Answer:
is a guideline to help an individual write and achieve well-specified goals.
Explanation:
An action plan is a guideline to help an individual write and achieve well-specified goals.
Answer:
yes, the guideline is to help an individual write and achieve well-specified goals.
Explanation:
water parks often include a log rolling area, in which participants try to stay upright while balancing on top of floating logs that are free to rotate in the water. if you've tried this, you know that the larger the diameter of the log, the easier it is to balance on top. (figure 1)
Buoyancy Force is the reason for the larger the diameter as the Larger the diameter larger the volume of log rolling and the higher the Buoyancy force which leads to floating the participants.
The floating of any dogy depends upon the Buoyancy force that the body is having or we can say the force which is applied on the water's surface to float on it. And However, Buoyancy depends on three things.
1. Gravitational pull(g)- the force applied by the planet to pull/attract ant mass towards itself. in the case of the earth, it is fixed which is 9.8 ms^-2.
2. The density(p)- It is the mass per volume of any liquid In the case of distilled water it is 997 kg/m³. It may barry for ocean water.
3. Volumn of the body(v)- It is the volume of the body which is floating on water.
So fb = g*p*v where fb( Buoyancy force) is directly proportional to the volume of the body.
So the Greater the volume of the body higher it will float.
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what is diffrence between damping and undamping?
Answer:
Oscillation whose amplitude reduce with time are called damped oscillation. This happen because of the friction. In oscillation if its amplitude doesn't change with time then they are called Undamped oscillation
Damped and undamped vibration refer to two different types of vibrations. The main difference between damped and undamped vibration is that undamped vibration refer to vibrations where energy of the vibrating object does not get dissipated to surroundings over time, whereas damped vibration refers to vibrations where the vibrating object loses its energy to the surroundings.
solve for a in the acceleration equation
To calculate acceleration, you use the equation a =Δv/Δt, where Δv is the change in velocity, and Δt is the time it takes for the change to occur.
In physics, acceleration is the change in velocity in a given unit of time. The acceleration of an object is caused by a force acting on the object, as explained in Newton's second law. The SI unit for acceleration is meters per second squared (m/s). Acceleration is the product of the velocity (m/s) divided by the time (s). So, the resulting formula is a = v/t.
Acceleration and the most basic velocity in acceleration are how fast a car can increase its speed, while velocity looks at how fast a car travels a certain distance.
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A water tower is a familiar sight in many towns. The purpose of such a tower is to provide storage capacity and to provide sufficient pressure in the pipes that deliver the water to customers. The drawing shows a spherical reservoir that contains 5.25 105 kg of water when full. The reservoir is vented to the atmosphere at the top. For a full reservoir, find the gauge pressure that the water has at the faucet in (a) house A and (b) house B. Ignore the diameter of the delivery pipes
The image of the water tower and the houses is in the attachment.
Answer: (a) P = 245kPa;
(b) P = 173.5 kPa
Explanation: Gauge pressure is the pressure relative to the atmospheric pressure and it is only dependent of the height of the liquid in the container.
The pressure is calculated as: P = hρg
where
ρ is the density of the liquid, in this case, water, which is ρ = 1000kg/m³;
When it is full the reservoir contains 5.25×10⁵ kg. So, knowing the density, you know the volume:
ρ = \(\frac{m}{V}\)
V = ρ/m
V = \(\frac{5.25.10^{5}}{10^{3}}\)
V = 525 m³
To know the height of the spherical reservoir, its diameter is needed and to determine it, find the radius:
V = \(\frac{4}{3}.\pi.r^{3}\)
\(r = \sqrt[3]{ \frac{3}{4\pi } .V}\)
r = \(\sqrt[3]{\frac{525.3}{4\pi } }\)
r = 5.005 m
diameter = 2*r = 10.01m
(a) Height for House A:
h = 15 + 10.01
h = 25.01
P = hρg
P = 25.01.10³.9.8
P = 245.10³ Pa or 245kPa
(b) h = 25 - 7.3
h = 17.71
P = hρg
P = 17.71.1000.9.8
P = 173.5.10³ Pa or 173.5 kPa
The gauge pressure at house A, and B, is the measurement of pressure
relative to the pressure of the atmosphere.
The gauge pressure at house A is approximately 244.5 kPa.The gauge pressure at house B is approximately 173.116 kPa.Reasons:
Question parameters;
Mass of water in the tower, m = 5.25 × 10⁵ kg
Shape of the reservoir = Spherical
Height of the bottom of the reservoir above the main ground level = 15.0 m
Height of the house A above the ground = 0
Height of the house B above the ground = 7.30 m
(a) Required:
The gauge pressure at house A
Solution:
The density of the water, ρ ≈ 997 kg/m³
\(\mathrm{Volume \ of \ water \ in \ the \ tank,} \ V = \dfrac{5.2 \times 10^5 \, kg}{997 \, kg/m^3} \approx 526.58 \, m^3\)
Volume of water in the filled tank = Volume of the tank ≈ 526.28 m³
\(\mathrm{Volume \ or \ a \ sphere, } V = \dfrac{4}{3} \cdot \pi \cdot r^3\)
Therefore;
\(\mathrm{Volume \ or \ the \ spherical \ tank} = \dfrac{4}{3} \cdot \pi \cdot r^3 \approx 526.28\)
Which gives;
\(r = \sqrt[3]{\dfrac{526.58}{\pi} \times \dfrac{3}{4} } \approx 5\)
The diameter of the tank = The height of the tank, h = 2 × r
∴ h = 2 × 5 m = 10 m
The gauge pressure is the pressure above the prevailing atmospheric
pressure;
For the system vented to the atmosphere, \(P_{gauge}\) = ρ·g·hTherefore;
The gauge pressure at house A, \(P_{gA}\) = 997 × 9.81 × (10 + 15) = 244514.25
The gauge pressure at house A, \(P_{gA}\) = 244514.25 N/m² ≈ 244.5 kPa
(b) Required:
Gauge pressure at house B
At house B, we have;
Gauge pressure at house B, \(P_{gB}\) = 997 × 9.81 × (10 + 15 - 7.3) = 173116.089
The gauge pressure at house B = 173116.089 N/m² ≈ 173.116 kPa
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Ken Warby holds the world record speed
on water. If he drove his motorboat a
distance of 1000.0 m in 7.045 s, how fast
was his boat moving?
Know
Find
Equation
Solve
Answer:
141.9m/s
Explanation:
know:
distance = 1000.0m
time = 7.045s
find:
speed = ?
equation:
v = d/t
solve:
v = d/t
= 1000.0m/7.045s
= 141.9m/s
therefore, his boat was moving 141.9m/s
How has Physics improved
or affected our society?
By supplying the fundamental knowledge required to create new instruments and techniques for medical use, physics enhances our quality of life
From can openers, light bulbs, and mobile phones to muscles, lungs, and brains; from paintings, piccolos, and pirouettes to cameras, vehicles, and cathedrals; from earthquakes, tsunamis, and storms to quarks, DNA, and black holes, physics aids us in understanding the workings of the world around us.
The science of physics is the most fundamental and has many applications in contemporary technology. Because it makes it possible for smartphones, computers, televisions, watches, and many other modern technologies to function automatically, physics is crucial to modern technology.
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Two loudsspeakers emit identical sound waves along the x axis. THe osund at a point on the axis has maximum intensity when the speakers are 40 cm apart. The sound intensity decreases as the distance between the speakers is increased, reaching zero at a separation of 50 cm. If the distance between the speakers continuse to increase, at what separation will the sound intensity again be a maximum?
Answer: 30 cm.
Solving
The situation described is that of two sources of sound waves that are separated by some distance. The two waves interfere with each other constructively at some points and destructively at others. When they interfere constructively, the amplitude (and intensity) of the sound wave is greater than when they interfere destructively.
When the speakers are 40 cm apart, the waves that they produce are in phase at some points on the axis, leading to constructive interference and a maximum in the intensity of the sound. As the distance between the speakers is increased beyond 40 cm, the points of constructive interference move farther apart, and the intensity of the sound decreases. When the speakers are 50 cm apart, the waves that they produce are exactly out of phase at some points on the axis, leading to complete destructive interference and a minimum in the intensity of the sound.
If the separation between the speakers continues to increase, the points of constructive interference will move closer together again, and the intensity of the sound will increase. The separation between the speakers at which the intensity of the sound will again be a maximum can be found using the following equation:
d = λ/2 + nλ
where d is the separation between the speakers, λ is the wavelength of the sound wave, and n is an integer that represents the number of half-wavelengths between the speakers.
At the maximum, the separation is an even multiple of half the wavelength, so we can use the formula above with n = 1. The wavelength can be found from the distance between the speakers at the minimum, which is 50 cm, and the distance at the maximum, which is 40 cm:
λ = 2(d_max - d_min) = 20 cm
Substituting λ and n into the formula gives:
d = λ/2 + nλ = 10 cm + 20 cm = 30 cm
Therefore, the sound intensity will be a maximum again when the separation between the speakers is 30 cm.
PLEASE HURRY
A 0.38 kg bucket of water is swung in a horizontal circle with a radius of 0.86 meters and a constant speed of 2.4 m/s.
What is magnitude of the centripetal force on the bucket of water?
A.) 0.78 N
B.) 1.1 N
C.) 2.5 N
D.) 6.7 N
The magnitude of the centripetal force on the bucket of water is = 1.1 N
What is centripetal force?Centripetal force is an inward force that is responsible for keeping an object in a curved path. It is required for an object to move in a circular path or orbit. The force acts towards the centre of the circle and is perpendicular to the velocity vector. The magnitude of the centripetal force is directly proportional to the mass of the object, the square of its velocity, and inversely proportional to the radius of the circle. Centripetal force is sometimes also referred to as an acceleration, as it is the force that causes an object to accelerate in a circular motion.
The magnitude of the centripetal force on the bucket of water is given by:
F = mv2/r
= (0.38 kg)(2.4 m/s)2/(0.86 m)
= 1.1 N
Therefore, The magnitude of the centripetal force on the bucket of water is = 1.1 N
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2 red and 2 blue overlapping balls in the center are surrounded by a green, fuzzy, circular cloud with a white line running through it. 2 green balls sit on the white line, and a line leading a bracket around the balls is labeled A. A line leading to a bracket overlapping the white line is labeled B. Which is a characteristic of the part of the atom marked "B”? It is very dense. It has a large mass. It is negatively charged. It is where neutrons move.
A characteristic of the part of the atom marked "B” is that it has a large mass. Option B. This is further explained below.
What is atom?Generally, Atom, the lowest possible unit into which matter may be split without releasing electrically charged particles.
In conclusion, the protons and neutrons are represented by the red and white spheres, respectively. Since it indicates both protons and neutrons, the line preceding the bracket around the balls (designated A) stands in for the atom's nucleus.The mass of the "B" section of the atom is very high.
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Answer:
it's b
Explanation:
i did the ed quiz
A ball travels in a circle of radius 7 m with a constant tangential velocity of 15 m/s. What is the magnitude and direction of the acceleration of the ball?
Given,
Radius of the circle r=7 m
The tangential velocity is v=15 m/s.
The acceleration is
\(a=\frac{v^2}{r}=\frac{15^2}{7}=32.14m/s^2\)The acceleration is towards the centre.
$3.49/ gallon and other is $1.25/L which container of milk is a better deal
Valid Expressions are; t = ∛(d²/va), a = d/t², a = √(vd/t³), v = at
while the Invalid expressions are; v = a/t and d = at
Explanation:
Given expressions
1) v = a/t
2) t = ∛(d²/va)
3) d = at
4) a = d/t²
5) a = √(vd/t³)
6) v = at
First we get our units of parameters
V = m/s, t = sec, d = m, a = m/s²
so
1)
v = a/t
we substitute in our units of parameters
v = m/s² / s = m/s² × 1/s = m/s³
v ≠ m/s³
therefore it is false
2)
t = ∛(d²/va)
we substitute
t = ∛(m² / m/s × m/s²)
t = ∛(m² / m²/s³)
t = ∛(s³)
t = s
correct, the expression is true
3)
d = at
we substitute
d = m/s² × s
d = m/s² × s/1 = ms/s² = m/s
d ≠ m/s (because d = m)
so expression is false
4)
a = d/t²
we substitute
a = m / s² = m/s²
correct
the expression is true
5)
a = √(vd/t³)
we substitute
a = √(m/s×m / s³) = √(m²/s / s³) = √(m²/s × 1/s³) = √(m²/s⁴) = m/s²
so a = m/s²
correct
the expression is true
6)
v = at
we substitute in the units
v = m/s² × s = m/s² ×s/1 = ms/s² = m/s
v = m/s
correct
the expression is correct
A wooden baseball bat and an aluminum baseball bat have the exact same size, shape, and mass. Aluminum is much denser than wood. Explain how the two bats could be the same size, shape, and mass.
Due to density, the two bats have the same size, shape, and mass.
How the two bats could be the same size, shape, and mass?The two bats could be the same size, shape, and mass if they have the same density because density is directly proportional to mass so if the density same, the mass will also be the same.
So we can conclude that due to density, the two bats have the same size, shape, and mass.
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A rocket has been fired upward to launch a stellite in its orbit name two forces acting on the rocket immediately after leaving the launching pad
Two forces acting on the rocket immediately after leaving the launching pad are the gravitational force and the thrust force.
1. Gravitational Force: The gravitational force is the force exerted by the Earth on the rocket due to their mutual gravitational attraction. It acts downward and is responsible for the rocket's weight.
This force can be represented by the equation Fg = mg, where Fg is the gravitational force, m is the mass of the rocket, and g is the acceleration due to gravity. The gravitational force acts to pull the rocket downward, opposing its upward motion.
2. Thrust Force: The thrust force is the force generated by the rocket's engines as they expel exhaust gases in the opposite direction. It acts upward and propels the rocket forward.
The magnitude of the thrust force depends on factors such as the design of the rocket engines, the amount of fuel burned, and the rate of exhaust gas expulsion. The thrust force must be greater than or equal to the gravitational force for the rocket to overcome Earth's gravity and achieve upward acceleration.
Initially, when the rocket is launched, the thrust force is at its maximum while the gravitational force remains constant. As the rocket gains altitude, the gravitational force decreases slightly due to the increasing distance from the Earth's center.
However, the thrust force continues to be the dominant force propelling the rocket upward.
It's important to note that other forces such as air resistance and wind may also act on the rocket, but immediately after leaving the launching pad, these forces are typically negligible compared to the gravitational force and thrust force.
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Using the periodic table of elements, fill in the chart below to identify and describe the properties of the noble gases
Answer:
Explanation:
1) Silicon (Si) is element with atomic number 14 (14 protons and 14 electrons).
Electron configuration of silicon atom:
₁₄Si 1s² 2s² 2p⁶ 3s² 3p² or [Ne] 3s² 3p², neon (Ne) is noble gas with atomic number 10.
2) Francium (Fr) is element with atomic number 87 (87 protons and 87 electrons).
Electron configuration of francium atom:
₈₇Fr 1s²2s²2p⁶ 3s² 3p⁶ 3d¹⁰ 4s² 4p⁶ 4d¹⁰ 5s² 5p⁶ 4f¹⁴ 5d¹⁰ 6s² 6p⁶ 7s¹ or [Rn] 7s¹, radon (Rn) is noble gas with atomic number 86.
3) Mercury (Hg) is element with atomic number 80 (80 protons and 80 electrons).
Electron configuration of mercury atom:
₈₀Hg 1s²2s²2p⁶3s²3p⁶3d¹⁰4s²4p⁶ 4d¹⁰ 5s² 5p⁶ 4f¹⁴ 5d¹⁰ 6s² or [Xe] 4f¹⁴ 5d¹⁰ 6s², xenon (Xe) is noble gas with atomic number 54.
4) Vanadium (V) is element with atomic number 23 (23 protons and 23 electrons).
Electron configuration of vanadium atom:
₂₃V 1s² 2s² 2p⁶ 3s² 3p⁶ 3d³ 4s² or [Ar] 3d³ 4s², argon (Ar) is noble gas with atomic number 54.
Tonya is modeling the discovery of electromagnetic induction. Which procedure should she use? moving a magnet into a coil of wire in a closed circuit moving a magnet into a coil of wire in an open circuit bringing a compass near a wire that has no electric current bringing a compass near a wire that has an electric current
To model the discovery of electromagnetic induction, Tonya should use the procedure of moving a magnet into a coil of wire in a closed circuit.
Tonya should use the procedure of moving a magnet into a coil of wire in a closed circuit.
Electromagnetic induction refers to the phenomenon of generating an electric current in a conductor by varying the magnetic field passing through it. This concept was discovered by Michael Faraday in the early 19th century. To model this discovery, Tonya needs to recreate the conditions that led to this breakthrough.
In Faraday's experiment, he observed that when a magnet is moved into or out of a coil of wire, it induces an electric current in the wire. This occurs when the magnetic field passing through the coil changes. Therefore, Tonya should use a similar setup to replicate this process.
Out of the given options, the most appropriate procedure for Tonya would be to move a magnet into a coil of wire in a closed circuit. By having a closed circuit, it means that the ends of the wire are connected to form a complete loop. When the magnet is moved into the coil, the changing magnetic field induces an electric current to flow through the wire.
This procedure demonstrates the principle of electromagnetic induction and shows how a changing magnetic field can produce an electric current. It allows Tonya to visually observe the effects of the induced current, which is essential in modeling the discovery of electromagnetic induction.
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Select the correct answer
A periodic wave travels from one medium to another. Which pair of variables are likely to change in the process?
A
velocity and wavelength
B
velocity and frequency
C
frequency and wavelength
D.
Frequency and Phase
E.
Wavelength and phase
Answer:
velocity and wavelength
Explanation:
When a ray of light moves from one medium to another, the ray of light changes the direction when it enters the second medium, refraction of light occurs.
When it changes the direction, the frequency will remain the same because it depends only on the source not on the medium.
As the refractive index of two medium is not same, it means the wavelength will change.
Also, speed = frequency × wavelength
So, wavelength and velocity changes. Hence, the correct option is (a).
Answer:
velocity and wavelength
Explanation:
Please help im stuck i need to complete an acrostic poem for homework. It should be about embryonic similarities and the information scientists use to support evolution.
Using these letters to start each sentence
E
M
B
R
Y
O
N
I
C
The Embryonic similarities have been a strong lead in the study of evolution.
How does embryonic similarities support evolution?Embryonic similarities are a type of evidence that support the theory of evolution by natural selection. The theory of evolution proposes that all living organisms share a common ancestry and have changed over time through the process of natural selection.
In summary, embryonic similarities support the theory of evolution by providing evidence of a shared ancestry and helping to explain the mechanisms of evolution.
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g An object with mass 1kg travels at 3 m/s and collides with a stationary object whose mass is 0.5kg. The two objects stick together and continue to move. What is the velocity of the two objects together after collision
Answer:
2
Explanation:
since the second object was in it stationary, it velocity is 0 m/s
3. An object with a mass of 3.2 kg has a force of 6.2 N applied to it. What is the resulting acceleration
of the object?
Answer:
The answer is 1.94 m/s²Explanation:
The acceleration of an object given it's mass and the force acting on it can be found by using the formula
\(a = \frac{f}{m} \\ \)
where
f is the force
m is the acceleration
From the question we have
\(a = \frac{6.2}{3.2} \\ = 1.9375\)
We have the final answer as
1.94 m/s²Hope this helps you
6. A picture of weight, w is hanging from a steel nail as shown in the figure below. The nail has a diameter of 1.50 mm and an original length, Lo = 5.0 mm. Useful Information: The shear modulus, G for steel is 80 x 10° N.m². (a) (b) (c) 1.50 mm 3 Ax = 1.80 μm W Lo = 5.00 mm M What kind of deformation occurs in this case? How are stress and strain in this deformation related to each other? [3] When the picture is hung from the nail, the head of the nail displaces vertically downwards by an amount Ax = 1.80 µm. Find the mass of the picture. Neglect the weight of the nail. [6] What angle does the nail make with the horizontal after the picture is hung from it? [2]
The mass of the picture is approximately 5.19 kilograms.
How to solve for the problemThe deformation in this case is called shear deformation, a type of deformation that occurs when parallel internal surfaces slide past one another. It is caused by shear stress in the structure. The shear stress (τ) is the force (F) applied divided by the cross-sectional area (A) of the nail. The shear strain (γ) is the displacement (Δx) divided by the original length (L0).
The relationship between shear stress and shear strain is given by the shear modulus (G) in the formula:
τ = G * γ
To find the weight of the picture, we need to calculate the shear stress first:
The cross-sectional area A of the nail is given by the formula for the area of a circle:
A = πr² = π(d/2)² = π(0.0015 m / 2)² = 1.767 x 10^-6 m².
The shear strain γ is given by:
γ = Δx / L0 = (1.80 x 10^-6 m) / (5 x 10^-3 m) = 0.36.
The shear stress τ can now be calculated by rearranging the formula:
τ = G * γ
=> τ = (80 x 10^9 N/m²) * 0.36 = 28.8 x 10^9 N/m²
The force F on the nail is equal to the weight w of the picture, and it can be calculated from the shear stress:
τ = F / A
=> F = τ * A = (28.8 x 10^9 N/m²) * (1.767 x 10^-6 m²) = 50.89 N.
Since weight w = m * g, where m is mass and g is the acceleration due to gravity (approximately 9.81 m/s²), we can find the mass m:
m = w / g = (50.89 N) / (9.81 m/s²) = 5.19 kg.
So, the mass of the picture is approximately 5.19 kilograms.
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the mass of the velociraptor and cage together is 175 kg. What is the gravitational potential energy added when when the velociraptor and cage is lifted from the ground to a height of 9 m?
The gravitational potential energy added when the velociraptor and cage is lifted from the ground to a height of 9 m is approximately 15,998.95 joules.
What is Potential Energy?
Potential energy is a form of energy that is stored in an object due to its position or configuration in a system. It is the energy that an object has the potential to possess, or the ability to do work, as a result of its position or state.
The gravitational potential energy (GPE) added when the velociraptor and cage is lifted from the ground to a height of 9 m can be calculated using the formula:
GPE = mgh
Where m is the mass of the velociraptor and cage, g is the acceleration due to gravity (approximately 9.81 m/\(s^{2}\)), and h is the height lifted.
Given that the mass of the velociraptor and cage together is 175 kg, and the height lifted is 9 m, we can substitute these values into the formula:
GPE = mgh
GPE = (175 kg) x (9.81 m/\(s^{2}\)) x (9 m)
GPE = 15,998.95 J (joules)
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Question 15 of 32
A bungee jumper jumps off a bridge and bounces up and down several times.
She finally comes to rest 30 m below the bridge from which she just jumped.
If her mass is 50 kg and the spring constant of the bungee cord is 10 N/m,
how much energy was lost due to air resistance while she was bouncing?
(Recall that g = 9.8 m/s²)
A. 7330 N
B. 9200 N
C. 10,200 N
D. 8605 N
C. 10,200 N is how much energy was lost due to air resistance while she was bouncing
How much energy was lostThe energy lost due to air resistance while the bungee jumper was bouncing can be calculated by finding the total mechanical energy of the system at the beginning of the jump and comparing it to the total mechanical energy at the end of the jump.
At the beginning of the jump, the total mechanical energy is given by:
Ei = mgh
where m is the mass of the bungee jumper, g is the acceleration due to gravity, and h is the height of the bridge. Therefore, at the beginning of the jump:
50 x 30 x 10 - 1/2 x 30^2 x 10
= 15000 - 4500
= 10,200 N
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prepare a report on why a vehicle needs to be maintained/serviced after a certain period of time. How is servicing different in a petrol/diesel and electric vehicle?
Vehicles need to be serviced for several reasons such as preventing costly repairs and improving fuel economy.
Why should cars be maintained and / or serviced ?First, regular maintenance can help to prevent costly repairs down the road. Second, maintenance can help to improve fuel economy and emissions. Third, maintenance can help to keep your vehicle safe and reliable.
The servicing requirements for petrol/diesel and electric vehicles differ in a number of ways. Petrol/diesel vehicles require oil changes more frequently than electric vehicles. This is because petrol/diesel engines use oil to lubricate the moving parts, while electric motors do not. Petrol/diesel vehicles also require tune-ups more frequently than electric vehicles.
This is because petrol/diesel engines have more moving parts that need to be synchronized, while electric motors have fewer moving parts.
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A train is travelling along a straight track at constant velocity from Western Station to Eastern station. The mile markers increase towards the east. A passenger notices that, at mile marker 25, the reading on this stopwatch is 15 minutes, and at mile marker 60, the reading on this stopwatch is 45 minutes. What is the velocity of the train in meters per second
Answer:
Explanation:
Displacement of train = 60 - 25 = 35 mile
= 35 x 1.6 = 56 km
duration of time = 45 - 15 = 30 minutes
= 30 x 60 = 1800 s
velocity of train = displacement / time
= 56 / 1800 = .03111 km /s
= 31.111 m / s
03: Hook's law suggests that F is directly proportional to -x, how much true you have found this statement in your experiment? Explain any differences.
Hooke's Law can be given as follows sometimes:
The restoring force of a spring is equal to the spring constant multiplied by the displacement from its normal position:
F = -kx
Where, F = Restoring force of a spring (Newtons, N)
k = Spring constant (N/m)
x = Displacement of the spring (m)
The negative sign relates to the direction of the applied force and by convention, the minus or negative sign is present in F = -kx. The restoring force F is directly proportional to the displacement (x), according to Hooke's law. When the spring is compressed, the displacement (x) is negative. It is zero when the spring is at its original length and positive when the spring is extended.
Practically, Hooke's Law is applicable only within a limited frame of reference, and through experimenting, this statement proves to be true. Because materials cannot be compressed beyond a certain size or expanded beyond a certain size without some permanent deformation or change of their original state.
The law only applies under some conditions such as a limited amount of force or deformation. Factually, many materials will noticeably deviate from Hooke's law even before those elastic limits are reached.
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A 50-cm-long spring is suspended from the ceiling. A 210 g mass is connected to the end and held at rest with the spring unstretched. The mass is released and falls, stretching the spring by 16 cm before coming to rest at its lowest point. It then continues to oscillate vertically.
The value of spring constant (k) is 25 N/m.
Conservation of energy, potential energy of a stretched spring, gravitational potential energy, frequency of oscillation in a spring coupled to a mass, and variation of acceleration due to gravity with altitude are the principles necessary to answer the given problem.
To begin, use energy conservation to equal change in gravitational potential energy on mass attached to spring and elastic potential energy of stretched spring. Then, in the equation, substitute the specified numbers and solve for the spring constant. Then, calculate the amplitude by taking half of the value of spring stretching from equilibrium, and the frequency of oscillation by using the calculation for frequency of oscillation in a stretched string in terms of mass and spring constant.
Formula apply
U=mgh
U=1/2kx^2
putting the value of K ,x ,mass and g then
k is 25N/m
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Please do number three for me step-by-step and explain the east and west thank you
the Given that the distance from mall to home is 1000 m.
The distance from home to the library is 1200 m.
So the total displacement is 1000 +1200 = 2200 m.
The displacement is from the library to the mall, so the displacement is towards the west.
So the displacement is 2200 m towards west.
b)A man walks 95 km, East, then 55 km, north. Calculate his RESULTANT
DISPLACEMENT( please provide magnitude and direction)
The resultant displacement of the man is 109.77 km in the direction N60°E.
DisplacementDisplacement is the distance travelled in a specified direction.
To calculate displacement, the straight line from starting point to end point of travel is taken and calculated.
Resultant displacement of the manIn the example above, a man walks 95 km, East, then 55 km, north.
The two distances form a right-angled triangle with two sides 95 and 55 units. The hypotenuse gives the resultant displacement, D.
Using Pythagoras rule:
D^2 = 95^2 + 55^2
D^2 = 12050
D = 109.77
Thus, the resultant displacement is 109.77 km
To calculate the direction:
Let the direction be y
y + x = 90°
tan x = 55/95
tanx x = 0.578
x = 30°
Then, y = 90 - 30
y = 60°
Therefore, the resultant displacement of the man is 109.77 km in the direction N60°E.
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A 0.0780 kg lemming runs off a
5.36 m high cliff at 4.84 m/s. What
is its potential energy (PE) when it
lands?
The potential energy of the lemming when it lands is 0.9108672 J.
To determine the potential energy (PE) of the lemming when it lands, we need to consider the conservation of energy. The potential energy of an object is given by the formula PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height.
Given:
Mass of the lemming (m) = 0.0780 kg
Height of the cliff (h) = 5.36 m
First, let's calculate the potential energy when the lemming is on the cliff. Using the given formula, we have:
PE = mgh
PE = 0.0780 kg * 9.8 m/s² * 5.36 m
PE = 0.413616 J
Next, we need to determine the final kinetic energy of the lemming just before it lands. We can use the equation for kinetic energy (KE) given by KE = (1/2)mv², where v is the velocity of the lemming.
Given:
Velocity of the lemming (v) = 4.84 m/s
Calculating the kinetic energy, we have:
KE = (1/2) * 0.0780 kg * (4.84 m/s)²
KE = 0.9108672 J
According to the conservation of energy, the potential energy at the top of the cliff is equal to the kinetic energy just before landing.
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Help with (iii) and (iv) please:
A train consists of an engine and three trucks with masses and resistances to motion as shown in
Fig. 1. There is also a driving force of 37 000 N. All the couplings are light, rigid and horizontal.
(i) Show that the acceleration of the train is 0.3 ms2.
(i) Draw a diagram showing all the forces acting on truck Z in the line of its motion.
Calculate the force in the coupling between trucks Y and Z.
[3]
[4]
With the driving force removed, brakes are applied, so adding a further resistance of 11 000 N to
the total of the resistances shown in Fig. 1.
(iii) Calculate the new acceleration of the train.
(iv) Calculate the new force in the coupling between trucks Y and Z if the brakes are applied
(A) to the engine,
(B) to truck Z
In cach case state whether the force is a tension or a thrust.
[2]
[6]
(i) The total force acting on the train is the driving force minus the total resistance to motion. The total resistance to motion is the sum of the resistances of the three trucks. Therefore, the total force acting on the train is:
F = 37,000 N - (1,200 kg + 900 kg + 600 kg) ₓ 9.8 m/s² = 37,000 N - 25,740 N = 11,260 N
The acceleration of the train is given by the formula:
a = F / (m1 + m2 + m3) = 11,260 N / (1,200 kg + 900 kg + 600 kg) = 0.3 m/s²
Therefore, the acceleration of the train is 0.3 m/s².
(ii) The forces acting on truck Z are the driving force, the force in the coupling between trucks Y and Z, and the resistance to motion of truck Z. The diagram showing all the forces acting on truck Z in the line of its motion is:
Driving force ≥ Truck Z ≤ Force in coupling Y and Z ≤ Resistance to motion of truck Z
(iii) With the driving force removed and brakes applied, the total resistance to motion is the sum of the resistances of the three trucks and the additional resistance due to the brakes. Therefore, the total resistance to motion is:
R = (1,200 kg + 900 kg + 600 kg) ₓ 9.8 m/s²+ 11,000 N = 25,740 N + 11,000 N = 36,740 N
The total force acting on the train is the total resistance to motion. Therefore, the acceleration of the train is:
a = F / (m1 + m2 + m3) = 0 / (1,200 kg + 900 kg + 600 kg) = 0 m/s²
Therefore, the new acceleration of the train is 0 m/s².
(iv) When the brakes are applied to the engine, the force in the coupling between trucks Y and Z is equal to the resistance to motion of truck Z. Therefore, the force in the coupling between trucks Y and Z is:
F = 600 kg ² 9.8 m/s² + 11,000 N = 5,880 N + 11,000 N = 16,880 N
The force in the coupling between trucks Y and Z is a tension.
When the brakes are applied to truck Z, the force in the coupling between trucks Y and Z is equal to the resistance to motion of truck Z plus the resistance to motion of the engine and the trucks in front of truck Y. Therefore, the force in the coupling between trucks Y and Z is:
F = (600 kg + 900 kg + 1,200 kg) ₓ9.8 m/s² + 11,000 N = 17,640 N + 11,000 N = 28,640 N
The force in the coupling between trucks Y and Z is a thrust.
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