the magnetic constant (equal to 4π x 10^-7 T m/A), I is current, and r is the radius of the loop. In this case, we are given the magnetic field strength B and the radius of the loop r, and we want to find the current I that will produce that field strength. Rearranging the formula, we get I = 2Br/μ₀. Plugging in the given values, we get I = 2 x 24e-6 T x 0.035 m / (4π x 10^-7 T m/A), which simplifies to 1.2 A. Therefore, a current of 1.2 A is required in the loop of wire to generate a magnetic field of strength 24e-6 T at the center of the loop.
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which things are audible? select all that apply. responses clouds forming clouds forming birds singing in the trees birds singing in the trees lightning streaking across the sky lightning streaking across the sky wind howling
Audible things: birds singing, wind howling. Clouds forming and lightning are not audible because they don't produce sound waves.
Of the choices given, two things are discernible: birds singing in the trees and wind yelling.
Mists framing and lightning streaking across the sky are not perceptible on the grounds that they don't deliver sound waves. Mists framing are a visual peculiarity brought about by changes in temperature and dampness in the air, and lightning produces electromagnetic waves however not sound waves.
Birds singing in the trees and wind crying are both perceptible in light of the fact that they produce sound waves. Birds produce sound by vibrating their vocal ropes, and the subsequent sound waves can head out through the air to be heard by people. Wind can make objects vibrate, delivering sound waves that can likewise be heard by people.
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a boy rides his bicycle 1.44 km. the wheels have radius 28.0 cm. what is the total angle (in radius) the tires rotate through during his trip?
The total angle (in radians) the tires rotate through during the trip is 2573.32 radians.
As given, a boy rides his bicycle 1.44 km. The wheels have a radius of 28.0 cm. We have to calculate the total angle (in radians) that the tires rotate through during his trip. Let us calculate the circumference of the tire with the given radius. We know that the circumference of the tire
=> 2πr= 2 × 22/7 × 28 cm
=> 176 cm
=> 1.76 meters
Now, the boy rode his bicycle for a distance of 1.44 km which is equal to 1440 meters. Let the number of times the tire rotates be N.
Then, from the above calculation, we know that the distance traveled by each tire in one rotation is the circumference of the tire. Thus the distance traveled by both tires in one rotation is
2 × 1.76 = 3.52 meters.
Therefore, the number of rotations of the tire, N = distance traveled by both the tires/distance traveled by the boy
= 1440 / 3.52= 409.09 approx.
Now, we know that in one rotation of the tire, the angle (in radians) that it rotates through is equal to 2π radians. Therefore, in N rotations, the angle rotated by the tire (in radians) is equal to 2πN.
Substituting the value of N, we have the Angle rotated (in radians)
=> 2 × 22/7 × 409.09= 2573.32 radians approx.
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how can sounds be changed and what is the cause of the change?
Sounds can be changed in a variety of ways depending on the source of the sound and the type of change you want to make. Here are a few examples:
PitchVolumeTimbreDurationWhat are the cause of the change in sound?The cause of the change depends on the type of change being made. For example, changing the pitch of a sound is caused by altering the frequency of the sound wave, while changing the volume is caused by altering the amplitude of the sound wave.
In general, changes to sound waves can be caused by physical manipulation of the sound source, such as adjusting the properties of a musical instrument, or by electronic processing of the sound signal using digital signal processing techniques.
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What is the initial velocity of a ball that is thrown downward at the rooftop of a 35 m building and falls to the ground after 2.25 s?
The initial velocity of the ball that was thrown downward from a height of 35 m is 4.53 m/s².
What is velocity?Velocity is the rate of change of displacement.
To calculate the initial velocity of the ball, we use the formula below,
Formula:
s = ut+gt²/2.................... Equation 1Where:
s = Distancet = Timeu = Initial velocityg = Acceleration due to gravityFrom the question,
Given:
t = 2.25 sg = 9.8 m/s² (Thrown upward)s = 35 mSubstitute these values into equation 1 and solve for u
35 = (2.25×u)+(9.8×2.25²)/235 = 2.25u+24.812.25u = 35-24.812.25u = 10.19u = 10.19/2.25u = 4.53 m/sHence, the initial velocity is 4.53 m/s².
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the sum of the second and eight term of an arithmetic progression is 52. if the difference between the third is. i common difference ii first term iii 20th term.
The common difference is (26-a)/4, the first term is (3a+26)/4, and the 20th term is (81a-494)/4.
What is the common difference?Let's call the first term of the arithmetic progression "a" and the common difference "d".
Then, the second term would be "a + d", the third term would be "a + 2d", and so on.
The second term is "a + d" and the eighth term is "a + 7d".
The sum of the second and eighth term is given as 52:
(a + d) + (a + 7d) = 52
Simplifying the equation:
2a + 8d = 52
Dividing both sides by 2:
a + 4d = 26
Now, to find the difference between the third terms:
The third term is "a + 2d".
The difference between the third and second term is the common difference "d".
So, d is the difference between (a + 2d) and (a + d).
d = (a + 2d) - (a + d)
d = a + 2d - a - d
d = d
Therefore, we know nothing about the difference between the third terms.
To find the values asked in the question:
i. The common difference is given as:
a + 4d = 26
4d = 26 - a
d = (26 - a)/4
ii. The first term can be found by substituting the common difference into the equation:
a + d = a + [(26 - a)/4] = (4a + 26 - a)/4 = (3a + 26)/4
iii. The 20th term can be found using the formula for the nth term of an arithmetic progression:
a_n = a + (n - 1)d
a_20 = a + 19d
Substituting the value of d:
a_20 = a + 19[(26 - a)/4]
a_20 = (81a - 494)/4
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after running three trials with a fan cart, which has a mass of 480 g, on a horizontal track you have collected the following data. trial 1 trial 2 trial 3 acceleration from x-t graph (m/s2) 0.642 0.622 0.651 acceleration from v-t graph (m/s2) 0.618 0.664 0.604 120 g is added to the cart and it is placed at rest on a track inclined at 4.5o (with respect to the horizontal). the fan is set to push the cart up the incline. will the cart accelerate up the incline, down the incline, or remain at rest? explain fully.
Based on the data collected from the three trials, we can find the average acceleration of the fan cart on a horizontal track. To do this, we will calculate the mean of the six acceleration values provided:
(0.642 + 0.622 + 0.651 + 0.618 + 0.664 + 0.604) / 6 = 3.801 / 6 = 0.634 m/s^2
Now, the mass of the fan cart is 480 g, which we will convert to kg:
480 g * (1 kg / 1000 g) = 0.48 kg
After adding 120 g to the cart, the new mass becomes:
0.48 kg + (120 g * 1 kg / 1000 g) = 0.48 kg + 0.12 kg = 0.60 kg
Next, we need to determine the gravitational force acting on the cart along the incline. This can be calculated using the formula:
F_gravity = m * g * sin(theta)
where m is the mass of the cart, g is the gravitational constant (approximately 9.81 m/s^2), and theta is the angle of inclination.
F_gravity = 0.60 kg * 9.81 m/s^2 * sin(4.5°) ≈ 0.60 kg * 9.81 m/s^2 * 0.078 ≈ 4.72 N
Now, we'll calculate the force exerted by the fan using the formula:
F_fan = m * a
where m is the mass of the cart, and a is the average acceleration calculated earlier.
F_fan = 0.60 kg * 0.634 m/s^2 ≈ 0.38 N
Since the gravitational force (4.72 N) is greater than the force exerted by the fan (0.38 N), the cart will not be able to overcome gravity and will accelerate down the incline.
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the work done on a sligshot is 40 to pull back a 0.10 kg stone. if the slingshot projects the stone straight up in the air, what is the maximum height to which the stone will rise?
The maximum height to which the stone can rise, given that the work done is 40 J, is 40.82 m
How do i determine the maximum height to which the stone can rise?First, we shall list out the given parameters from the question. This is given below:
Work done (Wd) = 40 JoulesMass of stone (m) = 0.10 KgAcceleration due to gravity (g) = 9.8 m/s² Maximum height (h) =?We can obtain the maximum height to which the stone can rise as follow
Wd = mgh
40 = 0.10 × 9.8 × h
40 = 0.98 × h
Divide both sides by 0.98
h = 40 / 0.98
h = 40.82 m
Thus, the maximum height to which the stone can rise is 40.82 m
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what is the maximum distance, in kilometers, at which the eye can resolve these two headlights at night? take the pupil diameter to be 0.4 cm.
The maximum distance at which the eye can resolve two headlights at night, given a pupil diameter of 0.4 cm, is approximately 11,937.3 meters or 11.937 kilometers.
To calculate the maximum distance at which the eye can resolve two headlights at night, we can use the formula for the angular resolution of the human eye, which is based on the Rayleigh criterion:
θ = 1.22 * (λ / D)
Where:
θ = angular resolution in radians
λ = wavelength of light (average wavelength of visible light is approximately 550 nm, or 5.5 x 10^-7 meters)
D = diameter of the aperture (pupil diameter, given as 0.4 cm or 0.004 meters)
First, calculate the angular resolution:
θ = 1.22 * (5.5 x 10^-7 m / 0.004 m) = 1.678 x 10^-4 radians
Now, to find the maximum distance (d) at which the eye can resolve two headlights, we can use the formula
d = L / tan(θ)
Where:
L = distance between the headlights (assuming a standard separation of 2 meters)
Before calculating, we need to make sure that the angular resolution (θ) is in the same unit (radians) as the tangent function requires:
θ = 1.678 x 10^-4 radians
Now, calculate the maximum distance:
d = 2 m / tan(1.678 x 10^-4) ≈ 11937.3 meters
Therefore, the maximum distance at which the eye can resolve two headlights at night, given a pupil diameter of 0.4 cm, is approximately 11,937.3 meters or 11.937 kilometers.
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