The four conducting cylinders shown in the figure are all made of the same material, though they differ in length and/or diameter. They are connected to four different batteries, which supply the necessary voltages to give the circuits the same current, I.
Rank the four voltages. V₁, V₂, V₃, and V₄. in order of decreasing value. Rank from largest to smallest. To rank items as equivalent, overlap them.
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Answers
The ranking of the voltages, V₁, V₂, V₃, and V₄ in the order of decreasing voltage value is; V₂ > V₃ > V₁ > V₄
What is the voltage of an electric circuit?A voltage is the difference in potential or pressure that pushes or causes the flow of electric current in a circuit or conducting loop.
The current flowing through the circuit can be found using the following formula;
[tex]I=\dfrac{V}{R}[/tex]
The formula for conductivity is presented as follows;
[tex]\sigma =\dfrac{l}{R\times A}[/tex]
Where;
σ = The conductivity of the material
l = The length
R = The resistance to electricity
A = The cross-sectional area of the conductor
Therefore;
[tex]R=\dfrac{V}{I}[/tex]
[tex]R=\dfrac{l}{A\times \sigma}[/tex]
[tex]\dfrac{V}{I} =\dfrac{l}{A\times \sigma}[/tex]
[tex]V=\dfrac{l \times I}{A\times \sigma}[/tex]
Based on the dimensions of the cylinders, obtained from a similar question, we get;
[tex]V_1=\dfrac{3\cdot L \times I}{\pi \cdot D^2\times \sigma} = 3\times \dfrac{ L \times I}{\pi \cdot D^2\times \sigma}[/tex]
[tex]V_2= \dfrac{2\cdot L \times I}{\pi \cdot \dfrac{D^2}{4} \times \sigma} = \dfrac{8\cdot L \times I}{\pi \cdot D^2\times \sigma} = 8\times \dfrac{ L \times I}{\pi \cdot D^2\times \sigma}[/tex]
[tex]V_3=\dfrac{L \times I}{\pi \cdot \dfrac{D^2}{4} \times \sigma} =\dfrac{4\cdot L \times I}{\pi \cdot D^2\times \sigma}= 4\times \dfrac{L \times I}{\pi \cdot D^2\times \sigma}[/tex]
[tex]V_4=\dfrac{L \times I}{\pi \cdot D^2\times \sigma} = 1\times \dfrac{ L \times I}{\pi \cdot D^2\times \sigma}[/tex]
Therefore;
V₁ = 3·V₄
V₂ = 8·V₄
V₃ = 4·V₄
The rank of the voltages in the order of decreasing value is therefore;
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Related Questions
The largest flowers in the world are the Rafflesia Arnoldii, found in Malaysia. A single flower is almost a meter across and has a mass up to 11.0 kg. Suppose you cut off a single flower and drag it along the flat ground. If the coefficient of kinetic friction between the flower and the ground is 0.39, what is the magnitude of the frictional force that must be overcome?
Answers
The magnitude of the frictional force that must be overcome is 42.04 N.
What is the magnitude of the frictional force?
The magnitude of the frictional force that must be overcome is calculated by applying Newton's second law of motion as follows;
Mathematically, the formula for the frictional force is given as;
F = μmg
where;
μ is the coefficient of frictionm is the mass of the flowerg is acceleration due to gravityThe magnitude of the frictional force that must be overcome is calculated as;
F = 0.39 x 11 kg x 9.8 m/s²
F = 42.04 N
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A 6 kg bowling ball is lifted 1.2 m into a storage rack. The acceleration of gravity is 9.8 m/s² Calculate the increase in the ball's potential energy. Answer in units of J.
Answers
Answer:
70.56 J
Explanation:
Gravitational Potential Energy= mass×gravitational pull× height
= 6×9.8×1.2= 70.56 J
Most space lawyers agree that the barrier between airspace and outer space lies somewhere between where
the highest planes fly and the lowest satellites orbit.
True
False
Answers
True. The majority of space lawyers concur that the line dividing airspace from outer space is located halfway between the altitude at which airplanes fly and the orbital altitude of satellites.
What purposes do satellites serve?They serve a variety of functions, including that of the Satellite Navigation System, amateur radio, television transmission, and weather forecasting. In order to conduct study and acquire data, they also employ telescopes to view outward somewhere at solar system.
Do satellites provide internet access?Over 99% of Americans have access to satellite internet, along with most other (but certainly not all) rural residents. You do not need to have a home internet connection because the broadband signal is transmitted from satellites.
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An airplane flies from Milwaukee to Chicago, a distance of 130 kilometers, and is in the air for 20 minutes. What is its average velocity? Show your work or explain how you got your answer.
Answers
The average velocity of the airplane between Milwaukee and Chicago is 1083.33 meter/second.
What is velocity?The rate at which a body's displacement changes in relation to time is known as its velocity. Velocity is a vector quantity with both magnitude and direction. SI unit of velocity is meter/second.
The total distance between Milwaukee and Chicago = 130 kilometer
= 1,300,000 meter.
Time interval = 20 minute = 20×60 second = 1200 second.
The average velocity of the airplane = total distance/time interval
= 1,300,000 meter / 1,200 second.
= 1083.33 meter/second.
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You are in the year where the earth has no more land available for houses you decide to build an apartment up and need things to survive in each earths 5 layers (troposphere,stratosphere, mesosphere, thermosphere, exosphere) Question: what things would you need to survive the mesosphere
PLS I RLLY NEED SOME HELP
Answers
The things that I will need to survive the layer of the earth called the mesosphere would be thick clothings.
What are the 5 layers of the earth?The five(5) layers of the earth include the following such as:
troposphere,stratosphere, mesosphere, thermosphere, and exosphere.The Mesosphere is one of the layers of the earth that is found directly above the stratosphere and then below the thermosphere.
The characteristics of the mesosphere is that the temperature rises due to reduced absorption of solar radiation and increased cooling by CO2 radiative emissions.
Therefore, for an individual to survive and live effectively at the Mesosphere layer of the earth, such needs thick clothings.
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The type of heat transfer responsible for your computer leaving your desk very hot after you've used it for awhile?
Answers
Answer:
Conduction
Explanation:
Conduction is a process whereby heat is transfer through solid state.
Those in mission control roles spend about 75 percent of their time actively communicating and controlling active space missions.
True
False
Answers
It is False that personnel in mission control spend roughly 75% of their time actively engaging with and managing running space missions, according to the evidence at hand.
What is Mission control centre?The NASA Johnson Space Center has a designated center called Mission Control Center.
Only 10% of the time that the MCC staff devotes to mission control is actually spent actually managing missions; the other 80% is spent planning and organizing, and the remaining 15% is spent on training and education.
A facility that oversees space flights is known as a mission control center (MCC; sometimes known as a flight control center or operations center), often from the point of launch until landing or the mission's conclusion. It is a component of spacecraft operations on the ground.
Therefore, It is False that personnel in mission control spend roughly 75% of their time actively engaging with and managing running space missions, according to the evidence at hand.
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For science class your teacher gives you and your partner a ball she ask you to figure out a way to Balance forces that you apply to the ball how do you partner show this?
Answers
Two forces are said to be balanced when their strengths are equal but their directions of action are opposing.
What is Balanced Force?The forces are balanced if the pullers are exerting equal force but going in the opposite direction on either side of the rope.
Forces that are balanced can cancel one another out. The thing stays in place whenever there is a balanced force.
To lift, turn, move, open, close, push, pull, and many other things requires forces. You apply force to a ball when you throw it in order for it to travel through the air. An object can be under the influence of multiple forces at once.
Therefore, Two forces are said to be balanced when their strengths are equal but their directions of action are opposing.
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The ocean’s tides are not only affected by the shape of the coastlines, or slope of the ocean floor, but also by the gravitational tug of the Sun and the Moon. Write a 600 word report on the effect of the Moon, and Sun, on tidal reaction, and high tides and low tides. What orientation are the Sun and Moon in to create high tides? Low tides? There are two special types of tides. What are they called and what positions are the Sun and the Moon in during these times?
Answers
The shape of the coastlines and the slope of the ocean floor, as well as the gravitational pull of the Sun and Moon, all have an impact on the tides of the ocean.
What are tides?Tides are extremely long-period waves that travel across the water as a result of the moon's and the sun's gravitational pull. The rise and fall of the sea's surface on a regular basis is what tides, which originate in the ocean, appear as as they move toward the coastlines.
High tide is when the wave's highest portion, or crest, reaches a specific area; low tide is when the wave's lowest portion, or trough, reaches that location. The term "tidal range" refers to the height difference between high tide and low tide.
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A block moving at a velocity of 18 m/s along a frictionless surface encounters a rough area with which it does have a coefficient of friction. It moves along this rough area for 30 meters before slowing to a speed of 6 m/s. Find the coefficient of kinetic friction between the block and this rough surface.
Answers
The coefficient of kinetic friction between the block and the rough surface is -0.6.
What is kinetic friction?Kinetic friction is a type of friction that occurs when two objects are in contact and moving relative to each other. It is also known as sliding friction or dynamic friction. Kinetic friction is caused by the interaction of the two surfaces as they move against each other. The force of kinetic friction acts in the opposite direction of the motion of the two objects and is proportional to the normal force between them. The coefficient of kinetic friction is a measure of the amount of friction between two surfaces and is determined by the materials of the two surfaces.
The coefficient of kinetic friction can be found using the equation:
μk = (vf - vi) / (d * a)
where μk is the coefficient of kinetic friction, vf is the final velocity, vi is the initial velocity, d is the distance traveled, and a is the acceleration due to gravity (9.8 m/s2).
Plugging in the given values, we get:
μk = (6 - 18) / (30 * 9.8)
μk = -0.6
Therefore, the coefficient of kinetic friction between the block and the rough surface is -0.6.
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To understand the nature of electric fields and how to draw field lines In (Figure 2), what is wrong with panel B7 (Pick only those statements that apply to panel B) Electric field lines are a tool used to visualize electric foiled
Part B
In (Figure 2), what is wrong with panel B? (Fick only those statements that apply to panel B) Check all that apply.
Field liner caneot cross each other
The fold lines should be paraller becauze of the sheers symunner.
The field lnes chould spread apart as they leare the sheet to indiate mhr woakering of the field with gistance.
The field lines should always end on negative charges of at infinity.
in panel B, the field lines do end on negative charges, so this is not a problem No credit lost Try again D Submit Previous Answers
Answers
In (Figure 2), the wrong with panel B is: Field line can not cross each other the field lines should be parallel because of the sheers summoner.
What is electric field line?In general, an electric field line is a curve drawn with each point's tangent pointing in the direction of that point's net field. To designate the direction of the electric field from the two potential directions provided by a tangent to the curve, an arrow on the curve is obviously required. A field line is a space curve, or a three-dimensional curve.
The wrong with panel B is: Field line can not cross each other.
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In a particular crash test, an automobile of mass 1245 kg collides with a wall and bounces back off the wall. The x components of the initial and final speeds of the automobile are 18 m/s and 2.9 m/s, respectively. If the collision lasts for 0.11 s, find the magnitude of the impulse due to the collision. Answer in units of kg · m/s. Answer in units of kg · m/s.
Answers
Answer:
Δp=-18799.5kg*m/s
Explanation:
Δv=Vf-Vi
Δv=2.9m/s-18m/s
Δv=-15.1m/s
m*Δv=Δp
1245kg*(-15.1m/s)=Δp
Δp=-18799.5kg*m/s
Extra:
Deriving mΔv=Δp
Δp=Pf-Pi
Δp=m*Vf-m*Vi
Δp=m(Vf-Vi)
Vf-Vi=Δv
Δp=m(Δv) or Δp=mΔv
Question 9 (Worth 4 points)
(02.06 HC)
a. Create and describe a scenario in which the forces acting on an object are unbalanced. Explain how you know the forces are unbalanced.
b. For your scenario, explain how Newton's third law of motion describes the forces involved.
Answers
a. When a football is kicked and it moves from one location to another, it indicates that unbalanced troops are responding to it and b. If an object A applies a force to another object B, then the other object B.
Describe how the effects of balanced and unbalanced forces on motion:The equilibrium of the forces is disturbed when an object's motion changes. Forces with opposite directions and equal sizes are said to be balanced forces. Motion remains constant when the forces are equal. In one of your scenarios from the previous section, you used the same amount of force on an object but pushed or pulled it in the opposite direction.
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In velocity time graph of a body, two points are given as A(40,5) and B(20,2). What is the acceleration of the body
Answers
Answer:
0.15 m/s²
Explanation:
Acceleration is rate of change of velocity-time function. We can find acceleration by finding the slope. The slope of graph can be found by:
[tex] \displaystyle{a = \dfrac{ \Delta v}{ \Delta t} \: \to \: \dfrac{v_f - v_i}{t_f- t_i}}[/tex]
Substitute in:
[tex] \displaystyle{a = \dfrac{5 - 2}{40 - 20}} \\ \\ \displaystyle{a = \dfrac{3}{20}} \\ \\ \displaystyle{a = 0.15 \: \text{m/s}^{2} }[/tex]
Therefore, the acceleration is 0.15 m/s²
The anterior cruciate ligament in a woman's knee is 2.5 cm long and has a cross- sectional area of 0.54 cm2. If a force of 3000 N is applied longitudinally, how much will the ligament stretch? assume that young's modulus (1.8x10¹0 N/m²)
Answers
If a longitudinal force exceeding 3000 N is applied. Young's modulus for that object equals DL = 0.0139m.
Which is better, a greater or lower Young's modulus?The greater the modulus, or the lesser elasticity strain that arises from the application of a given stress, the stronger that medium is. Young's modulus, sometimes referred to as mechanical performance, is a metric used to determine how stiff a material is. In other words, it is readily bent or stretched.
Young's modulus really measures a material's ability to withstand changes in length when compressed or under stress along its length. Divide the primary stresses by the strain to get Young's modulus, commonly known also as young's modulus.
Young's modulus Y= stress/strain
= (F/A) /(DL/L)
F=3000N,
A=0.54 cm²,
L=2.5cm,
Y=0.1 Gpa
0.1 * 10⁹ = (3000/(0.54* 10⁻⁴) (2.5 ⋆ 0.01/DL)
DL = 0.0139m
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n experimental vehicle starts from rest (0 = 0) at = 0 and accelerates at a rate given by
= (7m/s
3
). What is (a) its velocity and (2) its displacement 2 later?
Answers
The velocity of the experimental vehicle after 2 seconds is 14 m/s.
The displacement of the experimental vehicle after 2 seconds is 14 m.
What is the velocity and displacement of the experimental vehicle?The velocity of the experimental vehicle is the speed of the in a given direction starting from rest.
The velocity, v, of the experimental vehicle after 2 seconds is calculated using the formula below:
v = u + at
where;
u is the initial velocity = 0 m/s
a is the acceleration = 7 m/s²
t is time = 2 seconds
v = 0 + 7 * 2
v = 14 m/s
The displacement, s, of the vehicle is calculated below as follows:
v² = u² + 2as
14² = 0² + 2 * 7 * s
s = 196 / 14
s = 14 m
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A student conducts an experiment to test how the temperature affects the amount of salt that can dissolve in water. In the experiment, she uses 150 milliliters of water in each trial and stirs for five minutes each time.
Answers
The independent variable that we have in the experiment is the temperature. Option B
What is an experiment?We know that if we are talking about an experiment, what we have to look at is that we must consider the interplay of the variables that is taking place in the process. As we change one of the variables in the experiment, there would be a change in another variable in the experiment also.
Now, the variable that we usually beging to alter is the one that we call the independent variable. As we change the value of this particular variable, there would be a change in the independent variable.
We have been told that; a student conducts an experiment to test how the temperature affects the amount of salt that can dissolve in water.
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The uniform beam has a weight W and length L and is supported by a pin at A and cable BC ( figure 1)
Part A
Determine the horizontal and vertical components of reaction at A
Express your answers in terms of some or all of the variables W, R. Φ and θ). Enter your answers separated by a comma.
View Available Hint's)
Aa + Ay = ____
Parts B
Determine the one cable car necessary to hold the beans position shown
Express your answers in terms of some or all of the variables W, R. Φ and θ).
Answers
The reaction is in A in vertical direction is W(2cosϕsinθ−sinϕcosθ)/2sin(θ−ϕ).
What is Normal Stress and Strain?In terms of psychology, "stress" and "strain" are sometimes used interchangeably in popular culture, as in the expressions "I'm feeling stressed" or "I'm under a lot of pressure."
In engineering, these phrases have specific, technical meanings. If a hook in the steel wire is attached,
If you hang the wire from the ceiling while placing a weight on the lower end, it will sag. By dividing the length change by the starting length, the strain in the wire may be computed.
Thus, as per the given scenario, W(2cosϕsinθ−sinϕcosθ)/2sin(θ−ϕ) will be the equation.
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Net work W would accelerate an object from rest to velocity v. What net work is needed to accelerate the object from rest to velocity 2v?
Answers
The net work that is needed to accelerate a 2.0 kg mass from rest to velocity 2v is 4.0 m/s.
What is net work done?When a force acts on a body at rest or at uniform motion in a straight line, then it starts to accelerate.
Given that, the velocity is 5.0
Time is 2 sec
The given mass is 2.0 kg
First, we calculate the acceleration
Acceleration = v / t = 10 / 5.0 = 2
From Newton's second law, we know that
force = mass x acceleration
F = ma
F = 2.0 x 2 = 4.0 m/s
Therefore, the net work that is needed to accelerate a 2.0 kg mass from rest to velocity 2v is 4.0 m/s.
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The question is incomplete. Your most probably complete question is given below:
What net force is needed to accelerate a 2.0 kg mass from rest to a velocity of 10 m/s in 5.0 s?
It is a “new moon” (the Moon is totally dark in the sky). Using the masses of the Earth, Sun, and Moon and the average distances between the Earth-Moon and Earth-Sun, find the net gravitational force on the Earth from the Sun and the Moon combined.
Find also distance when it is full moon
Answers
It is a “new moon” (the Moon is totally dark in the sky). The gravitational force between the Earth and the Moon is:
2.9 x 10^20 N3.5 x 10^22 N3.5 x 10^22 NWhat is gravitational force?Generally, The gravitational force between two objects is given by the equation:
force = G * (mass1 * mass2) / distance^2
Where G is the gravitational constant (6.67 x 10^-11 N*(m/kg)^2), mass1 and mass2 are the masses of the two objects, and distance is the distance between the two objects.
The mass of the Earth is 5.972 x 10^24 kg, the mass of the Moon is 7.347 x 10^22 kg, and the mass of the Sun is 1.989 x 10^30 kg. The average distance between the Earth and the Moon is 384,400 km, and the average distance between the Earth and the Sun is 149.6 million km.
The gravitational force between the Earth and the Moon is:
force = (G * (mass of Earth) * (mass of Moon)) / (distance between Earth and Moon)^2 force
= (6.67 x 10^-11 N*(m/kg)^2) * (5.972 x 10^24 kg) * (7.347 x 10^22 kg) / (384400 x 10^3 m)^2 force
= 2.9 x 10^20 N
The gravitational force between the Earth and the Sun is:
force = (G * (mass of Earth) * (mass of Sun)) / (distance between Earth and Sun)^2 force
= (6.67 x 10^-11 N*(m/kg)^2) * (5.972 x 10^24 kg) * (1.989 x 10^30 kg) / (149.6 x 10^9 m)^2 force
= 3.5 x 10^22 N
To find the net gravitational force on the Earth from the Sun and Moon combined, we add the two forces we found above.
Net force = 2.9 x 10^20 N + 3.5 x 10^22 N
= 3.5 x 10^22 N
When it is a Full Moon the distance is the same 384,400 km
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Manipulation of equations:
mAvAi+mBvBi=mAvAf+mBvBf
Find mA
Answers
The value of mA is the equation of conservation of linear momentum is determined as mA = [ mB (vBi - vBf) ] / [ (vAf - vAi ) ].
What is the principle of conservation of linear momentum?
The principle of conservation of linear momentum states that in a closed or isolated system, the total momentum of the system is always conserved.
Mathematically, the formula for the principle of conservation of linear momentum is given as;
Pi = Pf
where;
Pi is the initial momentum of the systemPf is the final momentum of the systemmAvAi + mBvBi = mAvAf + mBvBf
where;
mA is the mass of the object AmB is the mass of the object BvAi is the initial velocity of object AvBi is the initial velocity of object BvAf is the final velocity of object AvBf is the final velocity of object BTo find the value of mA, we will make mA the subject of the formula as follow;
mAvAf - mAvAi = mBvBi - mBvBf
mA (vAf - vAi ) = mB (vBi - vBf)
mA = [ mB (vBi - vBf) ] / [ (vAf - vAi ) ]
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As shown in the picture above, an ice skater is skating at a constant speed in a circle. Is she accelerating? Explain your answer and draw the direction of the velocity in point A, B, C, and D.
Answers
Yes, the skater is accelerating.
Acceleration is a change in speed OR direction OR both. Since she's skating in a circle, her direction is constantly changing, so she is accelerating.
At A, her velocity points down.
At B, her velocity points right.
At C, her velocity points up.
At D, her velocity points left.
A lawnmower is pushed with a force of 72 Newtons at an angle of 40 degrees from the horizontal. How much work is done to the mower if it moves 740 meters?
Answers
The work done to the mower is the product of force and the distance covered by the object which is equal to 40,811 Joules.
What is Work done?Work done can be defined as the product of external force and the distance over which the force is being applied. Work is done on an object when a force is applied to an object and the object is moved through a particular distance.
From this we can see that:
X-Component:
cos(θ) = x/F
Then,
X= F cos(θ).…..(1)
Now putting the values of F and θ in equation (1) we get,
X = 72 N × cos(40)
X = 72 N × 0.766
X= 55.15 N this is the x-component force
The work done to the mower is:
W = F × d
W = 55.15 × 740
W = 40,811 Joules
The work done to the mower is 40811 Joules.
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with what speed will a clock have to be moving in order to run at a rest that is one half the rate of clock at rest
Answers
The speed at which a clock would have to be moving in order to run at half the rate of a clock at rest depends on the theory of relativity that you are using.
What is the clock speed about?In special relativity, time dilation is the phenomenon where time appears to pass differently for objects in motion relative to an observer at rest.
According to the theory, time appears to slow down for an object as it approaches the speed of light. The rate at which time appears to pass for an object is given by the equation:
T' = T / [tex]\sqrt{(1 - (v^2 / c^2))}[/tex]
Where T is the time as measured by an observer at rest, T' is the time as measured by an observer moving relative to the object, v is the velocity of the object, and c is the speed of light.
In addition, this is a theoretical scenario, practically in order to measure time dilation in a laboratory, it is required a very high precision of measurements, that are currently not possible.
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The reliability or reproducibility of a measurement is its _____
Answers
The degree of data stability when the measurement is replicated under identical circumstances is known as reproducibility or reliability.
What exactly are repeatability and reproducibility?Reproducibility determines how an entire study an experiment can be replicated, whereas repeatability assesses the variation in data made by a single equipment or human under similar circumstances.
What makes repeatability crucial?Science needs reproducibility because it enables more in-depth investigation, and replication validates our findings. There are several investigations and experiments, which result in a wide range of variables, unforeseen, and things that are either outside your influence or you cannot guarantee.
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What is the power of a lightbulb that has a current of 0.480 A at 120.0 V?
Answers
Answer:
The power is 57.6 watts
Explanation:
We can use the Electric Power Equation to evaluate the power.
Electric Power Equation
[tex]P=IV[/tex]
[tex]P[/tex] is the power in watts
[tex]I[/tex] is the current in amps
[tex]V[/tex] is the voltage in volts
Our lightbulb has current of 0.480 A and a voltage of 120.0 V.
[tex]I=0.480\\V=120.0[/tex]
Now we can evaluate power.
Substitute our values in for the variables.
[tex]P=0.480*120[/tex]
[tex]P=57.6[/tex]
How long will a boy sitting near the window of a train travelling at 36 km h see a train passing by in the opposite direction with a speed of 18 km h^-1.The length of the slow- moving train is 90 m.
Answers
Answer:
5/18 is used to convert km/hr into m/s
1 km = 1000 m
1 hr = 3600 sec
1 km/hr to m/s
1*1000/1*3600
1000/3600metre/sec
10/36metre/sec
5/18 metre/sec
Explanation:
srry if this is wrong!
The heaviest train ever pulled by a single engine was over 2 km long. Suppose a force of 1.13 X 10^8 N is needed to overcome static friction in the train's wheels. If the coefficient of static friction is 0.741, what's the train's mass?
Answers
The overcoming force is equal to the friction. The train's mass is 15,560,880.5 Kg
What is Friction ?Friction can simply be defined as a force that opposes the movement of an object in a plain surfaces.
Given that the heaviest train ever pulled by a single engine was over 2 km long. Suppose a force of 1.13 X 10^8 N is needed to overcome static friction in the train's wheels. If the coefficient of static friction is 0.741, what's the train's mass?
F = μN
Where
F = Frictional force = overcoming force = 1.13 X 10^8 Nμ = coefficient of static friction = 0.741N = Normal reaction = mgSubstitute all the necessary parameters
1.13 X 10^8 = 0.741N
N = 1.13 X 10^8/0.741
N = 152496626.2 N
N = mg
152496626.2 = 9.8m
m = 152496626.2/9.8
m = 15,560,880.5 Kg
Therefore, the mass of the train is 15,560,880.5 Kg.
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Periodic motion
This question is about the stretching of springs
The diagram below shows an unblocked spring of length 100 mm
hanging suspended from a clamp. When an object of mass 50g is
hung on the spring, it becomes 180 mm long.
The spring constant K=50N/m
100 mm
50g
1- Calculate x in (mm) then convert it to meter
X is the distance that the spring is stretched from its
equilibrium position.
2- Use Hooke's law to calculate the restoring force of the spring
Answers
Springs are elastic devices used to absorb shock, store energy, and provide support in a variety of applications.
1- The distance the spring is stretched from its equilibrium position is x = 180 - 100 = 80 mm. This can be converted to meters by dividing by 1000, so x = 0.08 m.
2- The restoring force of the spring can be calculated using Hooke's law, which states that F = kx, where F is the restoring force, k is the spring constant, and x is the distance the spring is stretched from its equilibrium position. In this case, F = 50 N/m × 0.08 m = 4 N.
What is Hooke's law?
Hooke's law is a basic law of physics that states that the force applied to a spring is proportional to the amount of displacement (or stretching) of the spring. In other words, the more you stretch a spring, the more force is needed to keep it stretched. This law is expressed mathematically as F = -kx, where F is the force, k is a constant known as the spring constant, and x is the displacement.
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1- A ball, M = 4 kg is released from rest (vi =0) at a height, h = 2 m above the ground. (a)
What is the kinetic energy of the ball just before it hits the ground? What is the change in the
potential energy, ΔU during this motion? (b) Find the kinetic energy of the ball at a height, y
= 1.2 m above the ground. (Take g = 10 m/s2
).
Answers
(a) The kinetic energy of the ball just before it hits the ground is 78.4 J.
(b) The kinetic energy of the ball at a height of 1.2 m is 31.36 J.
What is the kinetic energy of the ball?The kinetic energy of the ball just before it hits the ground is calculated as follows;
K.E ( bottom) = P.E (top)
P.E (top) = mgh
where;
m is the mass of the objecth is the height of the objectg is acceleration due to gravityP.E (top) = 4 x 9.8 x 2
P.E (top) = 78.4 J
The change in the potential energy of the ball during its motion is calculated as follows;
ΔU = P.Ef - P.E i
where;
P.Ef is the final potential energy at ground levelP.Ei is the initial potential energy at maximum heightΔU = 0 J - 78.4 J
ΔU = -78.4 J
The kinetic energy of the ball at a height of 1.2 m is the change in the potential energy of the ball and it is calculated as follows;
K.E = -ΔU
K.E = -mg (hf - hi)
K.E = (4 x 9.8)(2m - 1.2 m)
K.E = 31.36 J
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