Expansion stroke refers to the forward motion of a steam engine piston.The steam has a pressure of 103.45 kPa.
What is the pressure of the steam?Expansion stroke refers to the forward motion of a steam engine piston.The piston is propelled forward during the expansion stroke by the expansion of steam in the cylinder.Additionally moving is the piston's connecting crank shaft.
When the piston is expanding, the crankshaft's wheel rotates only halfway.
W = p * V is the formula, where W stands for work, p stands for pressure, and V is the change in piston volume.
We are aware of:
W = 0.6 J.
The piston measures 1.8 cm in diameter.
This indicates that r = 0.9 cm.
Since it moves 2.3 cm, a cylinder's height is given by h = 2.3 cm.
V = r2 h = 0.92 3.14 2.3 5.85 cm3 = 0.00000585 m3
The pressure is p = W/V = 0.6 J/0.00000585 m3 = 103,448.27 Pa, or p = 103.45 kPa.
The steam has a pressure of 103.45 kPa.
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The change in velocity divided by the time over which the change occurs is the
a) speed
b) average acceleration
c) velocity
d) displacement
A spring oscillates with a frequency of 2.09 Hz. What is its period?
(Unit=s)
Time period of a wave is the inverse of its frequency. The period of the wave with a frequency of 2.09 Hz is 0.47 seconds.
What is frequency ?Frequency of a wave is the number of wave cycles per unit time. Frequency is the inverse of the time period of the wave. Hence, it has the unit of s⁻¹ which is equivalent to Hz.
The higher frequency of a wave indicates more number of wave cycles in a short time. Frequency is directly proportional to the energy and inversely proportional to the wavelength.
Given the time period of the wave = 2.09 Hz
then frequency = 1/2.09 Hz = 0.47 s.
Therefore, the time period of the wave is 0.47 seconds.
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two particles with equal charge experiences a force of 12 nN where they are 30 cm apart. what is the magnitude of the charge on each particle
Considering the Coulomb's Law, the magnitude of the charge on each particle is 4.2426 C.
Definition of Coulomb's LawCoulomb's law or law of electrostatics is the relationship between the interactions of electric charges, that is, it explains the force experienced by two electric charges at rest.
This law says that the electric force with which two point charges at rest attract or repel each other is directly proportional to the product of the magnitude of both charges and inversely proportional to the square of the distance that separates them, expressed mathematically as:
[tex]F=k\frac{Qq}{d^{2} }[/tex]
where:
F is the electrical force of attraction or repulsion. It is measured in Newtons (N).Q and q are the values of the two point charges. They are measured in Coulombs (C).d is the value of the distance that separates them. It is measured in meters (m).k is a constant of proportionality called the Coulomb's law constant. It depends on the medium in which the charges are located. Specifically for vacuum k is approximately 9×10⁹ [tex]\frac{Nm^{2} }{C^{2} }[/tex].The force is attractive if the charges are of opposite sign and repulsive if they are of the same sign.
Magnitude of the charge on each particleIn this case, you know that:
F= 12 nN= 1.8×10⁻⁸ N (being 1 nN= 1×10⁻⁹ N)k= 9×10⁹ [tex]\frac{Nm^{2} }{C^{2} }[/tex]Q= qd= 30 cm= 0.3 m (being 100 cm= 1 m)Replacing in the Coulomb's Law:
[tex]1.8x10^{-8} N=9x10^{9} \frac{Nm^{2} }{C^{2} }\frac{Qq}{(0.3 m)^{2} }[/tex]
Being Q=q:
[tex]1.8x10^{-8} N=9x10^{9} \frac{Nm^{2} }{C^{2} }\frac{q^{2} }{(0.3 m)^{2} }[/tex]
Solving:
1.8×10⁻⁸ N÷ 9×10⁹ [tex]\frac{Nm^{2} }{C^{2} }[/tex]= q²÷ (0.3 m)²
2×10⁻¹⁸ C²/m²= q²÷ (0.3 m)²
2×10⁻¹⁸ C²/m²= q²÷ 0.09 m²
2×10⁻¹⁸ C²/m² ×0.09 m²= q²
1.8×10⁻¹⁹ C²= q²
√1.8×10⁻¹⁹ C²= q
4.2426 C= q= Q
Finally, each charge has a value of 4.2426 C.
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Two mirrors are inclined at an angle of 30 degrees a ray of light obliquely
Two mirrors are inclined at an angle of 30 degrees a ray of light obliquely at 180.
What are Inclined mirrors?
A mirror is said to be inclined when it is positioned perpendicular to a surface or if a flat mirror is positioned at an angle from the base (other than 90 degrees).
We first need to comprehend light in order to comprehend mirrors. According to the rule of reflection, a light beam that strikes a surface will bounce back like a tennis ball bounced against a wall.
Always equal to the angle leaving the surface, or the angle of reflection, is the entering angle, also known as the angle of incidence.
Therefore, Two mirrors are inclined at an angle of 30 degrees a ray of light obliquely at 180.
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A bike rider accelerates constantly to a velocity of 7.5m/s during 4.5s. The bike's displacement is 19m. What was the initial velocity of the bike?
The initial velocity of the bike was 3.75 m/s.
What was the initial velocity of the bike?The initial velocity of the bike is determined by examining the displacement and the time elapsed. The equation for displacement is displacement = initial velocity (m/s) x time (s). Thus, the initial velocity can be calculated by rearranging the equation, initial velocity = displacement (m) / time (s).In this case, the displacement is 19m and the time is 4.5s. Thus, the initial velocity can be calculated by plugging in the values to the equation, initial velocity = 19m / 4.5s. This evaluates to 4.22m/s. This means that the bike rider's initial velocity was 4.22m/s before accelerating to the velocity of 7.5m/s in 4.5s.To break it down, the bike rider was initially travelling at 4.22m/s and then accelerated constantly to a velocity of 7.5m/s in a period of 4.5s. The resulting displacement was 19m. This can all be determined using the equation displacement = initial velocity x time. By rearranging the equation and plugging in the values, we can determine the initial velocity of the bike as 4.22m/s.To learn more about The initial velocity refer to:
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An athlete exerts 3000 W of power when he takes 10.2 s to run the race. How much WORK does the athlete do?
Answer:
30600 J
Explanation:
Work = Power* Time
=30600 J
In a pipe of 90mm diameter, water is flowing with a mean velocity of 2m/s at a gauge pressure of 350KN/M². Determine the total head, if the pipe is 8m above the datum.
The total head of the pipe is 430,400 Pa.
What is the total head of the pipe?
The total head of the pipe is the total pressure of the pipe and it is calculated as follows;
Pt = Pi + ¹/₂ρv² + ρgh
where;
Pi is the gauge pressure ρ is density of waterv is the speed of the waterh is the height of the water above the groundPt = ( 350,000) + ¹/₂(1000)(2)² + (1000 x 9.8 x 8)
Pt = 430,400 Pa
Thus, the total head or total pressure of the pipe depends on the density of water, speed of water and height above datum.
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An 112 kg man drops from rest on a diving board 3.0 m above the surface of the water and comes to rest 0.55 s after reaching the water. How fast was he going as he hit the water? (use units of measurement)
Write the equation for finding speed (v) when given a displacement (difference between two positions X₁ and x2) and the corresponding interval (difference between two clock readings t₁ and t₂). After writing the equation, apply it to find the speed of Walking Dude.
The equation for finding speed is given by v = (x₂ - x₁) / (t₂ - t₁), where x is the displacement and t is the corresponding interval. The speed of the walking dude remains constant at 2 m/s.
How to calculate speed?To find the speed of Walking Dude, using v = (x₂ - x₁) / (t₂ - t₁), insert the values for x and t.
For t = 0 and 2 seconds, the displacement is x = 0 and 4 meters respectively. So,
v = (4 - 0) / (2 - 0) = 4 m/s
For t = 2 and 4 seconds, the displacement is x = 4 and 8 meters respectively. So,
v = (8 - 4) / (4 - 2) = 2 m/s
For t = 4 and 6 seconds, the displacement is x = 8 and 12 meters respectively. So,
v = (12 - 8) / (6 - 4) = 2 m/s
For t = 6 and 8 seconds, the displacement is x = 12 and 16 meters respectively. So,
v = (16 - 12) / (8 - 6) = 2 m/s
Thus, the speed of Walking Dude remains constant at 2 m/s during the entire time period.
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Which of the following is a vital component to creating an atmosphere?
A. Meter
B. Rhythm
C. Pulse
D. All of these answers
A) The atmosphere shields life on earth from harmful ultraviolet (UV) radiation, insulates the planet to maintain a comfortable temperature, and prevents temperature extremes between day and night.
The convection that results from the sun's heating of the atmosphere's layers is what drives global air currents and weather patterns.
What makes up the environment most importantly?While most life on Earth requires oxygen, oxygen does not make up the bulk of the planet's atmosphere. About 78% of the gases in the Earth's atmosphere are nitrogen, 21% are oxygen, 0.9 % are argon, and 0.1 % are other gases.
What are the early atmosphere's four constituent parts?The initial atmosphere of Earth was deficient in free oxygen but abundant in methane, ammonia, water vapor, and the noble gas neon.
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Think about how particles are arranged inside atoms. Please name and describe those three particles, and describe how the particles are arranged inside atoms. Some topics to include are: the charge of the particles, the mass of the particles, and where the particles are located.
The smallest unit of matter that may be divided without producing electrically charged particles is the atom.
What is Atoms?The rest consists of a positively charged nucleus of protons and neutrons surrounded by a cloud of negatively charged electrons.
The nucleus is small and dense compared with the electrons, which are the lightest charged particles in nature. Electrons are attracted to any positive charge by their electric force; in an atom, electric forces bind the electrons to the nucleus.
It is also the smallest piece of substance with chemical element-like characteristics. As a result, the atom serves as the fundamental unit of chemistry.
Therefore, The smallest unit of matter that may be divided without producing electrically charged particles is the atom.
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A baseball has a mass of 0.15 kg. It is thrown by a major league pitcher at a speed of 45 m/s (100 mph
What is the momentum of the baseball?
rage for
Momentum is P. p= mv. P = 0.15* 45= 6.75.
What is Momentum?Momentum is a commonly used term in sports. A team that has the momentum is on the move and is going to take some effort to stop. A team that has a lot of momentum is really on the move and is going to be hard to stop.
Momentum is a physics term; it refers to the quantity of motion that an object has. A sports team that is on the move has the momentum. If an object is in motion (on the move) then it has momentum.
Momentum can be defined as "mass in motion." All objects have mass; so if an object is moving, then it has momentum - it has its mass in motion.
Therefore, Momentum is P. p= mv. P = 0.15* 45= 6.75.
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The length of a steel beam increases by 0.79 mm when it’s temperature is raised from 22°C to 35°C.
What is the length of the beam at 22°C?
These characteristics include density, Cp, thermal conductivity, and Cp. The amount of thermal energy needed to raise a substance's temperature by 1°C is known as its heat capacity (with the value depending on which temperature scale is used).
What do matter class 11's thermal characteristics entail?As we now understand, a material's thermal properties determine its ability to conduct heat or, more specifically, determine its nature in the presence of heat. As a result, when heat moves through an object, it exhibits thermal qualities.
What are the crucial areas of matter's thermal properties?Thermal Expansion is one of the main elements of a substance's thermal characteristics. Temperature Stress Temperature Conduction.
We know that change in length ΔL=LαΔT
ΔT=40−20=20 , L=5m
ΔL=5×α×20
ΔL=5×1.2×10
−5
×20
=1.2×10
−3
=1.2mm
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Test you Two groups of students pull a box in two opposite directions as in the opposite figure. If the friction force between the box and the surface is F/4, then the box will move........
a) to the left with constant velocity
b) to the left with constant acceleration
c) to the right with constant velocity
d) to the right with constant acceleration
The box would move at a constant acceleration in the direction of F.
What direction will the box move?We know that the frictional force is the force that opposes the motion of an object. In this case, we can see that the image is not shown but we can be able to discuss the scenario in a general way.
Now is the force is about F/4 that means that it is less than the applied force and that the object would move in the first place. The direction in which the object would move would now depend on where the force F is directed.
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Please help me with the following problem.
The equivalent of what mathematicians refer to as a self-adjoint operator in physics is a Hermitian operator.
What are some examples of the Hermitian operator? Mathematicians refer to an object as a self-adjoint operator; this is the physicist's equivalent.This vector space V's linear operator has a positive definite inner product.Following Dirac, the conventional notation for an inner product in physics is a bra and ket.A function f(x) could, for instance, be multiplied by x using the operator x.A is a Hermitian operator2 if we assume that f(x)=2x + 3 and xf(x)=2x2 + 3x satisfy the condition that d is across all space.The equivalent of what mathematicians refer to as a self-adjoint operator in physics is a Hermitian operator.The fundamentals of quantum physics are two properties of hermitian operators.To learn more about Hermitian operator refer
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If a Tesla Model S P100D in "Ludicrous mode" is pushed to its limit, the first 3.0 s of acceleration can be modeled as
ax={(35m/s3)t14.6m/s2−(1.5m/s3)t0s≤t≤0.40s0.40s≤t≤3.0s
A)How long does it take to accelerate to 60 mph ? Your answer, which seems impossibly short, is confirmed by track tests.
B)What acceleration would be needed to achieve the same speed in the same time at constant acceleration? Give your answer as a multiple of g .
a. Time to accelerate to 60 mph is 2.18 s.
b. The acceleration would be needed to achieve the same speed at the same time at constant acceleration is 12.3 m/s² or 1.26g.
The complete question is in the attachment. Convert the velocity unit from mph to m/s
1 miles = 1,609.344 m1 h = 3,600 sv = 60 mph = 60 miles/hoursThe object has acceleration so the object moves in a non-uniform motion.
v = u + at
u = initial velocity v = final velocitya = accelerationt = timeAccording to the model of acceleration, there is two part to acceleration. Between 0 - 0.4 s and between 0.4 s - 3 s.
From 0s - 0.4s
The initial velocity = u = 0a = (35t) m/s²t = 0.4 sFinal velocityFrom 0.4s - t
The initial velocity = final velocity from first partUsing quadratic formula to calculate the time
a = 1.5b = - 14.6c = 21.22t₁₂ = (- b ± (√(b² - 4ac))) ÷ 2a
t₁₂ = (14.6 ± (√((- 14.6)² - (4 × 1.5 × 21.22)))) ÷ (2 × 1.5)
t₁₂ = (14.6 ± (√(213.16 - 127.32)) ÷ 3.0
t₁₂ = (14.6 ± (√85.84) ÷ 3.0
t₁₂ = (14.6 ± 9.26) ÷ 3.0
t₁ = (14.6 - 9.26) ÷ 3.0 = 5.34 ÷ 3.0 = 1.78 st₂ = (14.6 - 9.26) ÷ 3.0 = 23.86 ÷ 3.0 = 7.95 st = 1.78 s
Time travel to reach 60 mph
t = t first part + t second part
t = 0.4 s + 1.78 s
t = 2.18 s
In a constant acceleration
t = 2.18 su = 0v = 60 mph = 26.82 m/sAcceleration due to gravity = 9.8 m/s²v = u + at
26.82 = 2.18a
a = 26.82 ÷ 2.18
a = 12.3 m/s²
a = (12.3 ÷ 9.8) g
a = 1.26g
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Three forces of 12, 15, and 20 Newtons are in equilibrium. If the 12 Newton force is directed horizontally to the right, what two configurations in a vertical plane may the other two forces have?
There are two possible configurations:
F1 is directed upwards with a magnitude of 15 N and F2 is directed downwards with a magnitude of 20 N.F1 is directed downwards with a magnitude of 15 N and F2 is directed upwards with a magnitude of 20 N.What is force?Force is a physical quantity that represents an interaction between objects. It is a vector quantity, meaning it has both magnitude and direction. Forces can cause objects to accelerate, change their shape, or change their velocity.
There are several types of forces, including gravitational forces, electromagnetic forces, and frictional forces. Force is measured in units of Newtons (N) and can be calculated using Newton's laws of motion. Force plays a crucial role in the study of physics, and understanding its behavior is essential for understanding the motion and interactions of objects in the world around us.
For the three forces to be in equilibrium, the sum of the forces in the x-direction must be equal to zero and the sum of the forces in the y-direction must also be equal to zero.
So, the horizontal force (12 N) is balanced by the sum of the other two forces:
12 N = F1 + F2
where F1 and F2 are the magnitudes of the other two forces.
Since the forces are in a vertical plane, one of the forces must be directed upwards and the other downwards.
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The table to the right shows the time it takes three trucks to go from 0 to 60 km/h
The quantities that can be compared from four cars is the average acceleration. Answer A.
The question isn't complete. A similar question is in the attachment. When a truck or a car increases its velocity over time, it means it experiences acceleration. The vehicle moves in a non-uniform motion. The formula in non-uniform motion
v = u + atv² = u² + 2add = ut + 0.5at²where
t = time (s)d = distance (m)u = initial velocity (m/s)v = final velocity (m/s)a = acceleration (m/s²)The information in the question that four cars have a different time to travel but have the same
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A 100 kg person pushes a box up a ramp at constant speed. The mass of the box is 30 kg, the coefficient of kinetic friction between the box and the ramp is 0.2, and the ramp is inclined 25 degrees above the horizontal. The person (new at pushing boxes up ramps) pushes purely in the horizontal direction. HINT: you must draw complete FBDs to receive full credit. a) Find an expression for the magnitude of the normal force on the box due to the ramp. This answer should be left in variables, not numbers. b) Find the magnitude of the force on the box due to the person. c) Each step the person takes requires a force of static friction so that she does not slip. Find the magnitude of the force of static friction on the person due to the ramp. d) Find the minimum coefficient of static friction between the person's shoes and the ramp, so that this feat is possible.
Since cos(25) is approximately 0.906, the minimum coefficient of static friction is μs >= 0.906
How find the normal force?a) Substituting this into the previous equation, we get:
N - mg * sin(25) = μk * N
Solving for N, we get:
N = mg * sin(25) / (1 - μk)
b) Since the force applied by the person is horizontal, the horizontal component of the normal force must balance it. Therefore,
F = N * cos(25)
Solving for N, we get:
N = F / cos(25) = 0 / cos(25) = 0 N
c) Since the person is not slipping, the friction force must balance the horizontal component of the gravitational force. Therefore,
fs = μs * N
where μs is the coefficient of static friction.
Since N = mg * cos(25),
fs = μs * mg * cos(25)
d)Since cos(25) is approximately 0.906, the minimum coefficient of static friction is
μs >= 0.906
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Dogs can hear higher-
pitched whistles that humans do. How do you
think the sound frequencies that dogs can
hear compare to the frequencies that humans
can hear?
Dogs can hear sounds at higher frequencies than humans. The range of sound frequencies that dogs can hear is approximately 40 Hz to 60,000 Hz, while the range for humans is 20 Hz to 20,000 Hz. This means that dogs can hear ultrasonic sounds that are beyond the range of human hearing.
What is sound about?In terms of physics, sound is a vibration that travels through a transmission medium like a gas, liquid, or solid as an acoustic wave.
Sound is the reception of these waves and the brain's perception of them in terms of human physiology and psychology. Dogs have the ability to hear ultrasonic sounds that are audible only to them.
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Determine the normal boiling point of chloroform if its heat of vaporization is 31.4 kJ/mol and the vapor pressure is 190 mmHg at 25°C
Vapor pressure (or vapour pressure in English-speaking countries other than the US; see spelling differences) or equilibrium vapor pressure.
What is Vapor pressure?The equilibrium vapor pressure is an indication of a liquid's thermodynamic tendency to evaporate. It relates to the balance of particles escaping from the liquid (or solid) in equilibrium with those in a coexisting vapor phase.
A substance with a high vapor pressure at normal temperatures is often referred to as volatile. The pressure exhibited by vapor present above a liquid surface is known as vapor pressure.
As the temperature of a liquid increases, the attractive interactions between liquid molecules become less significant in comparison to the entropy of those molecules in the gas phase, increasing the vapor pressure.
Therefore, Vapor pressure (or vapour pressure in English-speaking countries other than the US; see spelling differences) or equilibrium vapor pressure.
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Water at 200
C flows through a horizontal pipe of radius 1.0cm. If the flow velocity at the center is
0.2m/s find the pressure drop along a 4m section of the pipe due to viscosity 1.6x10-3NSM-2
The pressure drop along a 4m section of the pipe due to viscosity is 0.00653 N/m.
What is viscosity?The resistance of a fluid to deformation at a specific rate is measured by its viscosity.
Temperature of water is = 20° C.
The radius of the horizontal pipe = 1.0 cm = 0.01.
The velocity of the center is = 0.2 m/s.
The viscosity of the water = 16×10⁻³ N-s-m⁻²
Hence, the pressure drop along a 4m section of the pipe due to viscosity = fLv²/2gD
= (16 ×10⁻³ )×(4 × 0.2²)/(2 × 9.8 × 2 ×0.01) N/m
= 0.00653 N/m.
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Which equation would you use to solve the following problem: A train
decreases speed from 30 m/s to 20 m/s while in 20s. What is the
displacement of the train?
O vf = vo+a*t
O x = 1/2* (vf+vo) * t
O x= vo*t + 1/2 *a* t^2
O we don't have an equation for this problem yet
The kind of equation that we can use to solve the problem is; x = 1/2* (vf+vo) * t. Option B
What are the equations of motion?Th equations of motion has to do with the equations that we cam be able to apply so as to solve the equations that are for the uniformly accelerated motion.
In the case of the problem that we have in this question, we have been told that A train decreases speed from 30 m/s to 20 m/s while in 20s. The formula that can be used to get the displacement of the train is x = 1/2* (vf+vo) * t.
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Two pieces of kryptonite, #1 and #2, have identical masses, but the net force applied to #1 is 20 N and to #2 is 400 N. The acceleration
of #1 is larger.
incorrect
depends on the weight of each piece of kryptonite.
of each piece of kryptonite is the same.
of #2 is larger.
What type of decay is this?
Beta decay will occur in isotopes with a N/Z ratio greater than 1, which translates to an overabundance of neutrons.
How do you know if its alpha or beta decay?Beta decay produces a new element that has one more proton and one fewer neutron while alpha decay produces a new element with some less protons and two fewer neutrons. When a nucleus from a higher energy state descends to a lower energy state and releases the excess energy through to the emission of high energy photons, this process is known as gamma decay.
Any one of three radioactive disintegration processes known as beta decay occurs when some unstable atoms spontaneously release surplus energy and undergo a shift in one unit of positive ions without changing their mass number.
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The graph shows the maximum amount of water vapor that air can hold at different temperatures.
Line graph of maximum humidity on a coordinate plane. X-axis labeled Temperature (degrees Celsius). Y-axis labeled Water Vapor Density grams per cubic meter. Line starts at (0, 2) and gradually rises through (30, 30), 35, 40), (40, 50), (45, 62).
Beth’s hygrometer is reading a temperature of 30°C and a relative humidity of 65%. The humidity in the air is
grams/cubic meter.
Beth’s hygrometer is reading a temperature of 30°C and a relative humidity of 65%. The humidity in the air is 19.5 grams/cubic meter.
What is the humidity?The actual vapor density or humidity can be determined from the relative humidity value and the saturation vapor density.
The formula that relates the actual vapor density or humidity, the relative humidity, and the saturation vapor density is given below:
relative humidity = (actual vapor density / saturation vapor density) x 100%Hence, the actual vapor density can be calculated as follows:
Actual vapor density or humidity = relative density * saturation vapor density / 100
From the graph;
saturation vapor density at 30°C = 30 g/cm³
relative humidity = 65%
Humidity = 65 * 30 / 100
Humidity = 19.5 g/cm³
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to two paragraph explain how we use Force in cur every day day lives
We can use Force in our everyday lives through the following below:
The force which is used to lift object by the hands.The force of the hair brush on hair when it is being brushed.What is Force?This is referred to as an influence that can change the motion of an object and the S.I unit is Newton. The formula is F = ma where m is mass and a is acceleration.
The use of force is important in our every day lives as it is used to perform basic activities such as lifting objects for use and brushing the hair to look good and tidy.
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(a) In the absence of air resistance, a golf ball projected from the point P follows a parabolic path and lands at the point Q. The initial velocity of the ball is u and at an angle of a with the horizontal
(i) Derive an expression for the horizontal distance PQ in terms of u, a, and the acceleration due to gravity g.
(ii) What is the value of the angle of projection a for the distance PQ to be maximum?
(b) A motorcycle stuntman who is moving horizontally takes off from a point 15.0 m above the ground and lands 60.0 m away as shown in the figure. Calculate:
(i) the time between taking off and landing
(ii) the speed of the motorcycle at take-off.
Answer:
a.
i. t = u^2 * sin(a) * cos(a) / g
ii. 90 degree
Explanation:
a.(i) The horizontal distance PQ can be expressed as:
PQ = u * cos(a) * t
Where t is the time taken for the ball to reach the ground, which can be determined using the vertical motion equation:
v = u * sin(a) - g * t
where v is the final velocity (0 m/s at the ground) and g is the acceleration due to gravity (9.8 m/s^2). Solving for t, we have:
t = (u * sin(a)) / g
Substituting t back into the expression for PQ:
PQ = u * cos(a) * (u * sin(a)) / g
t = u^2 * sin(a) * cos(a) / g
(ii) To find the angle of projection for maximum PQ, we need to find the maximum of PQ with respect to a. Taking the derivative of PQ with respect to a, setting it equal to zero, and solving for a, we have:
dPQ/da = (u^2 * cos^2(a) - u^2 * sin^2(a)) / g = 0
This gives us:
sin(2a) = 0
The maximum value of PQ occurs at:
a = 90° or a = 270°
So the angle of projection for maximum PQ is 90 degrees.
A 25-kg chandelier hangs from a ceiling on a vertical 4.0-m-long wire.
Part A: What horizontal force would be necessary to displace its position 0.16 m to one side?
Express your answer to two significant figures and include the appropriate units.
Part B: What will be the tension in the wire?
Express your answer to two significant figures and include the appropriate units.
The horizontal force required to displace the chandelier 0.16 m is equal to the restoring force divided by the displacement is 1500N
What is the horizontal force?A. To displace the position of the chandelier 0.16 m to one side, a horizontal force is necessary to balance the restoring force due to the tension in the wire. This restoring force can be calculated as the weight of the chandelier times the acceleration due to gravity:
Frest = W * g = 25 kg * 9.8 m/s^2 = 245 N
The horizontal force required to displace the chandelier 0.16 m is equal to the restoring force divided by the displacement:
Fhorizontal = Frest / (0.16 m) = 245 N / 0.16 m = 1531 N
Rounding to two significant figures, the answer is:
Fhorizontal = 1500 N
B. The tension in the wire can be calculated as the sum of the forces in the vertical direction, which is equal to the weight of the chandelier:
Tension = W = 25 kg * 9.8 m/s^2 = 245 N
Rounding to two significant figures, the answer is:
Tension = 250 N
Learn more about tension in brainly.com/question/15880959
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A car slows from 22m/s to 3m/s with a constant acceleration of -2.1m/s². How long does it take?
Answer:
The car takes approximately 6.3 seconds to slow from 22m/s to 3m/s with a constant acceleration of -2.1m/s². This is calculated using the equation vf = vi + at, where vf is the final velocity, vi is the initial velocity, a is the acceleration, and t is the time.
Explanation:
Answer:
The car takes approximately 6.3 seconds to slow from 22m/s to 3m/s with a constant acceleration of -2.1m/s². This is calculated using the equation vf = vi + at, where vf is the final velocity, vi is the initial velocity, a is the acceleration, and t is the time
Explanation: