The speed of the air flowing into the room (in ft/s) is equal to 0.944 when air flows through a heating duct with a square cross-section with 6-inch sides at a speed of 5.9 ft/s.
By the equation of continuity
(Rate of volumetric flow rate is constant)
A1v1 = A2v2
(6×6)×5.9(inch2ft/sec) = (15×15)×v2
V2 = 4.5(81/169) ft/sec
V2 = 0.944 ft/sec
In contrast to velocity, which describes the speed and direction of an object's movement, speed is the rate of movement along a path. Alternatively, velocity is a vector while speed is a scalar quantity. For instance, the speed of a car on a road is shown by 50 km/h (31 mph), but the velocity is indicated by 50 km/h west.
Physicists employ the fundamental units of speed and velocity to express how things move through space, time, and in a particular direction.
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When does one's body start storing fat either by increasing the number of fat cells or by increasing the size of existing fat cells?
When one's body starts storing fat, both the number of fat cell and the size of existing fat cells increases.
What is the process of fat tissue growth and development in humans?Adipose tissue expands during infancy and adolescence as a result of an increase in fat cell quantity and, to a lesser extent, fat cell size. In spite of a significant turnover (about 10% of the fat cells every year) when body weight is stable, the number of fat cells in adults remains constant over time.
In adults, losing weight primarily affects fat cell size (making them smaller), whereas gaining weight results in an increase in fat cell size and quantity. The bone marrow is a significant source of fat cell regeneration during the course of a person's lifetime. This is most noticeable in obesity, when around 20% of all fat cells are produced from bone marrow.
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a thermistor is a temperature sensor that contains metallic wire that changes its electrical resistance when the temperature changes
A thermistor is a type of temperature sensor that uses metallic wire to modify its electrical resistance in response to variations in temperature. Temperature can be used to define a metal's resistance.
What are the different varieties of thermistors?The resistance of thermistors is significantly more temperature-dependent than that of conventional resistors. The words thermal and resistor are combined to form the word thermistor. The conduction model used to classify thermistors.
Why are thermistors used?A thermistor's basic task is to gauge a device's internal temperature. The thermocouple is a minor but crucial component of a bigger system in a temperature-controlled system. The thermistor's temperature is kept under observation by a controller.
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A ball is tossed straight up from the surface of a small, spherical asteroid with no atmosphere. The ball rises to a height equal to the asteroids radius and then falls.
What forces if any act on the ball while it is traveling up?
A: Only a decreasing gravitational force that acts downward
B: Only a constant gravitational force that acts downward
C: Both a constant gravitational force that acts downward and a decreasing force that acts upward
D: No forces act at all
A: Only a decreasing gravitational force that acts downward
From Newton's gravitational law, the force between two objects (a planet) is directly proportional to the product of their masses and inversely proportional to the square of their distance apart.
What does gravity mean?The force of attraction between any two bodies is directly proportional to the product of their masses and is inversely proportional to the square of the distance between them, according to Newton's universal law of gravitation.
What is the name of Newton's law of gravity?Every particle in the cosmos attracts every other particle with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between their centers, according to Newton's law of universal gravitation.
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8. The horizontal and vertical components of a velocity are 46.1 m/s and 62.5 m/s respectively. What is the magnitude and direction of the velocity? Answer: 77.7 m/s, 53.6°
Answer:
The magnitude of the velocity is 77.7 m/s, and the direction is 53.6°.
Explanation:
To find the magnitude and direction of the velocity, we need to use the Pythagorean theorem and trigonometry. The magnitude of the velocity is given by the square root of the sum of the squares of the horizontal and vertical components:
magnitude = sqrt(46.1^2 + 62.5^2)
magnitude = 77.7 m/s
The direction of the velocity is given by the arctangent of the vertical component divided by the horizontal component:
direction = atan(62.5 / 46.1)
direction = 53.6 degrees
Thus, the magnitude of the velocity is 77.7 m/s, and the direction is 53.6°.
A car travels 10 miles east in 30 minutes. What is the car's velocity in miles per hour
Answer:
20 mph
Explanation:
10 miles per 30 minutes is the same as 10 miles per 0.5 hours
Constant Velocity [tex]= \frac{distance}{time} = \frac{10 miles}{0.5 hours}[/tex] = 20 miles per hour = 20 mph
although we have discussed single-slit diffraction only for a slit, a similar result holds when light bends around a straight, thin object, such as a strand of hair. in that case, a is the width of the strand. from actual laboratory measurements on a human hair, it was found that when a beam of light of wavelength 632.8 nm was shone on a single strand of hair, and the diffracted light was viewed on a screen 1.25 m away, the first dark fringes on either side of the central bright spot were 5.22 cm apart.
The width of the stand is [tex]d=30.306*10^{-6}m[/tex].
Young's Double Slit Experiment:
The presence of overlapping waves is unmistakably demonstrated by interference effects. Thomas Young proposed that light is a wave that is subject to the superposition principle. His greatest experimental accomplishment was to show that light may interfere in both a positive and negative way (c. 1801). A laser evenly illuminates two parallel slits in an otherwise opaque surface in a contemporary adaptation of Young's experiment, which differs from the original experiment only in the source of light. On a faraway screen, the light traveling through the two openings may be seen. The geometrical optics laws are upheld and the light produces two shadows and two illuminated zones on the screen when the slit widths are much larger than the light's wavelength.
Young's Double Slit formula,
[tex]Y = \frac{\lambda L}{d}\\[/tex]
where,
d = width of stand = ?
λ = wavelength = 632.8 nm = 6.328 × 10⁻⁷ m
L = Screen to hair distance = 1.25 m
Y = Width of central maxima = 5.22 cm = 0.0522 m
Therefore,
[tex]d = 2\frac{\lambda L}{Y}[/tex]
[tex]d=2\frac{(1.25)(632.8*10^{-9})}{0.0522}[/tex]
[tex]d=30.306*10^{-6}m[/tex]
Hence,
The width of the stand is [tex]d=30.306*10^{-6}m[/tex].
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14. Battery potential is 12 volts and current is 2.7 amps. What's the resistance?
Answer:
4.44 ohms
Explanation:
To find the resistance of a circuit, you can use Ohm's law, which states that the resistance of a circuit is equal to the voltage across the circuit divided by the current through the circuit. So in this case, the resistance would be 12 volts / 2.7 amps = 4.44 ohms.
An airliner arrives at the terminal, and the engines are shut off. The rotor of one of the engines has an initial clockwise angular speed of 1940 rad/s. The engine's rotation slows with an angular acceleration of magnitude 79.3 rad/s2. (a) Determine the angular speed after 10.0 s. (b) How long does it take the rotor to come to rest?
The angular speed after 10.0 seconds is approximately 2733 rad/s. it takes approximately 24.5 seconds for the rotor to come to rest.
In this problem, we are given the initial angular velocity of a rotor (1940 rad/s) and its angular acceleration (79.3 rad/s^2). We are asked to find the angular velocity after 10.0 seconds and the time it takes for the rotor to come to rest. To find the angular velocity after 10.0 seconds, we can use the formula omega_f = omega_i + alpha*t, where omega_f is the final angular velocity, omega_i is the initial angular velocity, alpha is the angular acceleration, and t is the time elapsed.
Plugging in the given values, we find that the final angular velocity is approximately 2733 rad/s. To find the time it takes for the rotor to come to rest, we set the final angular velocity to 0 and solve for t. We can use the same formula as before: omega_f = omega_i + alpha*t. Plugging in the values for omega_i and alpha, we find that it takes approximately 24.5 seconds for the rotor to come to rest.
In summary, the angular velocity of the rotor after 10.0 seconds is approximately 2733 rad/s, and it takes approximately 24.5 seconds for the rotor to come to rest.
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The 2.7-cm-diameter solenoid in (Figure 1) passes through the center of a 6.0-cm-diameter loop. The magnetic field inside the solenoid is 0.30 T .
A. What is the magnetic flux through the loop when it is perpendicular to the solenoid?
B. What is the magnetic flux through the loop when it is tilted at a 60 angle?
A. The magnetic flux through the loop, when it is perpendicular to the solenoid, is approximately 8.49 Weber (Wb).
B. The magnetic flux through the loop, when it is tilted at a 60-degree angle, is approximately 4.24 Weber (Wb).
A:
To find the magnetic flux through the loop when it is perpendicular to the solenoid, we can use the formula for magnetic flux:
[tex]\phi=BAcos(\theta)[/tex]
The area of the loop is given by:
[tex]A=\pi(d/2)^2[/tex]
B = 0.30 T and d = 6.0 cm
The magnetic flux is given as:
[tex]\phi= 0.30T\times (\pi \times (6/2)^2\\\phi=8.49\ Wb[/tex]
B:
To find the magnetic flux through the loop when it is tilted at a 60-degree angle, we need to consider the new angle (θ = 60 degrees) between the magnetic field and the loop's normal vector.
The magnetic flux:
[tex]\phi=0.30*(\pi*(6/2)^2)cos(60^o)\\\phi=4.24\ Wb[/tex]
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in music, two notes are said to be an octave apart when one note is exactly twice the frequency of the other. suppose you have a guitar string playing frequency
The wave length will be cut in half (1/2) in order to raise the frequency up one octave to 2f0.
What does energy frequency mean?In conclusion, waves transport energy. Their frequency and amplitude both affect how much energy they transport. The amount of energy increases with frequency and amplitude, respectively.
Briefing:The given parameters;
initial frequency, = F₀
final frequency, = 2F₀
Let the initial wave length = λ₁
Let the final wave length = λ₂
The formula for the connection among frequency and wavelength is;
To attain a twofold frequency, the wave's length must be reduced as shown below;
The wave length will thus be cut in half (1/2) in order to raise the frequency up one octave to 2f0.
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a current - carrying wire is pulled away from a conducting loop in the direction shown. As the wire is moving, is there a cw current around the loop, a ccw current or no current? Show the induced field and give clear explanation to your answer.
If the current increases continuously, then the direction of the induced current in the loop is clockwise.
A compass needle put above a straight wire carrying current points north (the magnetic south pole), hence the magnetic field at that location is towards geometric south, and using the right hand thumb rule, we can determine that the direction of the current is east. A counterclockwise current will be produced (ccw). The size of the loop shrinks as the bar ascends through the zone of constant magnetic field, and as a result, the flux through the loop also shrinks.
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the stellar spectral classification system used today depends primarily on which of the following parameters?
The temperature of the stellar photosphere, which is the outer layer that extends into the stellar surface, is a key factor in determining spectral types. A star's mass affects the star's actual temperature.
The hotter the star, which is likewise related to the colour of the star, the higher the mass. The Morgan-Keenan (MK) classification is the current system of classification. According to the following explanation, each star is given a spectral class using Roman numerals (from the earlier Harvard spectral classification, which excluded luminosity), as well as a luminosity class. A star's photosphere is its outer layer, where light is emitted. The word "light sphere" is formed from the words "light" and "sphere," referring to a sphere-shaped surface that appears to produce light.
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A block is initially sliding along a surface of negligible friction with a speed v0. A constant force F0 is then exerted on the block. Which of the following figures represents the situations in which the kinetic energy of the block will initially decrease? Select two answers.AThe figure presents a block on a horizontal flat surface. The block is moving to the right with a velocity v sub 0. A force, F sub 0, points upwards and to the right.BThe figure presents a block on a horizontal flat surface. The block is moving to the right with a velocity v sub 0. A force, F sub 0, points upwards and to the left.CThe figure presents a block on a horizontal flat surface. The block is moving to the right with a velocity v sub 0. A force, F sub 0, points downwards and to the right.DThe figure presents a block on a horizontal flat surface. The block is moving to the right with a velocity v sub 0. A force, F sub 0, points downwards and to the left.
Answer:b and d
Explanation:
cus they go opposite direction
What does an oscilloscope measuring electric current display
A. How resistance changes over time
B. How power changes over time
C. How current changes over time
D. How voltage changes over time
Three boxes are pushed on a floor with a constant force of magnitude F applied to box A. The boxes move to the right with an acceleration of 1.5 m/s2. The coefficient of kinetic friction between the bottom of a block and the floor is 0.4. 2.0 kg B 1.0 kg 3.0 kg What is the magnitude of the force that block B applies to block C? A) 1.5 N B) 4.5 N C) 7.3N D) 16.3 N E) There is not enough information to tell.
The magnitude of the force that block B applies to block C is 16.3 N .
Calculation :
Frictional force of this combination = 0.4*9.8(Ma + Mb)
= 0.4*9.8*3
F(ab)= 11.76 N
F(AB) = Net force of this combination = 3*1.5 = 4.5 N
since block ' c ' is also moving with the same acceleration ,
Net force on C by B = F - (F(ab) +F(AB) )
= 32.52 - (11.76 + 4.5)
= 32.52 - 16.26
= 16.3 N
The word "force" has a precise meaning. At this level it is appropriate to describe the force as pushing or pulling. A force does not contain or "have within" an object. A force is applied from one object to another. The idea of force is not limited to animate and inanimate objects.
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we will model the spine and upper body as a horizontal rigid rod of uniform density with a length of 50.0 cm and a mass of 40.0 kg. assume that the person attempts to lift an object with their arms, which we will model as attached at the far end of the rod. support of the back in this position is provided primarily by the erector spinalis muscle which we will model as being attached at one end to the spine at a point 33.0 cm from the hip at an angle of 10
Tension in the back muscle for this scenario is 3095.4 N and the compressive reaction force is 3048 N, and the ratio is 5.53.
Strings exert forces on object they are connected to Cables and ropes act the same way.The strings exert forces due to their tension, The ends of the string both exert a force of magnitude T on the supports where they are connected. T is the tension in the string.
Two forces are acting on the compartment, Gravity acting downward, Tension T in cable acting upward.
A) In equilibrium net torque about the hip = 0
T*sintheta*x - Fgup*L/2 - Fgob*L = 0
T*sin10*0.33 - 40*9.8*0.5/2 - 16.2*9.8*0.5 = 0
Tension(T) = 3095.4 N
B) Fv = FRx = T*costheta
Fv = 3095.4*cos10
= 3048 N
C) Fv/(wub + wobj) = 3048/((40+16.2)*9.8) = 5.53
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the speed of light in glass is group of ___answer choices: same as in a vacuum. smaller than that in air. unchanged from that in air. larger than that in air.
The speed of light in glass is SLOWER than that in air. Therefore, the correct answer is the second option: smaller than that in air.
The speed of light is a universal constant used and considered in many areas of physics. It is equal to 299,792,458 meters per second or 186,000 miles per second. That speed is measured in a vacuum.
Light travels faster in a medium that has a lower refractive index. Generally, the denser a medium is, the higher its refractive index is. Glass is obviously denser than air, which means it has a higher refractive index. Thus, light travels slower in glass than in air.
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compared with the usual classical measurement of momentum for a high-speed object, momentum measured relativistically
Momentum measured relativistically is greater than momentum measured classically for an object travelling at a high speed.
When there is no net external force acting on a system, momentum is preserved according to classical mechanics. As a result, momentum conservation can be used as a fundamental technique to study collisions. Since relativistic momentum is conserved, a lot of what we know about subatomic structure comes from studying the collisions of relativistic particles created by accelerators. The perceptual sense of classical momentum and relativistic momentum are identical. Large masses moving at high speeds are best for it. The conservation of momentum is guaranteed in all inertial frames by the definition of relativistic momentum. Relativistic momentum is conserved whenever a system has zero net external force, just like it is for classical momentum.
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based on galactic rotation curves and cluster dynamics, we think dark matter based on galactic rotation curves and cluster dynamics, we think dark matter will have no effect on the fate of the universe. comprises over 90% of the entire mass of the universe. will doom the universe to collapse, overcoming the redshifts we now observe. is a minor component of the entire mass of the universe. is best detected from the x-rays it produces in the intergalactic medium.
Based on galactic rotation curves and cluster dynamics, we think dark matter comprises over 90% of the entire mass of the universe.
Galactic Rotation Curves:
The rotation curve of a disc galaxy is a representation of the orbital speeds of the visible stars or gas in that galaxy against their radial distance from the galaxy's center (also known as a velocity curve).
Dark Matter:
Since dark matter is made up of particles that do not absorb, reflect, or emit light, it is impossible to identify it through electromagnetic radiation observation. The unseen matter is referred to as dark matter. Because of the impact, it has on items that we can directly view, we are aware that dark matter exists.
Unlike normal matter, dark matter does not interact with electromagnetic force. This means it does not absorb, reflect or emit light, making it extremely hard to spot.
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The motion of a nightingale's wingtips can be modeled as simple harmonic motion. In one study, the tips of a bird's wings were found to move up and down with an amplitude of 8.8 cm and a period of 0.90 s.
A)What is the wingtips' maximum speed?
Express your answer with the appropriate units.
B)What is the wingtips' maximum acceleration?
Express your answer with the appropriate units.
Simple harmonic motion can be used to simulate the motion of a nightingale's wingtips. Maximum wingtip speed is 0.614 m/s, and maximum wingtip acceleration is 4.289 m/s2.
SHM IS an equation represented by
x = A Sin (wt +Ф)
V = dx/dt=A W cos (wt +Ф)
a = d²x/dt²= -Aw² sin(wt+Ф)
a) Maximum velocity = Aw
V = A W
V= A (2π/T)
= 8.8×10⁻² x 2π/0.9
V= 0.614 m/s m/s
b) Maximum acceleration:
a = A w²
= A (2π/T)²
= 8.8x10² (2π/0.9)² m/s² =
a = 4.289 m/s²
Simple harmonic motion, also known as SHM, is a particular type of periodic motion of a body that arises from a dynamic equilibrium between an inertial force that is proportional to the body's acceleration away from the static equilibrium position and a restoring force on the moving object that is directly proportional to the magnitude of the object's displacement and acts towards the object's equilibrium position. If friction or any other form of energy loss is absent, it leads to an oscillation that may be represented by a sinusoid and that lasts indefinitely.
The oscillation of a mass on a spring when it is subject to linear elastic restoring is a good example of simple harmonic motion, which may be used as a mathematical model for many different motions.
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TRUE OR FALSE A skydiver opens a parachute after 3 seconds of a free fall. If the tension force in the straps of the parachute equals the gravitational force acting on the skydiver, there would be no change and the skydiver continue in free fall
The skydiver continue to descend, but at a consistent speed, in accordance with the supplied statement.
How does science define force?The word "force" has a specific meaning in science. At this level, calling a force a pushing or a pull is entirely appropriate. A power is not something an object "has in it" or that it "contains." One thing receives a force from another. The idea of a force encompasses both life and semi things.
What are example and force?Force is used to describe a body's tendency to change or modify its state as a result of an external cause. When force is applied, the item can also alter its size, shape, and direction. Using a ball to kick.
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a straight, 2.80 m wire carries a typical household current of 1.50 a (in one direction) at a location where the earth's magnetic field is 0.550 gauss from south to north.
The force is 2.3925*10⁻⁴.
What is current?
The speed at which electrons go past a particular location in an electrical circuit is known as current. Current = flow in the simplest terms. The international unit for measuring current is an ampere, pronounced "amp" (AM-pir).
What is magnetic field?
The area around a magnetic material or a moving electric charge where the force of magnetism acts is known as the magnetic field. a visual representation of the magnetic field that explains the distribution of the magnetic force within and around a magnetic material.
using right hand thumb rule
finger : in direction of current
curd it : in direction south - north
there will be point upward
hence force is directed upward
(F) = I (l*b)
F= IlB Sin∅
F= 1.50*2.20*0.55*10⁻⁴
F= 2.3925*10⁻⁴ N
Finger: upward direction
Curd it: In north direction
Force is directed in east to west
F = IlB
F= 1.5*2.90*0.55*10⁻⁴
F= 2.3925*10⁻⁴
since current and field is opposite direction so, < ∅ = 80°
No force will cut on wire ∝
F₃= 0
Therefore, the force is 2.3925*10⁻⁴.
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A 4.0 kg bucket of water is raised from a well by a rope.
The acceleration of gravity is 9.81 m/s2 .
If the upward acceleration of the bucket is 2.6 m/s2, find the force exerted by the rope on the bucket of water.
Answer in units of N
If the upward acceleration of the bucket is 2.6 m/s2, the force exerted by the rope on the bucket of water is 10.4 N.
The force exerted by the rope on the bucket of water, you can use Newton's second law of motion, which states that the force acting on an object is equal to the object's mass multiplied by its acceleration. In this case, the force acting on the bucket of water is the force exerted by the rope, and the object's mass is 4.0 kg and its acceleration is 2.6 m/s^2. Therefore, you can use the following equation to find the force:
= F = ma
Putting values from the problem gives:
= F = (4.0 kg) x (2.6 m/s^2)
= 10.4 N
So, the force exerted by the rope on the bucket of water is 10.4 N.
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a real heat engine working between heat reservoirs at 980 k and 630 k produces 700 j of work per cycle for a heat input of 2800 j .
Its thermal efficiency is 25%.
What is thermal efficiency?Thermal efficiency is the ratio of an engine's or machine's useful output energy to its total energy input. It is a measure of how well energy is converted from one form to another, and is expressed as a percentage. Thermal efficiency is an important factor in determining the cost-effectiveness of many energy systems such as engines, power stations and industrial processes. Increasing the thermal efficiency of a system can lead to significant cost savings and environmental benefits.
Thermal Efficiency = (Work Output / Heat Input) x 100
= (700 J / 2800 J) x 100
= 25%
Therefore, the thermal efficiency of the heat engine working between heat reservoirs at 980 k and 630 k is 25%.
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Complete questions as follows-
200 word and should plag free
a real heat engine working between heat reservoirs at 980 k and 630 k produces 700 j of work per cycle for a heat input of 2800 j . Its thermal efficiency is
Name the type of spherical mirror which
1 . has positive focal length .
2. always forms a virtual image .
Answer:
convex mirror
Explanation:
(answer need to be atleast 20 character long)
The jumper has a mass of 55 kg, and the bridge's height above the river is 150 m. The rope has an unstretched length of 8 m and stretches a distance of 5 m before bringing the jumper to a stop. Determine the maximum speed of the jumper and the spring constant of the rope. In your calculation, use g 10 N/kg. m/s Vmax k = N/m E. Now suppose the jumper has a mass of 80 kg. Do you think the maximum speed of the jumper will increase, decrease, or stay the same?Will the rope need a larger, smaller, or the same spring constant to bring the jumper to a stop in the same distance as part D? (Your answers to these questions are not graded for correctness.)The maximum speed of the jumper will This answer has not been graded yet. The rope will need spring constant that is This answer has not been graded yet. Now calculate the maximum speed of this more massive jumper and the spring constant of the rope needed to bring the jumper to a stop after the = 10 N/kg for your calculations.) Were your predictions correct? rope stretches 5 m. (Again, use g m/s Vmax k = N/m
The speed of jumper is 54.22 m/s and the spring constant of the rope is 6468N/m.
Given data
Jumper weighs 55 kg, which is its mass.
The bridge is 150 meters tall above the river.
The stretched length of the rope is 8 meters (L).
The length after stretching is L' = 5m.
In this situation, the jumper's potential energy will be transferred into the spring potential energy of the rope when they jump. Potential energy of a jumper will then equal the potential energy of a spring in a rope.
The spring constant in this case is k.
Making the following calculation: mgh = 1/2 Kl2 55 90.8 150 = 1/2 k 5 5 k=6468 N/m
Applying the third kinematic equation of motion, find the jumper's final speed as v2 = U2 + 2as.
We discover U=54.22 m/s.
As a result, we can say that the speed of jumper is 54.22 m/s and the spring constant of the rope is 9187.5 N/m.
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we are not yet capable of detecting life on planets around other stars. but as our technology develops, our first real chance of detecting such life will probably come from .
"We are not yet capable of detecting life on planets around other stars. But as our technology develops, our first real chance of detecting such life will probably come from examining spectral lines from the atmospheres of distant planets."
Astronomers can identify an element by its spectral lines, as well as its temperature and density within the star. The magnetic field of the star is also shown by the spectral lines. How quickly the material is travelling can be determined by the line's width. We can also learn about winds in the stars.
Infrared heterodyne spectroscopy allows astronomers to retrieve information about planetary atmospheres. In order to find moons and planets with atmospheres, it uses the infrared region of the spectrum.
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a ball is thron upward witha an intial velocity of 61 feet per second from an initial height of 12 feet express the heigs in feet of the ball as a function of the time t (insecond ) how long will the ball be in the air
The time at which the ball remains in the air after it is thrown vertically upward with an initial velocity of 61 feet per second from an initial height of 12 feet is 4 seconds.
Motion that is normal to a defined horizontal surface is often referred to as vertical motion. The height of a ball launched from a certain height while maintaining a constant speed is modeled as h(t) = at²+bt+c where h(t) is the height of the ball, t is time, and a, b, and c are constants.
At the initial height h = 12 feet and t = 0,
12 = a(0)²+b(0)+c
c = 12
Differentiating equation h(t) = at²+bt+c concerning t, we get, [tex]\frac{dh(t)}{dt}&=2at+b[/tex]
Substituting t = 0 and dh(t)/dt = 61, we get,
[tex]\begin{aligned}61&=2a(0)+b\\b&=61\end{aligned}[/tex]
Again differentiating [tex]\frac{dh(t)}{dt}&=2at+b[/tex] concerning t, we get, [tex]\frac{d^2h(t)}{dt^2}=2a[/tex]
The acceleration caused by gravity on Earth is 32 feet per second. Since the ball travels downward, the value becomes negative. Substituting this in the above equation.
[tex]\begin{aligned}-32&=2a\\a&=-16\end{aligned}[/tex]
Substituting values of a, b, and c in h(t) = at²+bt+c, we get,
h(t) = -16t²+61t+12
Substituting h = 0 in the above equation, the time the ball remains in the air will be,
0 = -16t²+61t+12
0 = 16t²-61t-12
Using the quadratic formula,
[tex]\begin{aligned}t&=\frac{-(-61)\pm\sqrt{(-61)^2-4\times16(-12)}}{2\times16}\\t&=\frac{61\pm67}{32}\\t&=\frac{61+67}{32}\;\text{or}\;\frac{61-67}{32}\\t&=4\;\text{or}\;-\frac{3}{16}\end{aligned}[/tex]
Time cannot be negative, therefore, t = 4 seconds is the answer.
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SITUANARIO: A sled with mass ms=20 kg is pulled horizontally across snow. The coefficient of kinetic friction between sled
and snow is uk1= 0.27. A penguin with mass mp=25 kg rides on the sled, as in the figure above. The coefficient of static
friction between penguin and sled is us2 = 0.68.
Determine the maximum horizontal force Fapp that can be exerted on the sled before the penguin begins to slide off the
sled. HINT: Draw separate FBD diagrams for the penguin and the sled.
The horizontal force that can be exerted on the sled before the penguin begins to slide off is equal to 312.7 N.
What is friction?Friction can be described as the force resisting the motion of solid surfaces, fluid, and material elements sliding against each other.
The weight of the sled, W₁= m₁g = 20(9.8) = 197 N
The weight of the penguin, W₂= m₂g = 25 (9.8) = 245 N
The total weight of the system, W = 197 + 245 = 442 N
The normal force on the penguin due to the sled is:
N₁= W₁= 197 N
The normal force of the whole system, N₂ = W = 442 N
The sliding acceleration, a = f₁/m₁
a = μ₂g
a = 0.68 ×9.8 = 6.67 m/s²
The total force in the x-direction can be written as:
[tex]F_x = F-f_2[/tex]
[tex]F = \mu_1W +\frac{W_2}{g}a[/tex]
F = (0.27) (442) + (442/9.8) (6.67)
F = 312.7 N
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consider a diffuser operating in an adiabatic process. the device decelerates the flow, causing a decrease in the kinetic energy of the fluid. noting from the first law that energy cannot be destroyed, describe physically what happens to the lost kinetic energy.
A diffuser is an adiabatic device that slows down a fluid to reduce its kinetic energy.
The transfer of heat from one system to another is caused by heat, temperature, and external variables. When heat is transferred, things do change. A process is referred to as adiabatic if there is no heat transfer.
Consider the internal combustion engine (ICE) found in classic automobiles. The ICE won't be able to function without the air pressure generated in the combustion chamber to move the piston inside a cylinder. Similar to this, the steam engine, which was widely employed throughout the early stages of the Industrial Revolution, functions according to the same theory. Heat is delivered to a small space, which causes the wet air to expand and force cylinders to rise and fall.
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