There is a change of -20 J in the gas's internal energy.
Adiabatic expansion is the method of volume expansion in which no heat is exchanged inside the system from the surrounding, or the heat exchange is zero. During extension, the exchange of energy takes put as work.Since we given with 4-kg mass of gas expands adiabatically and does 20 j of work.
According to the first law of thermodynamics
ΔQ = ΔU + W
where Q is the heat supply or received, U is the internal energy and W is the work done
since in case adiabatic process , ΔQ = 0
so, ΔU = -ΔW
wince a work done is done by the system, so the work done = +20 J
ΔU = -(+20) = -20 J
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a man falls 2.0 m to the floor (assume down to be negative) how long does the fall take? what is his velocity when he hits the floor?
The time taken for the man to reach the ground is 0.64 s and his velocity on reaching the round is 6.26 m/s.
How long does it take the man to fall?Given that we can be able to use the equations of kinematics to obtain the time that it took the man to fall to the floor. Using the equation;
v^2 = u^2 + 2gh
v = final velocity
u = initial velocity
g = acceleration due to gravity
h = height attained
Note that u= 0 m/s since he dropped from a height;
v= √2gh
v = √2 * 9.8 * 2
v = 6.26 m/s
Again;
v = u + gt
Again u= 0 m/s
v = gt
t = v/g
t = 6.26 m/s/9.8 m/s
t = 0.64 m/s
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A parallel-plate capacitor is constructed of two square plates, size l×l, separated by distance d. The plates are given charge ±q. Let's consider how the electric field changes if one of these variables is changed while the others are held constant.
Parallel Plate Capacitors are formed by an association of electrodes and insulating material or dielectric. A parallel plate capacitor can simplest shop a finite quantity of electricity before a dielectric breakdown happens.
A capacitor works on the precept that the capacitance of a conductor suggests boom whilst an earthed conductor is added near it. therefore, the capacitor has parallel plates dealing with each other in contrary instructions and are separated through ways or holes.
The most effective layout for a capacitor is a parallel plate, which consists of two metallic plates with an opening among them: electrons are located onto one plate the terrible plate, while an equal amount of electrons are removed from the opposite plate the fantastic plate.
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A horizontal force of 20 N is applied to the object.
Draw a free body diagram with the forces to scale.
Determine the force of friction.
Determine the acceleration of the object.
The acceleration of the object with a horizontal force of 20N is 4.4 m/s².
How to Determine Horizontal Acceleration in Frictional Systems
Here, the angle of repose
a = tan⁻¹ (45)
a = tan⁻¹(1/5)
a = 11.3°
The angle of inclination is greater than the angle of repose.
The friction force on the block will act in an upward direction.
For the acceleration of the block:
MgsinΘ - μN = Ma
a = gsinΘ - μg cosΘ
a = g (sinΘ - u cosΘ)
a = 10 (sin37 - μ cos37)
a = 10 (0.6 - 0.2 * 4/5)
a = 10 ( 0.6 -0.16)
a = 4.4 m/s²
Thus the acceleration of the object is 4.4 m/s².
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20.) In an experiment that measures how fast a student reacts, a meter stick dropped
from rest falls 0.20 meter before the student catches it. The reaction time of the student approximately
a)0.30s
b)0.20s
c)0.10s
d)0.40s
The reaction time of the student is approximately 0.2 s (Option B)
How do I determine the reaction time of the student?Considering the question given above, the following formula can be use to obtain the time
h = ½gt²
Where
h is the heightg is the acceleration due to gravityt is the timeNow, let us calculate the reaction time of the student. This is shown below:
Height (h) = 0.20 meterAcceleration due to gravity (g) = 9.8 m/s²Reaction time (t) = ?h = ½gt²
0.20 = ½ × 9.8 × t²
0.20 = 4.9 × t²
Divide both side by 4.9
t² = 0.20 / 4.9
Take the square root of both side
t = √(0.20 / 4.9)
t = 0.2 s
Thus, the reaction time is 0.2 s (Option B)
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Explain how the distances between particles in a solid, liquid, and a gas help determine the desitys of each.
Answer:
The particles have more distance in them which impacts the density.
Explanation:
A solid's particles are much more closer together than that of a liquid's particles. Same thing goes for gas particles(they are much more far apart than liquid particles). This is why solids usually are more denser than liquids and gas, due to the way their particles are structured. Hope this helps!
a trash compactor can reduce the volume of its contents to 0.808 their original value. neglecting the mass of air expelled, by what factor is the density of the rubbish increased?
The factor by which the density is increased F = 2.86.
What is density?The amount of something per unit of length, area, or volume: as the substance's mass per unit volume given in grams per cubic centimeter is density.How much "stuff" is contained in a specific quantity of space is factor of its density. For instance, a block of the harder, lighter element gold (Au) will be denser than a block of the heavier element lead (Pb) (Au). Styrofoam blocks are less dense than bricks. Mass per unit volume serves as its definition.This equation can be used to determine an object's or substance's density: Mass in kilograms divided by volume in meters cubed gives density in kilograms per square meter (p = m/v).To learn more about density from the given link :
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2. if water vapor comprises 1% of an air parcel whose total pressure is 1000 mb, the water vapor pressure would be ( ) mb?
Since water vapor makes up 1% of the air mass while that there are 1,000 mb of total pressure, the water evaporation rate would be 35 mb.
What is an illustration of pressure?By applying a scalpel to a slice of fruit, one can observe a basic pressure. The surface won't be cut if you press the flat section of the sword against the fruit. The force is dispersed over a broad region.
How can pressure be determined?Absolute, gauge, & differential pressure measurements are the three types. While gauge and difference pressures are reference to another pressure, such as the outside air pressure or the pressure in a nearby vessel, absolute pressure is defined as the maximum stress in a vacuum.
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5. a 100 gram ball on the end of a 60 cm long string is swung in a horizontal circle. what is the minimum period of the ball if the string will break when 100 n of tension is placed on it?
The minimum period in which the string will break will be 0.534 sec.
Mass = 100 gm =0.1 kg
Length = 60 cm =0.6 m
Tension on string = 5N
Height of center of circle = 200 cm = 2m
At the bottom point , mv2r / mg
Now, 5N = ( 0.1 kg( v x v) /0.6 m + (0.1 kg) ( 9.8 m/s2)
hence the value of v = 4.91 m/s.
So the height of the wall will fall is 200 cm - 60 cm = 140 cm
The distance travelled can be calculated by the s = ut + 1/2 gt2
as u = 0 and s =H
H= 1/ 2 gt 2
t = √2 H / g
Substituting the values we get time as t = 0.534 sec
Distance = 4.91 m/sec x 0.534 sec
= 2.62 meters
How to calculate period of motion in physics?
The period of an oscillating system can be defined as the time taken to complete one cycle. It is the reciprocal of frequency in physics, which is the number of cycles per unit time. To calculate the period of a wave or a simple harmonic oscillator by comparing it to orbital motion.
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a 1.0 m long wire is placed perpendicular to a magnetic field of strength 0.20 t. if the wire experiences a force of 0.60 n, what is the magnitude of the current moving through the wire?
I = 3.0A
What is current?
A stream of charged particles, such as electrons or ions, traveling through an electrical conductor or a vacuum is known as an electric current. The net rate of electric charge flowing through a surface or into a control volume is how it is calculated.
For a current-carrying wire running perpendicular to a magnetic field, the magnetic force acting on the wire is given by:
F = ILB
F = magnetic force, I = current, L = wire length, B = magnetic field strength
Given values:
F = 0.60N, L = 1.0m, B = 0.20T
Plug in and solve for I:
0.60 = I(1.0)(0.20)
I = 3.0A
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how many times more energy would need to be transferred to the plastic for it to get as warm as the glass? assume that the mass and the change in temperature are the same for both materials.
The energy will be transferred unless both the plastic and glass are at the same temperature, and there's no heat transfer.
The total amount of energy in the universe has never changed and will never change because it cannot be created or destroyed. This does not imply that energy cannot change forms or even move between objects though; it does.
The internal energy of a system as a result of its temperature is referred to as thermal energy. The molecules that make up a substance move more quickly as it is heated, gaining thermal energy via the transmission of heat. The term "heat" refers to the thermal energy being transported from a hotter system to a cooler one. Temperature is used to assess the degree of "hotness" or "coldness" of an object. There are three methods by that thermal energy can be transferred: conduction, convection, and radiation.
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A mass of 0. 55 kg is suspended from the ceiling by a spring which then oscillates with simple harmonic motion. If the period of oscillation is measured to be 0. 75 sec, what is the spring constant?.
The spring constant is 38.6 N/m
Simple harmonic movement is a unique kind of periodic motion in which the restoring force on the shifting item is without delay proportional to the value of the item's displacement and acts toward the item's equilibrium role.
Calculation:-
A. Time period T = 2π√m/K
T² = (2π)² m/k
⇒ K = 4π²m/k
⇒ K = 4π²m/T²
= 4π²×0.55/(0.75)²
⇒ K = 38.6 N/m
Simple harmonic motion is defined as a periodic motion of a factor alongside an instant line, such that its acceleration is usually towards a hard and fast factor in that line and is proportional to its distance from that factor.
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What is the SECOND major step?
O Revising and editing
O Writing a rough draft
O Organizing your essay
O Generating ideas and choosing strategies
Answer:
O Writing a rough draft
Explanation:
Thats the second step after generating ideas and choosing.
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pat wants to move a 11.3 kg box across a level floor. the coefficient of kinetic friction between the box and the floor is 0.41. after pat has started the box moving, what strength push force (in n) will be required to keep the box moving at a constant speed?
The force required to keep the box moving at a constant speed is 45.4 N
What is friction force?Friction is the force that resists relative motion as elements of solid surfaces, fluid layers, and materials slide over each other. A type of contact force that exists between contact surfaces.
We know that;
Fₙ = m × a
Where, Fₙ = Net force
m = mass of the object (11.3 kg)
a = acceleration
Since the box is moving with a constant speed which means there is no acceleration.
Fₙ = 11.3 × 0
Fₙ = 0
Now,
Fₓ = μmg
Where, Fₓ = Friction force
μ = coefficient of kinetic friction (0.41)
m = mass of the box (11.3 kg)
g = gravitational acceleration (9.8m/s²)
Fₓ = 0.41 × 11.3 × 9.8
Fₓ = 45.4 N
We know that,
Fₙ = Fₐ - Fₓ
Where, Fₙ = Net force
Fₐ = Applied force
Fₓ = Friction force
Since Fₙ = 0, then:
0 = Fₐ - 45.4
Fₐ = 45.4 N
Therefore, if the kinetic friction force is equal to the applied force, the acceleration will be zero and the body will move with constant velocity.
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What is the main difference between vulnerability scanning and penetration testing?.
The main difference between vulnerability scanning and penetration testing is the automation.
A vulnerability scan is an automated, high-level test which looks for potential vulnerabilities and reports those vulnerabilities. A vulnerability scan is also known as vulnerability assessment. It assesses computers, systems and networks for security weaknesses.
A penetration test is done by a real person rather an automated machine. It is a detailed hands on examination that tries to detect and exploit weaknesses in your system. A penetration test simulates a hacker's attempt to get into a business system through research and the exploitation of vulnerabilities.
Therefore, the main difference between vulnerability scanning and penetration testing is the automation.
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The following steps lead to convection in the atmospheres of giant planets. Place the following in order, following (a).
a. Gravity pulls particles toward the center.
b. Warm material rises and expands.
c. Particles fall toward the center, converting gravitational energy to kinetic energy.
d. Expanding materials cools.
e. Thermal energy heats the material.
f. Friction converts kinetic energy to thermal energy.
Place the following in order, following (a) are:
a. Gravity pulls particles toward the center.
c. Particles fall toward the center, converting gravitational energy to kinetic energy.
f. Friction converts kinetic energy to thermal energy.
e. Thermal energy heats the material.
b. Warm material rises and expands.
d. Expanding materials cool.
In physics, gravity is an essential interplay that reasons mutual appeal between all things with mass or electricity. Gravity is, through a long way, the weakest of the 4 essential interactions, approximately 1038 instances weaker than the sturdy interaction, 1036 times weaker than the electromagnetic force, and 1029 instances weaker than the susceptible interplay. As an end result, it has no tremendous influence on the extent of subatomic debris. but, gravity is the biggest interaction between gadgets on the macroscopic scale, and it determines the movement of planets, stars, galaxies, or even light.
The gravitational enchantment between the authentic gaseous count within the Universe allowed it to coalesce and shape stars which in the end condensed into galaxies, so gravity is answerable for some of the huge-scale systems within the Universe. Gravity has a limitless range, despite the fact that its consequences emerge as weaker as objects get farther away.
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How many more seconds are required for the fan to come to rest if the angular acceleration remains constant at the value calculated in part A?
An electric fan is turned off, and its angular speed decreases uniformly from 720 rev/min to 200 rev/min in a time interval of period 3.25.
In mechanics, acceleration is the price of trade of the rate of an item with recognition to time. Accelerations are vector quantities. The orientation of an item's acceleration is given by means of the orientation of the internet force performing on that item.
According to Newton's second regulation of movement, the acceleration of an object equals the internet force performing on it divided via its mass, or a = F m . This equation for acceleration can be used to calculate the acceleration of an object while its mass and the internet force appearing on it are regarded.
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a young's double-slit interference experiment is performed with monochromatic light. the separation between the slits is 0.38 mm. the interference pattern on the screen 3.8 m away shows the first maximum 4.7 mm from the center of the pattern. what is the wavelength of the light in nm?
The wavelength of the light is 470 nm.
Explain Young's double-slit interference experiment?
The Young's double-slit experiment is a proof in current physics that light and matter can exhibit properties of both classically defined waves and particles. It also shows that quantum mechanical processes are inherently probabilistic.
Bright Fringes' Position
A brilliant fringe to appear at P with maximal intensity
Path difference, z = n, where n = 0, 1, 2,...
Therefore, xd/D = n.
x = nλD/d
The nth brilliant fringe is located at a distance of
xn = nλD/d
Ist order maximum= λD/d
4.7 x 10^-3 = λ x 3.8 /0.38 x 10^-3
4.7 x 0.38 x 10^-6 / 3.8 = λ
λ = 0.47 x 10^-6 m
= 470 x 10^-9 m
Hence, The wavelength of the light is 470 nm.
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Calculate the effective value of g, the acceleration of gravity, at (a) 6400 m, and (b) 6400 km, above the earth's surface.
The gravitational acceleration at 6400 m is 9.74 m/s² and at 6400 km is 2.43 m/s².
We need to know about the gravitational field to solve this problem. The gravitational field is the area where affected by gravitational force. The magnitude of the gravitational field can be calculated by this equation
g = G . m / (R+r)²
where g is the gravitational field, G is gravitational constant (6.67 x 10¯¹¹ Nm²/kg²), m is the mass of the planet and r is the radius of the planet
From the question above, we know that
m = 5.94 x 10²⁴ kg
R = 6371000 m
ra = 6400 m
rb = 6400000 m
Find the gravitational acceleration at 6400 m
g = G . m / (R + r)²
g = 6.67 x 10¯¹¹ . 5.94 x 10²⁴ / (6371000 + 6400)²
g = 9.74 m/s²
Find the gravitational acceleration at 6400 km
g = G . m / (R + r)²
g = 6.67 x 10¯¹¹ . 5.94 x 10²⁴ / (6371000 + 6400000)²
g = 2.43 m/s²
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Rutherford's gold foil experiment using alpha particle scattering concluded that.
Rutherford's gold foil experiment using the alpha particle scattering method concluded that the atom consists of a small massive, positively charged nucleus with the negatively charged electrons being at a great distance from the center.
The experiment showed the existence of a nuclear atom a small, positively-charged nucleus surrounded by empty space and then a layer of electrons to form the outside of the atom.
In his experiment, most of the alpha particles did pass straight through the foil he concluded that the atom is mostly empty space.
He also discovered that a small number of alpha particles were deflected by large angles as they passed through the foil he concluded that there is a large concentration of positive charge in an atom.
He also discovered that a small number of alpha particles came straight back off the foil this made him conclude that positive charge and mass are concentrated in a tiny volume in the atom
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A train traveled 250 kilometers (km) from its starting point in 5 hours (h). Calculate the speed of the train.
The calculated value of speed is 250km/hr x 5h = 50km/hr. The typical top speed of high-speed trains is 300-350 km/h.
Speed is calculated as follows: speed = distance * time. Knowing the units for distance and time is necessary to calculate the units for speed. The units will be in metres per second (m/s) in this example since the distance is measured in metres (m) and the time is measured in seconds (s). A megabit is one million bits, which are incredibly small pieces of data. Our internet activity should run more quickly the higher your Mbps (megabits per second) figure is.
speed =distance / time
= 250/5
=50 km / h
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6. If displacement of a particle is zero, the distance covered by
a.may or may not be zero
b.must be zero
c.must not be zero
d. Must be unity
A 20-kg block slides down a frictionless incline from point A to point B A force (magnitude P = 3.0 N) acts on the block between A and B, as shown Points A and B are 2.0 m apart If the kinetic energy of the block at A is 10 J,what is the kinetic energy of the block at B?
The kinetic energy of the block at B is 24J
we can solve this by using law of conservation of energy,
Ki = 10J Uf = 0 ( placed at origin point B)
Kf=?
Ui =mgh
To find height, h = 2 sin 30 = 1m
from this Ui = mgh = 20x1 = 20 J
law of conservation of energy,
Ki+ Ui + W = Kf + Uf - (1)
work = - F X D = 3X2 = - 6 N
substituting in equation 1
10+20- 6 = Kf + 0
30-6 = Kf
Kf = 24 J
hence, KE at B is 24J
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An airplane is delivering food to a small island. It flies 100 m above the ground at a speed of 155 m/s. Determine the horizontal distance at which the parcel should be dropped away from the island in order to be landed there. Neglect air resistance.
The horizontal distance at which the parcel should be dropped away from the island in order to be landed there is 697.5 m.
What is the horizontal distance travelled by the plane?
The horizontal distance travelled by the plane is calculated as follows;
X = vt
where;
v is the horizontal speed of the planet is the time of motion of the food from the given heighth = ut + ¹/₂gt²
where;
u is initial vertical velocity = 0t is the time of motionh = 0 + ¹/₂gt²
h = ¹/₂gt²
2h = gt²
t = √(2h/g)
t = √(2 x 100 / 9.8)
t = 4.5 seconds
Horizontal distance = 155 m/s x 4.5 s
Horizontal distance = 697.5 m
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The longest snake ever found was a python that was 10.0m long. Suppose a coordinate
system large enough
to measure the python's length is drawn on the ground. The snake's
tail is then placed at the origin and the snake's body is stretched so that it makes an angle
of 60.0° with
the positive x-axis. Find the x and y coordinates of the snake's head. (Hint:
The y-coordinate is positive.
The snake's length is approximately equal to its x-coordinate. Use the Pythagorean theorem to find the x-coordinate.)
The x coordinate is approximately equal to 10.0 * cos(60.0) = 8.66
The y coordinate is approximately equal to 10.0 * sin(60.0) = 5.00
What is x-coordinate?
Let's make sure humans know what it means to coordinate before we discuss an x-coordinate. Coordination establishes structure and direction for the relationship between the individuals or things. The same principle applies to an x-coordinate. The first digit in an ordered pair is known as an x-coordinate. The ordered pair consists of the x- and y-coordinates. For instance, the x-coordinate in the ordered pair (5, 3) is 5. Consider the alphabet when trying to recall which number is which. The letter x precedes the letter y in the alphabet. When referencing x-coordinate, the same holds true. The x-value coordinate's indicates how far we are from the origin and which way we are moving along the x-axis. The x-coordinate oscillates in a horizontal plane.
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jumping up before the elevator hits. after the cable snaps and the safety system fails, an elevator cab free-falls from a height of 36 m. during the collision at the bottom of the elevator shaft, a 90 kg passenger is stopped in 5.0 ms. (assume that neither the passenger nor the cab rebounds.) what are the magnitudes of the (a) impulse and (b) average force on the passenger during the collision? if the passenger were to jump upward with a speed of 7.0 m/s relative to the cab floor just before the cab hits the bottom of the shaft, what are the magnitudes of the (c) impulse and (d) average force (assuming the same stopping time)?
( a) By energy conservation, the speed of the passenger when the elevator hits the floor is
1 / 2 mv2 = mgh
v = √2gh
Substituting the values we can find the value of v = 26.6 m/s
The magnitude of the impulse is
J=∣Δp∣=m∣Δν∣=mν=(90kg)(26.6m/s)≈2.39×10 3 N⋅s .
(b) With duration of Δt=5.0×10 −3 s for the collision , average force is
F avg = J /Δt
= 2.39×10 N⋅s / 5.0×10 −3 s N⋅s
≈4.78×10 5 N .
(c) If the passenger were to jump upward with a speed of ν =7.0m/s , then the resulting downward velocity would be
ν ′′ =ν−ν =26.6m/s−7.0nm/s=19.6m/s ,
and the magnitude of the impulse becomes
J ′′=∣Δp ′′ ∣=m∣Δν ′′ ∣=mν ′′
=(90kg)(19.6m/s)≈1.76×10 3 N⋅s .
(d) The corresponding average force would be
F avg′′= J ′′Δt = 1. 76×10 3 N⋅s / 5.0×10 −3 s
≈3.52×10 5 N .
This is how we can determine impulse , average force before collision and at the stopping time.
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A spacecraft orbits mars (mass = 6.40 x 10^23 kg) in a circular orbit of radius 8.01 x 10^5 km. What is the period of the spacecraft?
Answer:
Explanation:
Given:
M = 6,40·10²³ kg
R = 8.01·10⁵ km = 8.01·10⁸ m
G = 6.67·10⁻¹¹ N·m²/kg²
____________________
T - ?
Orbital speed:
V = √ ( G·M / R) = √ (6.67·10⁻¹¹·6,40·10²³ / 8.01·10⁸) ≈ 220 m/s
Orbit length:
D = 2·π·R = 2·3.14·8,01·10⁸ = 5·10⁹ m
Period:
T = D / V = 5·10⁹ / 220 ≈ 23·10⁶ s = 266 days
a 200 lb man carries a 20 lb can of paint up a helical staircase that encircles a silo with radius 15 ft. if the silo is 120 ft high and the man makes exactly four complete revolutions, how much work is done by the man against gravity in climbing to the top? ft-lbs
The work is done by the man against gravity in climbing to the top with a 20 lb can of paint up a helical staircase that encircles a silo with a radius of 15 ft. if the silo is 120 ft high and the man makes exactly four complete revolutions is 25200 lb-ft.
What is Work done?When an external force moves an object over a distance, at least a portion of that force must be exerted in the direction of the displacement. Physics refers to this as work. If the force acting along the path is constant, the amount of work can be calculated by multiplying the length of the path by the force's component.
Formally, W = fd means that the work is equal to the force f times the length d. If the force is applied at an angle to the displacement, the work is W = fd cos.
Given:
The mass of man, m = 200 lb,
The mass of the can, M = 20 lb,
Calculate the work done y the following formula,
W = [tex]\int\limits^{120}_0} \,(215 -1/12y ) dy[/tex]
Here W is work done
Integrate the above equation, and we get,
W = 25200 lb ft.
Therefore, work is done by the man against gravity in climbing to the top with a 20 lb can of paint up a helical staircase that encircles a silo with a radius of 15 ft. if the silo is 120 ft high and the man makes exactly four complete revolutions is 25200 lb ft.
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If a sonar wave takes 5.4 seconds to return to a ship, how far away is the object it bounced off?
2.05×10^9 m distance far away is the object it bounced off.
velocity= distance/time
velocity= 3×10^8 m/s
time= 5.4
velocity= distance/time
distance= 3×10^8×5.4
distance=2.05×10^9 m
Distance is the length between two locations or things, independent of direction. Since distance is a scalar property, it only takes into consideration the total magnitude and ignores the start and finish positions. Since distance is a scalar attribute, it can only have a positive or zero value; it cannot have a negative value.
The most common unit of measurement for distance is the meter (m), while larger distances can also be stated in kilometers (km), while smaller distances can be expressed in centimeters (cm) or millimeters (mm). When calculating distance, the letter D is often used to represent the distance traveled.
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using energy considerations and assuming negligible air resistance, show that a rock thrown from a bridge 20.0 m above water with an initial speed of 15.0 m/s strikes the water with a speed of 24.8 m/s independent of the direction thrown.
Using energy considerations Since Ef=Ei, a rock thrown from the tip of a bridge doesn't matter which direction it is thrown in.
Given that,
Height of the bridge is 20m
Initial before he throws the rock
The height is hi = 20 m
Then, final height hitting the water
hf = 0 m
Initial speed the rock is throw
Vi = 15m/s
The speed at final is at which the rock hits the water
Vf = 24.8 m/s
Using given energy conservation
Ki + Ui = Kf + Uf
Where
Ki is initial kinetic energy
Ui is initial potential energy
Kf is final kinetic energy
Uf is final potential energy
Then,
Ki + Ui = Kf + Uf
Where
Ei = Ki + Ui
Where Ei is initial energy
E i =1/2mVi² +m*g*hi
E i =1/2m × 15² + m *9.8*20
E i = 112.5m + 196m
E i = 308.5m J
Now,
E f = Kf + Uf
E f =1/2mVf² + m*g*hf
E f =1/2m*24.8² + m*9.8* 0
E f = 307.52m + 0
E f = 307.52m J
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a tank circuit contains a capacitor and an inductor that produce 30 of reactance at the resonant frequency. the inductor has a q of 15. the voltage of 277 v is connected to the circuit. what is the total circuit current at the resonant frequency?
The total circuit current at the resonant frequency is 0.61 amps
What is a LC Circuit?
A capacitor and an inductor, denoted by the letters "C" and "L," respectively, make up an LC circuit, also referred to as a tank circuit, a tuned circuit, or a resonant circuit. These circuits are used to create signals at particular frequencies or to receive signals from more complicated signals at particular frequencies.Q =15 = (wL)/R
wL = 30 ohms = Xl
R = 2 ohms
Zs = R + jXl = 2 +j30 ohms where Zs is the series LR impedance
| Zs | = 30.07 <86.2° ohms
Xc = 1/(wC) = 30 ohms
The impedance of the LC circuit is found from:
Zp = (Zs)(-jXc)/( Zs -jXc)
Zp = (2+j30)(-j30)/(2 + j30-j30) = (900 -j60)2 = 450 -j30 = 451 < -3.81°
I capacitor = 277/-j30 = j9.23 amps
I Zs = 277/(2 +j30) = (554 - j8,310)/904 = 0.61 - j9.19 amps
I net = I cap + I Zs = 0.61 + j0.04 amps = 0.61 < 3.75° amps
Hence, the total circuit current at the resonant frequency is 0.61 amps
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