The magnitude of the velocity of the second runner relative to the first is 1.50 m/s
The velocity of the second runner relative to the first runner can be found using the following formula:
v_rel = v_2 - v_1
Where v_rel is the relative velocity, v_2 is the velocity of the second runner (4.75 m/s), and v_1 is the velocity of the first runner (3.25 m/s). Plugging in the values, we get:
v_rel = 4.75 m/s - 3.25 m/s = 1.50 m/s
The magnitude of the velocity of the second runner relative to the first is the absolute value of v_rel:
|v_rel| = |1.50 m/s| = 1.50 m/s
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if a digital multi-meter measures the electric potential of a circuit element to be 2.04 volts, then the least count of the voltmeter is assumed to be
The least count of the digital multi-meter measuring the electric potential of a circuit element is 0.01.
The least count of any device is that minimum reading above zero that the device can measure.
Here, the digital multi-meter measures the electric potential of a circuit element to be 2.04 Volts.
Now, what we can see from here is that the digital multi-meter can measure upto two decimals after the main reading. It means the smallest reading that it can measure is 0.01 Volts.
So, the least count of the digital multi-meter is found to be 0.01.
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The process by which we detect physical energy from our environment and send the information to our brain is called __________.
The sensation is the mechanism by which we pick up physical energy from our surroundings and communicate it to our brains.
What procedure do we use to find physical energy?The process through which humans recognize environmental physical energy and encode it as brain signals is referred to as sensation. In this chapter, the senses of sight, hearing, taste, touch, smell, kinesthesis, and vestibular perception are discussed. Additionally, it displays the results of investigations on subliminal activation.
Where in the brain does sensory information get processed?The parieto-occipital sulcus, which is located behind the central sulcus, divides the parietal lobe from the occipital lobe. It houses the somatosensory cortex and is in charge of processing sensory data.
In what sense is the primary source of data for the brain?Sight. More than any other sense, a sight most likely reveals a lot about the world to us. On the retina, light that enters the eye creates an upside-down image. The retina converts light into nerve signals that the brain can understand.
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A degree can be further divided into arcminutes and arcseconds. One degree contains 60 arcminutes, and one arcminute contains 60 arcseconds. Given this information, how many degrees is 15 arcseconds? A. 15° B. 0.1667° C. 0.25° D. 0.015° E. 0.00417°
If one degree contains 60 minutes of arc, and one minute of arc contains 60 seconds of arc. Hence, 15 seconds of arc is 0.00417⁰ (option E)
A measure of angle equal to 1/3600 of a degree or 1/60 of an arc minute. It indicates the second arc. (which should not be mistaken with the symbol representing an inch.
The resolution of this tiled collection from the 3D Elevation Program (3DEP) is 1 arc-second, or roughly 30 meters. This Digital Elevation Model (DEMelevations )'s depict the topographic bare ground surface.
A star's distance and parallax angle can be calculated using the straightforward formula d = 1/p. The parallax angle, p, and the distance, d, are both measured in arcseconds. Many astronomers choose to estimate distances in parsecs because of this straightforward relationship.
The normal range of the human eye's angular resolution is 40 arcseconds to 1 arcminute. It takes at least three photoreceptors lined up in a row to see two distinct spots.
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all energy eventually becomes ______, which is disordered energy that results from the random movements of molecules.
Heat, the disordered energy that originates from the irrational motion of molecules, is the final state of all energy.
What are energy and its measure?Energy is the capability to accomplish labor. The amount of labor an organism's stored energy is capable of performing after it is expended. energy is a scalar quantity. The term "joule" refers to the SI unit of energy. The quantity of energy required to do one photon of activity is one joule.
What is the simplest definition of energy?Scientists refer to energy as the ability to work. Modernity is feasible because people have learned how to transfer information from one media to another and then use it to complete tasks.
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nasa launches a rocket at seconds. its height, in meters above sea-level, as a function of time is given by . assuming that the rocket will splash down into the ocean, at what time does splashdown occur? the rocket splashes down after seconds. how high above sea-level does the rocket get at its peak? the rocket peaks at meters above sea-level.
The rocket will splash down into the ocean at the time of 68.92 sec and the rocket get at its peak till 5946.6m.
(a) When h(t) = 0, the rock crashes down. Use the quadratic formula to find t after setting h(t) = 0.
0 = − [tex]4.9t^2[/tex]+ 334t + 255
t = -0.75, 68.92
Time cannot be negative, so disregard the negative response.
t = 68.92 sec
(b) When the trajectory's slope is zero, the rock is at its highest point. The objective is to determine when the slope of this trajectory—which is also the tangent line—is zero. To accomplish this, set h'(t) to 0 and take the derivative of h(t).
h'(t) = -9.8t + 334
0 = -9.8t + 334
t = 34.08 sec
Utilize this moment to determine the ball's height, h(t), so that h (34.08 sec).
h(t) = − [tex]4.9\times 34.08^2[/tex] + 334(34.08) + 255
h(t) = 5946.6m
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please help me out with this physics problem!!
match each question with the right image
1. All elastic potential
2. Elastic + gravitational potential
3. All kinetic
The first image is has All elastic potential energy. The second image has Elastic + gravitational potential energy. The third image has All kinetic energy.
What is potential energy?Potential energy is the energy stored by an item as a result of its location relative to other objects, internal tensions, electric charge, or other reasons. Potential energy is stored energy that is affected by the relative location of various components in a system. When a spring is squeezed or extended, its potential energy increases. A steel ball has higher potential energy when lifted above ground than when it falls to Earth. Potential energy is defined as energy that is stored or conserved in an item or material. This stored energy is determined by the object's or substance's location, arrangement, or condition. Consider it to be energy with the 'potential' to accomplish work.
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a sound wave used in pta that causes resonance close to the apex of the basilar membrane has a relatively: a. short wavelength. b. high intensity. c. low pitch. d. large phase shift.
A sound wave employed in pta has a relatively low pitch when it generates resonance near the basilar membrane's apex.
The correct statement is C.
What is the sound waves?The pattern of disruption brought about by the movement or energy through a material (such as air, water, or any other solid or liquid matter) as it spreads away from the origin of sound is known as a sound wave. Pressure waves are generated by item vibrations that cause sound waves, such as those from a ringing phone.
What do you name a sound wave?Because air compressions and rarefactions create sound waves, they are known as longitudinal waves. Parallel to the propagation direction, the air molecules vibrate.
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2. a race car is moving with 53 km/h and starts accelerating at a rate of 3.4 m/s2. after traveling 40 seconds at that acceleration rate, the driver applies the brakes and changes the acceleration to 4.6 m/s2. how far the car travels to its complete stop after the breaks were applied?
The car travels approximately 150.65 meter distance to completely stop after applying the breaks.
First we need to consider both its initial velocity and its acceleration. initial velocity is 53km/h and acceleration is 3.4 m/s². If we convert velocity into m/s, 53km/h = 53×5/18 = 14.72 m/s.
So by the end of 40 seconds the final velocity will be 14.722 + (3.4 x 40) = 95.02 m/s . Now we know initial velocity = 14.72 m/s and final velocity = 95.02 m/s.
When the driver applies the brakes, it changes the acceleration to 4.6 m/s². So now acceleration is -4.6 m/s².
The distance that the car travels can be calculated using the equation for average velocity:
distance = (initial velocity + final velocity) / 2 × t
where t is the time taken for car to completely rest.
We know, velocity final= Velocity initial + a × t . So if velocity final is zero and solving for t,
0 = 95.022 - 4.6t
t = 95.022 / 4.6 = 20.67 seconds
Finally, we can use the equation for average velocity to determine the distance traveled:
d = (14.722 + 0) / 2 × 20.67 = 150.65 meters
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Which mass is undergoing the greatest amount of acceleration? 1 kg subjected to a force of 1 N, 100 kg subjected to a force of 100 N 100 kg subjected to a force of 1 N 100 kg subjected to a force of 100 N
When 1 N of force is applied to 1 kg, this same mass accelerates most speedily.
What is the simplest definition of acceleration?The measurement of a velocity change called acceleration. Acceleration typically indicates a change in speed, albeit not necessarily. Even though the direction of motion is changing, something rotating at a constant speed is still moving forward.
What are the 3 types of acceleration?The three main types of accelerated motions are homogeneous acceleration, non-uniform acceleration, overall average acceleration. The motion in which an item moves in some kind of a straight line while increasing in velocity at regular intervals is referred to as uniform acceleration.
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you travel 30 miles west of your home and then turn around and start going back home. after traveling 10 miles east, what is your displacement from your home?
In this case, you traveled 30 miles west and 10 miles east, so your displacement from your home is 20 miles to the west. The direction of the displacement is the same as the direction of the final position, which is to the west, away from your home.
Displacement is a vector quantity that represents the change in position of an object relative to its starting point.
You travelled in west = 30 miles
You travelled in east = 10 miles back
Displacement = 30 - 10 = 20 miles in west direction
It is calculated as the final position minus the initial position, and it measures the distance and direction of an object's change in position. Displacement can be expressed in any unit of length, such as meters, feet, or miles. It is an important concept in physics and engineering, as it provides a way to quantify the change in position of an object over time. Displacement is related to other physical quantities such as velocity, acceleration, and time, and it is an essential component of many equations used to describe the motion of objects in physics. Displacement is also an important concept in everyday life, as it is used to describe the position of objects and the change in their positions over time.
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work against friction results in an increase in blank , which is a type of energy change that takes place. multiple choice question. temperature kinetic energy potential energy
Work against friction results in an increase in kinetic energy, which is a type of energy change that takes place.
When work is done against friction, it requires energy to overcome the resistance of the friction. This results in an increase in kinetic energy, which is the energy associated with the movement of an object. The increase in kinetic energy causes the object to move faster or with more force, which is an example of a type of energy change that takes place due to work done against friction.
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Answer: temperature
Explanation:
work against friction results in an increase in temperature. temperature is a manifestation of the kinetic energy of the particles making up an object
8. compare the representations of water, sound, and light waves. describe the similarities and differences with images from the simulation to support your ideas.
Some of the similarities and differences between the representations of water, sound, and light waves are as follows:
Similarities:
Wavefronts, which are lines that depict the position of the wave at a specific point in time, may be used to depict all three types of waves.They all possess the wave qualities of wavelength, frequency, and amplitude, which govern how the wave will behave.They all move through a medium, like air, water, or solids, and the characteristics of that medium affect how quickly they move.Differences:
The environment in which the wave travels: sound waves travel through solids or air, and light waves can travel in a vacuum. Water waves travel in water.In terms of how quickly they move, light waves are the quickest, with sound waves moving at a slower rate than both.The wave's kind: Sound waves are longitudinal waves, which implies they travel parallel to the direction of the wave, whereas water waves flow perpendicular to the wave's direction. Transverse and longitudinal electromagnetic waves make up light waves.These are a few examples of how light, sound, and water waves are each represented differently and similarly.
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a 36 n force is required to push the block up the incline with constant velocity. what is the weight of the block?
Answer:
The weight of the block can be calculated using the equation of force balance, which states that the sum of all forces acting on an object is equal to zero.
Given that a 36 N force is required to push the block up the incline with constant velocity, we can assume that the only other force acting on the block is its weight, which is acting downwards. Therefore, we have:
36 N - the weight of block = 0
So, the weight of the block is 36 N.
imagine a charge in the center of a conducting, hollow sphere. there is no net charge on the sphere, and the sphere is not connected to ground. what will happen if the charge is moved a little away from the center?
If a charge is placed in the center of a conducting, hollow sphere and is then moved a little away from the center, the electrons in the sphere will rearrange themselves to neutralize the external charge and restore the overall neutrality of the sphere.
This rearrangement will cause an induced surface charge on the inner surface of the sphere, with a positive charge facing the external charge and a negative charge facing away from it.
Since the sphere is not connected to ground, it cannot discharge the induced surface charge, and the electric field within the sphere will change. The electric field lines will no longer be radial, but will instead be curved around the external charge, with the field pointing away from the positive surface charge and towards the negative surface charge.
In other words, the presence of the external charge will cause the electric field within the sphere to be distorted, leading to a change in the distribution of electric charge on the inner surface of the sphere. The sphere will remain neutral overall, but the surface charge distribution will change in response to the presence of the external charge.
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Deena made a chart to summarize features of a velocity vs. time graph for objects with constant acceleration and objects with constant velocity.
Which best describes Deena’s error?
The line for constant velocity is not horizontal; it is diagonal and slopes downward.
The area of the rectangle and the triangle under the line should be added together for constant acceleration
Find acceleration by finding the area of the rectangle above the line.
Find velocity by calculating the slope of the line.
The error is like that Instead of being level, the line for constant velocity is diagonal and slopes downhill.
How can this graph be formulated?A horizontal line on the acceleration graph indicates constant acceleration. The slope of the velocity graph is the acceleration. For the velocity graph, constant acceleration Equals constant slope = straight line. The position graph exhibits a constant slope while the velocity is constant. It begins below the origin and is a straight line that slopes upward. The displacement is the region under the velocity graph's curve.
So, The error is like that Instead of being level, the line for constant velocity is diagonal and slopes downhill.
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two identical resistors are connected in series across the terminals of an ideal battery with a voltage v and a current i flows through the circuit. if one of the resistors is removed from the circuit and the remaining one connected across the terminals of the battery, how much current would flow through the circuit?
if one of the resistors is removed from the circuit and the remaining one is connected across the terminals of the battery, the current flowing through the circuit would be twice as much as when both resistors were connected in series.
The equivalent resistance of the circuit is equal to double the resistance of each resistor when two identical resistors are connected in series across the terminals of a battery.
Ohm's law determines the amount of current flowing through the circuit:
I = V / R
When I is the current, V is the battery's voltage, and R is the circuit's equivalent resistance.
Let R represent each resistor's resistance. When both resistors are connected, the circuit's equivalent resistance is 2R.
Calculations for the circuit's current flow are as follows:
I = V / (2R) (2R)
The equivalent resistance of the circuit is R, or the resistance of a single resistor, when one of the resistors is removed.
Comparing the two equations for I, we can see that the current flowing through the circuit is doubled when one of the resistors is removed.
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overall the human leverage system is built for speed and range of movement at the expense of force generation. true false
The statement is true that overall the human leverage system is built for speed and range of movement at the expense of force generation.
What does the human body's lever system entail?The bodily pieces that act as levers to enable human movement are bones, ligaments, and muscles. To put it more simply, a joint—where two or more bones come together and form the axis (or fulcrum), and the muscles that crossed the joint exert the force sufficient to move a weight or resistance.
The human arm is what kind of a lever?There are hundreds of third-class levers in the human body. The arm serves as one of the most set of features for this. To exercising those powers held in the hand, the elbow serves as the fulcrum, the biceps brachii as the effort, and the forearm as the beam.
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a rock is dropped at the same time a rock is thrown downward in the grand canyon the acceleration of both rocks are?
Acceleration of both the rocks are the same.
An object that is moving only because of the action of gravity is said to be free falling and its motion is described by Newton's second law of motion.
A rock is dropped. It will freely fall under gravity with acceleration value g, that is called acceleration due to gravity.
At the same time a rock is thrown downward in the grand canyon, the acceleration of this rock will be the acceleration due to gravity. As the canyon is not accelerating the rock will fall on it own under the influence of gravity.
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Please answer by tomorrow at 6, thank you so much!
The menstrual cycle is the monthly series of changes a woman's body goes through in preparation for the possibility of pregnancy. Each month, one of the ovaries releases an egg — a process called ovulation.
What is Menstrual cycle?At the same time, hormonal changes prepare the uterus for pregnancy. If ovulation takes place and the egg isn't fertilized, the lining of the uterus sheds through the vagina. This is a menstrual period.
The menstrual cycle, which is counted from the first day of one period to the first day of the next, isn't the same for every woman. Menstrual flow might occur every 21 to 35 days and last two to seven days.
For the first few years after menstruation begins, long cycles are common. However, menstrual cycles tend to shorten and become more regular as you age.
Therefore, The menstrual cycle is the monthly series of changes a woman's body goes through in preparation for the possibility of pregnancy. Each month, one of the ovaries releases an egg — a process called ovulation.
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how is it possible to be accelerating and traveling at a constant speed
Speed is the measure of velocity's magnitude. It is possible for an object moving at a steady velocity to change direction. This indicates that even though an object is moving at a constant pace, it may be accelerating.
Which definition of acceleration is the most basic?Acceleration is the rate during which velocity varies. Acceleration often indicates a change in speed, but not necessarily. An item that follows a circular course while maintaining a constant speed is still moving forward as the vector of its motion is shifting.
What causes a speedup?An object's motion is altered by a net force; the larger the positive force, so greater the acceleration. To accelerate at the same rate as less massive objects, higher net forces are needed.
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a car sitting at a red light begins to accelerate at 2 m/s^2 when the light turns green. it continues with this acceleration until it reaches a speed of 20m/s. it then travels at this speed for another few minutes. how far does the car travel in the first 30 seconds after the light changes to green.
The total distance covered by car which accelerate at 2 m/s² in first 30 sec after the light changes to green is found to be 500m.
How does velocity impact acceleration?A travelling item accelerates when its velocity changes. Take into consideration that velocity is a calculation that accounts for both direction and speed. This means that a change in velocity might be either a change in the speed or a change in the direction of motion of an object.
What changes in acceleration occur throughout time?acceleration: the rate at which the speed and direction of a moving body vary over time. A point or object heading straight ahead is accelerated whenever it accelerates or decelerates.
[tex]a= 2 m/s^2; v_f = 20m/svi=0 since it starts from restvf = vi + at;20 = 0 + 2 \times tt = 10secs= vi\times t+ 1/2 a t^2s = 1/2 x 2 x 10^2 = 100m[/tex]
Total time the car traveled = 30 sec
First 10 sec, the distance traveled is 100m
For next 20 sec, the distance traveled = v x t
= 20 x 20 = 400m
The total distance covered in first 30 sec is 400+100= 500m
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a capacitor initially uses a dielectric material with a dielectric constant of 5. if that dielectric layer is replaced with a new material having identical size to the initial material but with a dielectric constant of 15, what happens to the capacitance of the capacitor?
The addition of dielectric in a capacitor reduces the effective charge on the plate and hence increases capacitance.
What happens to a capacitor's capacitance when a?Because capacitance is connected to the dielectric constant k, the capacitance of a capacitor increases when a dielectric is put between its plates.
The introduction of a dielectric substance increases the capacitance of a set of charged parallel plates. The capacitance between the plates is inversely proportional to the electric field between them, and the dielectric decreases the effective electric field.
Enhance the surface area, lower the gap between the plates, and utilize a dielectric material to increase the capacitance of a parallele plate capacitor.
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a point particle with charge q is somewhere outside a gaussian surface in the form of a cube, very close to the center of one side. the net electric flux through the cube is
Even if the Gaussian surface's radius is doubled, the electric flux that is projected outside of the system won't change. This is so because the charge contained by the surface is the only factor that affects electric flux.
When a point charge Q is at the centre of a cube, what happens?Since the charge is located in the cube's centre, the cube's electric flux lines spread out equally from each side. As a result, q is the same as the electric flux coming out of the cube.
Which of the following claims about a Gaussian surface is accurate?According to Gauss' Law, the total electric field flux across every simply linked closed surface is equal to the entire charge enclosed by that surface, divided by the material's electric permittivity.
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a 1800 kg sports car accelerates from rest to 32.0 m/s in 5.20 s. what is the average power output of the automobile engine?
The average horsepower of today's vehicles, when taken into account for each new model, ranges from 200 to 250.
What is a motor's maximum power?The ratio of a motor's speed to torque determines its power. The speed that produces the most power is around halfway between the loaded speed. No torque at highest speed. and the stagnant condition. highest torque with no speed. The power output in watt is about equal to 9.57 x (torque) x (rpm).We are given : mass of sports car, m = 1000 kg. car accelerates from rest to final speed v = 95 km/h = 95×518 =26.39 m/s.
What is the engine's specific power?One way to gauge an engine's performance in a car or power plant is by looking at its power rating or power-to-weight ratio. Its definition is its output of power divided only by mass, usually expressed in units as W/kg or hp/lb.
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10 POINTS!
Match the scientists with their inventions or discoveries.
1 .
Oersted
batteries
2 .
Westinghouse
magnetism/electricity
3 .
Faraday
induced currents
4 .
Edison
light bulb
5 .
Volta
alternating current electricity
Oersted discovered magnetism/ electricity, Westinghouse discovered alternating current electricity, Faraday discovered induced current, Edison discovered Light bulb, and Volta discovered Battery.
What is Magnetism?Magnetism is the branch of physical attributes which are mediated by a true magnetic field. Magnetism refers to the capacity of the current to induce the attractive and repulsive phenomena in the other entities.
Oersted - Magnetism/ Electricity
Westinghouse - Alternating current electricity
Faraday - Induced current
Edison - Light bulb
Volta - Battery
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What happens to the freezing point when a nonvolatile solute is added to a pure solvent?
Every time a non-volatile solute is added to a pure solvent, a solution's vapour pressure decreases.
What is nonvolatile solute in a solvent?A nonvolatile solute is a material that is difficult to evaporate. Additionally, when dissolved in the solvent, it does not raise its vapor pressure of a solution. Nonvolatile liquids have a high melting point and a low vapor pressure as traits.
Is sugar an inert solute?Volatile substances are ethanol and pentane, while nonvolatile ones include sodium chloride and sugar. As comparison to a vapor pressure of the pure solvent, the presence of a solute results in a colloquial property known as the "reduction of a vapor pressure of the solution."
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a small sphere of mass m 5 7.50 g and charge q1 5 32.0 nc is attached to the end of a string and hangs vertically as in figure p15.4. a second charge of equal mass and charge q2 5 258.0 nc is located below the first charge a distance d 5 2.00 cm below the first charge as in figure p15.4. (a) find the tension in the string. (b) if the string can withstand a maximum tension of 0.180 n, what is the smallest value d can have before the string breaks?
The tension in the string is 0.115 N and the smallest value of d before the string breaks is 1.25 cm.
The tension (T) in the string can be calculated by considering the forces acting on the upper sphere, which includes the gravitational force (mg) and the electrical force (Fe) from the lower sphere. The equation for T is
[tex]T = mg + (d^2 * k * |q1| * |q2|)[/tex]
where d is the distance between the two spheres, k is Coulomb's constant, and |q1| and |q2| are the magnitudes of charges on the spheres. Substituting the given values, T = 0.115 N.
To find the smallest value of d, the equation
[tex](d^2 * k * |q1| * |q2|) = T_{max} - mg[/tex]
is used, where [tex]T_{max}[/tex]is the maximum tension the string can withstand. Solving for d, d = 1.25 cm.
Complete question:
A small sphere of mass m = 7.50g and charge q1 = 32.0nC is attached to the end of a string and hangs vertically as in Figure. A second charge of equal mass and charge q2 = −58.0nC is located below the first charge a distance d = 2.00cm below the first charge as in Figure.
(a) Find the tension in the string.
(b) If the string can withstand a maximum tension of 0.180N, what is the smallest value d can have before the string breaks?
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a car accelerates from 10 m/s to 30 m/s in 4 seconds, and then slows down to 20 m/s in 2 seconds. what can you say about the net force acting on the car for both intervals?
From 10 m/s to 30 m/s in 4 seconds, the net force acting on the car is in the forward direction. From 30 m/s to 20 m/s in 2 seconds, net force acting on the car is in the opposite direction.
What can you say about net force acting on the car for both the intervals?The net force acting on the car is proportional to the acceleration of the car. During the first interval, the car's acceleration is from 10 m/s to 30 m/s in 4 seconds, which means it is accelerating and therefore there must be a net force acting on the car in the forward direction. During the second interval, the car slows down from 30 m/s to 20 m/s in 2 seconds, which means it is decelerating and therefore there must be net force acting on the car in opposite direction.
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two tubes are connected to two water reservoirs and open to the atmosphere as shown below. the area of the base of the tube on the right is three times that of the tube on the left. the height of the water is the same for both cases. the relation between the pressures p1 and p2 at the base of the tubes is: . . . .
The pressure p1 & p2 just at bottom of the tube are inversely proportional: p2 = p1. As seen below, a U-tube manometer connected to two air tanks at various pressures is filled with water.
What is the tube pressure law?Pressure & volume are inversely related for an ideal gas with a fixed mass maintained at a fixed temperature. Boyle's law, another gas law, states that there is an inverse relationship between a gas's pressure and volume. When the temperatures is held constant, pressure decreases as volume increases and vice versa.
How is pressure in a tubes measured?Using a piezometer tube, often known as a "pressure measuring tube," is the easiest way to gauge a fluid's pressure in a pipe. This is a tube that holds a fluid under pressure and allows the fluid to raise to a lengths that correspond to the fluid's excess pressure over the area around it.
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what is the distance (in meters) of an object that has an angular diameter of 75 arcseconds and a linear diameter of 65 meters?
The distance (in meters) of an object that has an angular diameter of 75 arcseconds and a linear diameter of 65 meters is 178762.96 meter.
As per the data given the angular diameter is of 75 arcseconds.
And the linear diameter is of 65 meters.
Angular diameter, [tex]$\delta[/tex] = 75 arcsecs.
Linear diameter, α = 65 meters
Here we have to determine the distance (in meters) of an object.
Distance D =?
We know that:
Linear diameter: The distance between the two specified sites or objects is the linear measurement.
Angular diameter: The apparent diameter of a planet or other celestial object as determined by the observational angle it assumes.
[tex]\delta=2 \arctan \left(\frac{d}{2 D}\right)[/tex]
For the small angle approximations
[tex]$ \left.\delta=\frac{d}{D}[/tex]
[tex]& \delta[/tex] = 75 ( 1 arcsec = 4.8481 [tex]\times 10^{-6}[/tex] Radians)
[tex]& \delta[/tex] = 75 × 4.8481 [tex]\times 10^{-6}[/tex] Radians
[tex]& \delta[/tex] = 0.00036361 Radian
Hence distance can be calculated by:
D = [tex]$\frac{d}{\delta} \\[/tex]
D = [tex]$\frac{65}{0.00036361} \\[/tex]
D = 178762.96 meter
Therefore the distance (in meters) of an object is 178762.96 meters.
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