The objects must be of opposite charge because the electric force of attraction between them increases when they are released and free to move.
This means that the electric force must be a repulsive force that pushes the objects away from each other. Opposite charges attract and as charges repel, the objects must be of opposite charge for the electric force to increase when the objects are released and free to move.
Therefore when two small objects carry the same amount of charge, the magnitude of the electric force exerted by one object on the other is 0.10 N when they are held 30 mm apart. If the force magnitude increases when the objects are released and free to move, then we can say that they are opposite charges.
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an explorer walks 22 km north, then 47 km at 55o south of east. what is her resultant displacement?
Answer:
Below
Explanation:
Vertical components
22 - 47 sin 55 = - 16.5 km
Horizontal components
47 cos 55 = 26.96
Use Pythagorean Theorem
d^2 = (-16.5)^2 + 26.96^2
d = 31.6 km
The Jendrassik maneuver is sometimes used when a subject needs to be distracted, and usually results in a larger reflex test response. Was this true for you? Explain what happened
he JM will heighten (exaggerate) lower limb tendon reflexes by countering some of the normal descending inhibition the brain sends to the reflex arc.
What happens during the Jendrassik maneuver?A medical technique called the Jendrassik manoeuvre involves the patient clenching their teeth, flexing both sets of fingers into a hook-like shape, and interlocking those sets of fingers. The patellar reflex is then induced by striking the tendon below the patient's knee with a reflex hammer.
When the technique is not being used, the reflex outcome of the same movement is compared to the induced reaction. When a patient is focused on the technique, a bigger reflex reaction is frequently seen: "Afferent activity brought on by such muscle tension may activate a weak or seemingly absent reflex.
This is the actual justification for the procedure, not that it is intended to divert the patient's attention, a common misperception that persists to this day." This result
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3. Calculate the force of gravity that Saturn (mass = 5. 7 x 1026 kg) exerts
on a woman on Earth (mass = 61 kg) when Saturn is closest to Earth,
1. 2 x 10° km.
The force of gravity that Saturn (mass = 5. 7 x 1026 kg) exerts on a woman on Earth (mass = 61 kg) when Saturn is closest to Earth = 1. 2 x 10° km.
Explanation of the given answer:Formula used in step two. F = G m 1 m 2 r 2. Step 3: Determine the gravitational force.
Calculating the gravitational force is step three. F = 6.7 10 11 by changing the values in the formula above. 2 × 10 30 × 6 × 10 24 1 .5 × 10 11 2 F = 3 .
The formula for the gravitational constant of the universe is G = 6.674 x 10 - 11 m3/kg s2. Thus, this is the gravitational pull of the sun on the planet.
F = Gm1m2R2, where G is the gravitational constant of the universe. The gravitational force between two bodies of equal mass that are kept at an equal distance from one another constitutes the universal gravitational constant.
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when a falling firecracker explodes, the momenta of its pieces _______.
when a falling firecracker explodes, the momenta of its pieces vectorially add up to equal the initial momentum of the firecracker.
When the firecracker bursts, the vector sum of the momenta of its fragments adds up to the firecracker’s momentum just before bursting.
A falling firecracker explodes into two pieces. The momenta of the fragments combine by vector rules to equal the original momentum of the falling firecracker. Momentum is equal to mass multiplied by velocity.
According to the conservation of momentum, the initial momentum of the system is equal to the final momentum. The condition for the validity of momentum conservation is that no external force should exert on the system.
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How is Pythagorean Theorem used in baseball?
Bill James came up with the Pythagorean Theorem of Baseball, which connects the amount of runs a club has scored and given up to its actual winning %.
Its uses are:The Pythagorean Theorem is the idea that a baseball team's record may be roughly estimated by taking the square of team runs scored and dividing it by the square of team runs scored plus the square of team runs allowed. Bill James, a baseball analyst, made this idea famous.
The Pythagorean Winning % approach uses the relationship between a team's victories and losses and the number of points scored and allowed to calculate the predicted winning percentage. To follow Pythagorean winning percentages for the seasons, consult the team statistics.
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an astronomer observes a magnitude 18 star, but needs 10 times as many. what's the faintest star he can see and still get enough photons.
As according Scientific American, even one photon can result in a visible burst of light.
How so many photons are necessary for you to see a star?The human eye can see about 10 photons.To an eye accustomed to the dark, the weak light may appear to be flashing, yet each twinkling just represents a few photons.When shooting images of the cosmos from orbit with very sensitive equipment at very low temperatures, a photon stream would be sufficient.
Can you see a single photon?The answer is yes because the receptors in the retina can respond to a single photon.However, brain filters only allow a signal to pass through and activate the brain when five to nine additional signals do the same in less than a hundred milliseconds.
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A car traveling at a constant speed covers a distance of 750 m in 25 s.What is the cars speed
Answer:
30 m/s
Explanation:
Answer:
The speed is equal to Distance divided by Time.
The SI Unit of Speed is m/s or meters per second.
V = S/T
= 750/25
= 30 m/s
4. What is the frequency of an electromagnetic wave if it has a wavelength of 1.0 km?
The radio wave's wavelength is 1.0 m. A waveform signal that is carried in space or down a wire has a wavelength, which is the separation between two identical places (adjacent crests) in the consecutive cycles.
Calculation:The following formula was used to determine the frequency:
radio wave speed, c = radio wave frequency / radio wave length
c = f x λ
Because a radio wave is an electromagnetic wave and travels at the same speed as light, its speed, c = 3 x 108 m/s, is equal to the speed of light in this case.
When the formula
3 x 108= f x 1.0
f = 3 x 108/1
f = 3 x 108 Hz is used,
Radio waves therefore have a frequency of 3 x 108 Hz.
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the effect of a stress raiser is more significant for which of the following types of materials?
a Ductile
b.Gaseous
c Volatile
d. Brittle
Option A is the correct Answer. The effect of a stress raiser is more significant for Ductile materials.
Ductility is the ability of a material to be drawn or plastically deformed without fracture. The ductility of steels varies depending on the types and levels of alloying elements present.
Examples: aluminum, copper, and magnesium alloys.
Uses of Ductile materials:
Ductility is mostly used in metalworking, as materials that crack, break or shatter under stress cannot be manipulated using metal-forming processes such as hammering, rolling, drawing, or extruding.High degrees of ductility occur due to metallic bonds, which are found predominantly in metals; this leads to the common perception that metals are ductile in general.The ductility of steel varies depending on the alloying constituents. Increasing the levels of carbon decreases ductility.To know more about Ductile materials:
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A copper rod of length 0.77 m is lying on a frictionless table (see the drawing). Each end of the rod is attached to a fixed wire by an unstretched spring that has a spring constant of k = 76 N/m. A magnetic field with a strength of 0.14 T is oriented perpendicular to the surface of the table.
(a) What must be the direction of the current in the copper rod that causes the springs to stretch?
The current flows (left-to-right/right-to-left) in the copper rod.
(b) If the current is 14 A, by how much does each spring stretch?
________ m
Answer:
a) The direction of the current in the copper rod that causes the springs to stretch is left-to-right. This is because the magnetic field is oriented perpendicular to the surface of the table and the force exerted on the rod by the magnetic field is given by F = qVB, where F is the force, q is the charge of the particle, V is the velocity of the particle, and B is the strength of the magnetic field. Since the force is perpendicular to the velocity of the particle, the direction of the current that produces this force must be parallel to the magnetic field. In this case, the magnetic field is oriented perpendicular to the surface of the table, so the current must flow in the direction left-to-right to produce a force that stretches the springs.
b) To find by how much each spring stretches, you can use the formula F = kx, where F is the force exerted by the spring, k is the spring constant, and x is the distance the spring stretches. In this case, the force exerted by the spring is given by F = qVB, and the spring constant is k = 76 N/m. The charge of the particle is q = Ie, where I is the current and e is the charge of an electron. The velocity of the particle is V = L / t, where L is the length of the rod and t is the time it takes the particle to travel the length of the rod. Since the current is 14 A and the length of the rod is 0.77 m, the velocity of the particle is V = 0.77 m / (1 / 14 A) = 10.78 m/s. The strength of the magnetic field is 0.14 T, so the force exerted by the spring is F = (14 A)(1.60 x 10^-19 C)(10.78 m/s)(0.14 T) = 2.40 x 10^-17 N. Therefore, the distance each spring stretches is x = F / k = 2.40 x 10^-17 N / 76 N/m = 3.16 x 10^-19 meters.
What is the wavelength of longitudinal wave
Press the hotspot that indicates the location that a string will experience the least tension during vertical circular motion. Assume that the speed of the ball remains constant.
which one will experience the least tension t3 t2 t1 or t4
The least tension will be experienced by T3
The weight of a moving object causes tension, which is the force applied along the length of a string, rope, or cable. The force that maintains an object moving in a circular direction when it is in a vertical circular motion is called tension. Perpendicular to the circle's radius, the tension in the string is pointed in the direction of the circle's centre.
Due to the centripetal force required to maintain the object moving in a circular motion, the tension in the string varies as the object moves in a vertical circle, with the highest tension occurring at the top of the circle and the least tension occurring at the bottom. In the given case, T3 will experience the least tension during vertical circular motion, assuming that the speed of the ball remains constant. This is because T3 is the point on the string that is closest to the circle's centre, and thus is subject to the least amount of tension as the ball moves in a vertical circle.
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Of the following objects, on which one would time on its surface run most slowly?
a. An object with the same mass as the Sun but twice as large in radius
b. The Sun
c. An object with the same mass as the Sun but only half as large in radius
The time on the surface of an object would run most slowly on an object with the same mass as the Sun but twice as large in radius.
What is mass?
Mass is a measure of the amount of matter in an object and is typically expressed in kilograms (kg). It is an intrinsic property of matter and is different from weight, which is a measure of the force of gravity acting on an object. Mass is an important factor in determining the physical properties of an object, such as density, momentum, and inertia. Mass is also used to calculate the gravitational force between two objects, as well as the energy required to move it.
This is because the surface gravity of an object is inversely proportional to the square of its radius. Therefore, the object with the same mass as the Sun but twice as large in radius would have a much lower surface gravity, and time would run more slowly on its surface.
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What type of resource is solar and wind?
Solar and wind are renewable resource types.
A renewable resource is an energy source that comes from nature. This is renewable and unlimited. It can be created by utilizing increasingly sophisticated technological developments so that it can become an alternative energy source.
Apart from solar and wind power, renewable energy can also be obtained from hydropower, geothermal, biomass, solar power, wind power, sea heat, waves, and tidal.
Some of the benefits of renewable resources are:
• Minimizing the effects of global warming
• Unlimited energy sources
• Save resources as well as expenses
• In several countries it can create jobs and opportunities
• Easier and cheaper maintenance
• Some technologies are easy to implement in remote areas.
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The hammer throw is a track-and-field event in which a 7.1-kg ball (the ''hammer''), starting from rest, is whirled around in a circle several times and released. It then moves upward on the familiar curving path of projectile motion. In one throw, the hammer is given a speed of 26.0 m/s. For comparison, a .22 caliber bullet has a mass of 2.6 g and, starting from rest, exits the barrel of a gun with a speed of 403 m/s. Determine the work done to launch the motion of both the hammer and the bullet.
The work done to launch the motion of both the hammer and the bullet are 3.1×10³ Joule and 2.2×10² Joules respectively.
As we know,
Work = Kinetic Energy
= (0.5)(mv^2)
For Work in Joules, the mass is in units of Kg, and the velocity is in units of m/s.
KE(hammer) = 1/2mv^2 = 1/2 x 7.3 x (29)^2 = 3.1 x 10^3 J
and KE(bullet) = 1/2mv^2 = 1/2 x 2.6 x 10^-3 x (410)^2 = 2.2 x 10^2 J
To solve this problem, we must assume that energy is conserved. (This isn't stated in the problem, and is not true in general in these real-world examples, however we must assume conservation of energy in order to solve the problem with the information given).
When an object moves while a force is being exerted on it, then work is being done on the object by the force. If an object moves through a displacement d while a constant force F is acting on it, the force does an amount of work equal to W = F · d = F d cos φ where φ is the angle between d and F.
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A 2.5-kg cart is rolling along a frictionless, horizontal track towards a 1.3-kg cart that is held initially at rest. The carts are loaded with strong magnets that cause them to attract one another. Thus, the speed of each cart increases. At a certain instant before the carts collide, the first cart's velocity is 4.6 m/s, and the second cart's velocity is -1.8 m/s. (a) What is the total momentum of the system of the two carts at this instant
The required total momentum of the system at this instant is calculated to be 9.16 kg m/s.
Given that,
Mass of the first cart, m₁ = 2.5 kg
Mass of the second cart, m₂ = 1.3 kg
Velocity of the first cart before collision, u₁ = 4.6 m/s
Velocity of the second cart before collision, u₂ = -1.8 m/s
The total momentum of the system before collision is calculated as follows,
P t = P₁ + P₂
P t = m₁ u₁ + m₂ u₂ = 2.5 × 4.6 + (1.3 × -1.8) = 11.5 - 2.34 = 9.16 kg m/s
Thus, total momentum of the system of the two carts at this instant is 9.16 kg m/s.
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A certain light truck can go around a flat curve having a radius of 150 m with a maximum speed of 34.5 m/s. With what maximum speed can it go around a curve having a radius of 60.0 m
With 20.23 ms⁻¹, maximum speed can it go around a curve having a radius of 60.0 m
What's the maximum speed?The highest rate of speed a person can reach is called maximum speed. When athletes alter the magnitude (how quickly they are moving) or direction (or both) of their motion, or both, their acceleration changes as well since acceleration is related to velocity, which has both a magnitude and a direction connected with it.
ac max = V² max / R ....(1)
Inserting given values we get
ac, max = (34.5)² / 150 = 7.935 ms⁻²
For a changed radius of the curve of 60.0 m, the maximum safe speed from (1) becomes
Unew, max= √ac, max R new
Unew, max = √6.826 x 60
Unew, max 1 = 20.23 ms⁻¹, rounded to one decimal place.
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The scale on a map states that 1 centimeter corresponds to 20 kilometers. On the map, two cities are 0.3 cm apart. Find the actual distance.a.6 kmc.0.6 kmb.600 kmd.60 km
The actual distance is 6 km. The solution to the problem is as follows: By ratio and proportion: 1:20 = 0.3:x, Cross multiplying: 20(0.3) = x, x = 6
Therefore the answer is the first choice or letter A which is 6 km.
How would a surface without friction feel?It just seems slick, almost like touching ice but without the frigid sensation, according to my firsthand experience of both. Sorry, it's really nothing exceptional. Any surface would be sufficient if it had some lubrication oil on it.
Is there any surface in the world without friction?In reality, there are no frictionless planes. If they did exist, items on them would almost certainly behave exactly as Galileo predicted if they did. Despite not existing, they are extremely valuable for designing things like engines, motors, roads, and even tow truck beds, to mention a few.
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Find the gravitational force between Jupiter and its natural satellite Callisto. The mass of Jupiter is
1.99 x 10^27 kg and the mass of Callisto is 1.08 x 10^23 kg. The distance between Jupiter and
Callisto is 1.88 x 10^9m.
The gravitational force between Jupiter and its natural satellite Callisto is 3.76×10∧21 Newton.
What exactly is the gravitational force?The attraction force that exists in between two masses is directly proportional to the product of their mass and is inversely related to the square of the distance between them, according to Newton's universal law of gravitation.
The mass of Jupiter is 1.99 x 10^27 kg
the mass of Callisto is 1.08 x 10^23 kg
By using the formula
F = G M1×M2/ r²
(G = 6.67×10∧-11 )
F = ( 6.67×10∧-11 ×1.99 x 10^27 × 1.08 x 10^23 ) / (1.88 x 10^9)²
F = (13.28×10∧39)/3.534×10∧18
F =3.76×10∧21 Newton.
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During a walk-around inspection, ensure there are no cracks on the brake drums that are more than ____ of the width of the friction area.
It's crucial to inspect the brake drums as part of your walk-around examination before setting off on a journey. If any brake drum has a crack that is more than half the breadth of the friction region.
What causes brake drums to crack?Overheating and undercooling of the brake pedal during operation might result in cracked drums.
What should you do if the brake drum develops a crack?Drums with cracks need to be changed right away. Blue ground -High temperatures, braking imbalance, abrupt stops, dragging brakes, or glazed brake pads can all result in blue drums. If no cracks have appeared, blue drums can still be utilized.
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Justine is ice-skating at the Lloyd Center. What is her final velocity if she accelerates at a rate of 2. 0 m/s for 3. 5 seconds?
2. How long would it take Jesse with an acceleration of -2. 50 m/s2 to bring his bicycle with an initial velocity of 13. 5 m/s to a complete stop?
When Justine is ice-skating, her final velocity if she accelerates at a rate of 2.0 m/s² for 3. 5 seconds is 7 m/s and it would take Jesse 5.4 seconds to stop the bicycle moving at an initial velocity of 13.5 m/s by accelerating at -2.50 m/s².
To find Justine's final velocity, we can use the equation:
v = u + at
where v is the final velocity, u is the initial velocity (which is assumed to be 0 in this case), a is the acceleration, and t is the time. So
v = 0 + (2.0 m/s²) × (3.5 s) = 7.0 m/s
To find the time it would take for Jesse to bring his bicycle to a stop, we can use the equation:
v = u + at
where v is the final velocity (which is assumed to be 0 m/s in this case as bicycle is brought to a stop), u is the initial velocity, a is the acceleration, and t is the time.
Given that a = -2.5 m/s² (negative sign indicates deceleration) and u = 13.5 m/s.
so t = (v - u) / a = (0 - 13.5 m/s) / -2.5 m/s² = 5.4 seconds
It would take Jesse 5.4 seconds to bring his bicycle to a complete stop.
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(TCO A) The primary reason for networking standards is to
Student Answer:simplify cost accounting for networks. Make it more difficult to develop hardware and software that link different networks. Ensure that hardware and software produced by different vendors can work together. Ensure that all network components of a particular network can beprovided by only one vendor. Lock customers into buying network components from one vendor
Make sure that software and hardware developed by various manufacturers can cooperate.
What exactly do vendors mean?A vendor is generally anybody who buys and sells goods or services. A vendor purchases products and services to resale them to different companies or individuals. Several different vendors provide the goods that big box stores like Target buy at deep discounts and then resale at higher retail rates.
The five major types of vendors are manufacturers, wholesalers, merchants, services and maintenance providers, independent vendors, and trade show representatives. Suppliers are sometimes referred to as the first link in a supply chain because they exclusively conduct business with other businesses. Contrarily, a vendor is a business or person that purchases things from a company and then sells them to another party.
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An object that is moving in a circle at a constant speed has a velocity vector that is directed ________and an acceleration vector that is directed ________.
A directed velocity vector and a directed velocity acceleration vector characterise an item travelling in a circle at a constant speed.
When an item is travelling in a circle at a constant speed, what is its acceleration?Consequently, an object travelling in a circle at constant speed is speeding up its approach to the circle's centre. Centripetal acceleration is the term used to describe the speed toward the centre of the circle.
What happens to an object's velocity when it rotates in a circle at a constant speed?There is a fluctuating velocity for an object in a circular orbit travelling at a constant speed. Considering that velocity is a vector quantity that depends on both speed and direction, this makes sense. Accelerating is the object in orbit.
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A block of substance has a width of 4.9 cm, a length of 5.1 cm, and height of 1.9 cm . Its mass is 0.54 kg. Calculate the density of the substance.
The 4.7 g/cm3 is the density of the substance.
What is density ?
How tightly something is packed can be used to gauge a material's density. Formally, it is defined as the mass per unit of volume. Formula for Density or Density Symbol: D D = m/V, where m is mass and V is volume, stands for density.
What is mass ?
The most basic characteristic of matter, it is one of the fundamental quantities in physics. As a way to gauge how much matter is there in a body, we might use the term mass. Kilograms are the SI unit of mass (kg).
density = mass of sample/ volume of sample
mass = 1.5 kg = 1500 g
volume = W*L*H
Vol = 3.2*17.1*5.8 cm3 = 317.376 cm3
Now,
D = mass/V = 1500/317.376
D = 4.726255 g/cm3
=4.7 g/cm3
Therefore, 4.7 g/cm3 is the density of the substance.
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Two spheres A and B of mass 6. 5 kg and 8. 3 kg, respectively, are separated by a distance of 0. 56 m. (a) Calculate the magnitude, in N, of the gravitational force A exerts on B and B exerts on A. Force A exerts on B N force B exerts on A N (b) If the force between the spheres is now 3. 50 10-9 N, how far apart are their centers, in meters
Add the x- and y-component squared values together, then take the square root of the result to determine the force's magnitude.
The distance between a vector's starting point P and ending point Q is its magnitude. The magnitude of PQ is represented symbolically as | PQ |. The Distance Formula can be used to determine a vector's magnitude if its start and end points' coordinates are known. We must add together all the forces acting on the item in the x and y directions in order to calculate the net gravitational force. The square root of the sum of the squares of these two values is then used to calculate.
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A toy elevator is raised from the ground floor to the second floor in 20 seconds. The power needed using 1000 J of work, is
A toy elevator is raised from the ground floor to the second floor in 20 seconds. The power needed using 1000 J of work, is 50 W, the calculation is like 1000J of work / 20 seconds = 50W.
Power is measured in Watts (W) which is a unit of energy per time. This means that when you divide the total energy (1000J) by time (20 seconds) it will give you the power (50W). In other words, power is the rate at which energy is expended over a given period of time. The higher the power, the faster the elevator will go. In this case, 1000J of work divided by 20 seconds gives you a power of 50W, which is enough to move the elevator from the ground floor to the second floor in 20 seconds.
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A brain-imaging method using radio waves and magnetic fields of the body to produce detailed images of the brain is called __________.
Magnetic Resonance Imaging is a technique for producing precise pictures of the brain that uses radio waves and the magnetic fields of the body.
What imaging processes make use of magnetic fields and radio waves?A magnetic field and radio waves produced by a computer are used in the medical imaging procedure known as magnetic resonance imaging (MRI), which produces precise pictures of your body's organs and tissues.
Describe an MRI picture.The noninvasive medical imaging procedure known as magnetic resonance imaging, or MRI, creates precise pictures of virtually every internal bodily structure, including the organs, bones, muscles, and blood arteries. A sizable magnet and radio waves are used in MRI scanners to produce pictures of the human body.
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2.1 The sketch below shows a large suitcase with a mass of 32 kg rests on a rough incline at an angle of 30 to the ground. 2.1.1 Define normal force in words. 2.1.2 Draw a labelled free-body diagram of all the forces acting on the suitcase. 2.1.3 Calculate the magnitude of the force of friction that keeps the suitcase stationery on the incline. (2) (3) (3) 2.1.4 Calculate the coefficient of static friction between the suitcase and the incline, if the suitcase is just about to move on the incline. (3)
Answer:
Explanation:
1) Normal force is the upward force applied by the ramp (incline) on the suitcase as the reaction to the downward force of the Weight (Fg) of the suitcase
2) sorry, can't supply a FBD. Brainly doesn't have drawing tools available.
3) Fg = mg = (32 kg)(9.8 m/s²) = 313.6 N
N= y-component of Fg = cos30(313.6 N) = 271.6 N
Ff = (coeff. friction)(N)
3) Ff = x-component of Fg = sin30(313.6) = 156.8 N
4) coeff. friction = Ff/N = 156.8N/271.6N = 0.58
Matt i a 85kg lifeguard, he lide down a water lide that i inclined at 35 degree to the horizontal into a wimming pool. If the coefficient of kinetic friction of the lide i 0. 9. What i Matt’ rate of acceleration a he goe down the lide
The rate of acceleration at which Matt goes down the slide is equal to 5.32 m/s².
The normal force or [tex]F_{N}[/tex] acts perpendicular to the object.
The angle of inclination = 35°
cosθ = [tex]F_{N}[/tex]/mg
[tex]F_{N}[/tex] = mgcosθ = 85 × 10 × cos 35
= 850 × 0.819 = 696.15 N
To find the force of friction,
μ = 0.050
[tex]F_{f}[/tex] = μ × [tex]F_{N}[/tex]
= 0.050 × 696.15 = 34.80 N
To find the downward component of weight that pulls him down the slide.
sinθ = [tex]F_{d}[/tex]/mg
[tex]F_{d}[/tex] = mgsinθ
= 85 × 10 × sin35
= 850 × 0.5736 = 487.56 N
To find the acceleration,
[tex]F_{net} = F_{d} - F_{f}[/tex]
= 487.56 - 34.80 = 452.76 N
To solve for acceleration,
F = force = 452.76 N
m = mass = 85 kg
Force = mass × acceleration
a = F/m = 452.76/85 = 5.32 m/s²
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Two speakers are driven by the same amplifier. The first speaker is placed in the origin, the second one is free to move along the x-axis (see figure). A receiver is placed on the on the y-axis, a distance L from the origin. The speakers emit sound at frequency f, the velocity of sound in the air is v. The second speaker is initially in the origin and it is the slowly moved toward the positive x-axis. Write the results in terms of L, f, and v.
a) What is the wavelength of the sound waves in the air?
b) Find the first position x of the second speaker at which the receiver does not get any sound (destructive interference).
c) Find the first position x of the second speaker at which the receiver gets maximum intensity (constructive interference). Exclude the x=0 position
The results in terms of wavelength, velocity, and frequency i.e (L,f,v) are as follow,.
(a) λ = v/f
(b) The value of the first minimum will be [tex]x =\sqrt{\frac{v^2}{4 f^2}+\frac{v L}{f}}[/tex]
(c) The position for the first maxima of 2nd speaker = [tex]$$x=\sqrt{\frac{v}{f}\left(\frac{v}{f}+2 L\right)}$$[/tex]
A waveform signal that is carried in space or down a wire has a wavelength, which is the separation between two identical places (adjacent crests) in the consecutive cycles. This length is often defined in wireless systems in meters (m), centimeters (cm), or millimeters (mm) (mm).
(a) Relation among velocity, wavelength and frequency can be defined the expression: v = fλ
From above, we can write, (λ) (wavelength) can be equal to velocity (v) / Frequency (f)
So, λ = v/f
(b) path difference can be determined by using the expression: [tex]\Delta x=x_2-x_1 \\[/tex]
[tex]\Delta x=\sqrt{L^2+x^2}-L\end{aligned}$$[/tex]
So, for the first minimum, we can conclude the following:
[tex]$\left\{n x=\frac{d}{2}=\frac{v}{2 f}\right.$$$\frac{v}{2 f}=\sqrt{L^2+x^2}-L$$[/tex]
[tex]\left(\frac{v}{2 f}+L\right)^2 & =L^2+x^2 \\\\x^2 =\frac{v^2}{4 f^2}+L^2+\frac{v L}{f}-L^2 \\\\x =\sqrt{\frac{v^2}{4 f^2}+\frac{v L}{f}}[/tex]
(c) for first order maxima
[tex]$$\begin{aligned}& \Delta x=\lambda \\& \frac{v}{f}=\sqrt{L^2+x^2}-L\end{aligned}$$[/tex]
[tex]$$\begin{aligned}x^2 & =\frac{v^2}{f^2}+L^2+\frac{2 V L}{f}-L^2 \\x & =\sqrt{\frac{v^2}{f^2}+\frac{2 v L}{f}}\end{aligned}$$[/tex]
So, the position for the first maxima of 2nd speaker will be:
[tex]$$x=\sqrt{\frac{v}{f}\left(\frac{v}{f}+2 L\right)}$$[/tex]
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The missing diagram is attached below: