Answer:
KE= (1/2)mv^2
given m, the remaining components of the equation are=
1/2v^2?
Explanation:
KE= (1/2)mv^2
plug in...
=(1/2)(27 kg)(3 m/s)^2= 121.5
KE= 121.5 J
Answer:
Multiplying the mass of any student by a factor of 4.5 gives the kinetic energy of the student.
A block of weight w = 25.0 N sits on a frictionless inclined plane, which makes an angle θ = 30.0 ∘ with respect to the horizontal, as shown in the figure. (Figure 1)A force of magnitude F = 12.5 N , applied parallel to the incline, is just sufficient to pull the block up the plane at constant speed.
A: The block moves up an incline with constant speed. What is the total work Wtotal done on the block by all forces as the block moves a distance L = 3.80 m up the incline? Include only the work done after the block has started moving at constant speed, not the work needed to start the block moving from rest.
B :What is Wg , the work done on the block by the force of gravity w⃗ as the block moves a distance L = 3.80 m up the incline?
C: What is WF , the work done on the block by the applied force F⃗ as the block moves a distance L = 3.80 m up the incline?
D: What is WN , the work done on the block by the normal force as the block moves a distance L = 3.80 m up the inclined plane?
a ) The total work Wtotal done on the block by all forces = 0
b ) The work done on the block by the force of gravity = - 47.5 J
c ) The work done on the block by the applied force F = 47.5 N
a ) The total work Wtotal done on the block by all forces,
Since, only the work done after the block has started is considered, the total work done is the change in kinetic energy. Since, the block is moving at a constant speed there is no change in kinetic energy and so total work Wtotal done is zero.
b ) The work done on the block by the force of gravity,
Wg = Fg * h * cos θ
Fg = W = 25 N
sin 30 = h / 3.8
h = 1.9 m
Wg = 25 * 1.9 * cos 180
Wg = - 47.5 J
c ) The work done on the block by the applied force F,
WF = F * d * cos θ
WF = 12.5 * 3.8 * cos 0
WF = 47.5 N
d ) The work done on the block by the normal force,
Normal force acts perpendicular to the surface. The movement is towards the right side of the surface. So cos θ will be cos 90 which is equal to zero. So the work done will be zero.
Therefore,
a ) The total work Wtotal done on the block by all forces = 0
b ) The work done on the block by the force of gravity = - 47.5 J
c ) The work done on the block by the applied force F = 47.5 N
d ) The work done on the block by the normal force = 0
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Learning Goal: To understand that centripetal acceleration is the acceleration that causes motion in a circle. Acceleration is the time derivative of velocity. Because velocity is a vector, it can change in two ways: the length (magnitude) can change and/or the direction can change. The latter type of change has a special name, the centripetal acceleration. In this problem we consider a mass moving in a circle of radius R with angular velocity ω, r⃗ (t)=R[cos(ωt)i^+sin(ωt)j^] =Rcos(ωt)i^+Rsin(ωt)j^. The main point of the problem is to compute the acceleration using geometric arguments. (Figure 1) Part A What is the velocity of the mass at a time t? You can work this out geometrically with the help of the hints, or by differentiating the expression for r⃗ (t) given in the introduction. (Figure 2) Express this velocity in terms of R, ω, t, and the unit vectors i^ and j^. V⃗ (t) = Part Assume that the mass has been moving along its circular path for some time. You start timing its motion with a stopwatch when it crosses the positive x axis, an instant that corresponds to t=0. [Notice that when t=0, r⃗ (t=0)=Ri^. ] For the remainder of this problem, assume that the time t is measured from the moment you start timing the motion. Then the time − t refers to the moment a time t before you start your stopwatch. Part B What is the velocity of the mass at a time − t? Express this velocity in terms of R, ω, t, and the unit vectors i^ and j^. V⃗ (−t) = SubmitMy AnswersGive Up Part C What is the average acceleration of the mass during the time interval from − t to t? (Figure 3) Express this acceleration in terms of R, ω, t, and the unit vectors i^ and j^.
Part A :The position of the particle in vector form is given by\(r⃗ (t)=R[cos(ωt)i^+sin(ωt)j^]\)where R is the radius of the circle and ω is the angular velocity.The velocity of the particle is given by taking the derivative of the position vector with respect to time.
Taking derivative with respect to time on both side we get \(v⃗ (t)=d/dt R[cos(ωt)i^+sin(ωt)j^]= R[-in(ωt)ωi^+cos(ωt)ωj^]=ωR[-sin(ωt)i^+cos(ωt)j^]v⃗ (t)=ωR[-sin(ωt)i^+cos(ωt)j^]\)Thus the velocity of the mass at a time t is given by \(v⃗ (t)=ωR[-sin(ωt)i^+cos(ωt)j^]\).
Part B :
We have to find the velocity at time -t. The velocity of the particle is given by taking the derivative of the position vector with respect to time. Thus the velocity of the mass at a time -t is given by \(v⃗ (-t) = ωR[sin(ωt)i^ - cos(ωt)j^]\)
\(v⃗ (-t) = ωR[sin(ωt)i^ - cos(ωt)j^]\)Part C :
The average acceleration of the particle can be computed using the formulaa = \(Δv/Δt\)The velocity at time t is given by\(v⃗ (t) = ωR[-sin(ωt)i^+cos(ωt)j^]\)
The velocity at time -t is given by \(v⃗ (-t) = ωR[sin(ωt)i^ - cos(ωt)j^]\)
\(v⃗ (-t) = ωR[sin(ωt)i^ - cos(ωt)j^]\)The change in velocity over the interval from -t to t is therefore
\(Δv = v(t) - v(-t) = 2ωR[sin(ωt)i^ + cos(ωt)j^]\)
The time interval over which this change occurs is\(Δt = 2t\)Thus the average acceleration of the particle is given by a = \(Δv/Δt = ω^2R[sin(ωt)i^ + cos(ωt)j^]/t\)
\(a = Δv/Δt = ω^2R[sin(ωt)i^ + cos(ωt)j^]/t\)
The acceleration can be expressed in terms of R, ω, t, and the unit vectors \(i^ and j^\) as \(a = ω^2R[sin(ωt)i^ + cos(ωt)j^]/t\).
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Based on this cell from the periodic table, which statement is true for the
element magnesium?
A. A magnesium atom contains 12 protons, and neutral magnesium
atoms contain 24 electrons.
B. A magnesium atom contains 12 protons, and most magnesium
atoms contain 12 neutrons.
C. The atomic number of magnesium is 24.3, and its atomic mass is
12
D. The atomic number of magnesium is 12, and its average atomic
mass is 12
Answer: B
Explanation:
The top number is its atomic number, also known as the number of protons in the atom.
The bottom number is the atomic mass, which is the sum of the number of protons and neutrons.
Based on this cell from the periodic table C. The atomic number of magnesium is 24.3, and its atomic mass is 12 is true
What is atomic and mass number ?
Upper part represents mass number which is sum of protons and neutrons
Lower part represents atomic number which is number of electron
number of electrons are equal in number of protons for a neutral atom and
from image it can be concluded that correct answer will be
C. The atomic number of magnesium is 24.3, and its atomic mass is
12
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Which statement is true of a
simple machine?
A. Simple machines are used to create friction.
B. Simple machines have many moving parts.
C. Simple machines are very basic and make
work easier.
D. Simple machines are always electrical.
A machine is a physical system that use power to exert forces, regulate movement, and carry out an activity. Simple machines are very basic and make work easier.
What is machine ?
A machine is a physical system that use power to exert forces, regulate movement, and carry out an activity. The phrase is frequently used to describe both natural biological macromolecules, such as molecular machines, and man-made devices, such as those using engines or motors.
Any tool that simplifies work by adjusting a force is a machine. Every time a force pushes an item over a distance, work is done. Work = Force x Distance is an equation that measures the amount of work that is completed. You exert force on a machine when you operate it.
Simple machines are often used to lift big items with a pulley, to ride a bicycle, or to cut with a pair of scissors. It should be noted that a machine cannot be both a force multiplier and a speed multiplier.
Thus, option C is correct.
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A ball has a 8 J of kinetic energy and its mechanical energy is 25 J. If the ball has a mass of 3.2 kg, what is its height above the ground?
Answer:
0.531m
Explanation:
Soln
Mass = 3.2kg
Kinetic energy = 8 J
Mechanical energy = 25 J
Recall,
Mechanical energy = K.E + P.E
But P.E = mass × g × h
where g = acceleration due to gravity = 10ms² and h = height.
Mechanical energy = K.E + mass × g × h
25 = 8 + 3.2×10×h
25 - 8 = 32×h
17 = 32×h
divide both sides by 32
17/32 = h
h = 0.531 metres.
Problem 1 The following curve data describes the centerline of a certain two-lane highway: Da= 9 30': PI Sta. 13+00. The lanes are 12-feet wide and a continuous wall approximately 6-feet high is located along the inside of the curve, exactly 25.6 ft from the center of the highway. Based on this data. what should be the maximum safe design speed of this highway?
The maximum safe design speed of this highway, based on the given curve data, is approximately 2157.93 mph.
Determine the maximum safe design speed of the highway based on the given curve data, we can use the design speed formula that considers the radius of curvature, superelevation, and friction factor.
The formula to calculate the design speed is:
V = sqrt((g * R * e) / f)
where:
V is the design speed,
g is the acceleration due to gravity (32.2 ft/s^2),
R is the radius of curvature (in feet),
e is the superelevation (expressed as a decimal), and
f is the friction factor.
Da = 9° 30' (degree-minute format)
PI Sta. = 13+00
Lanes width = 12 ft
Wall distance from the center of the highway = 25.6 ft
We need to convert the degree-minute format to decimal format for the degree of curvature (Da).
9° 30' = 9 + (30/60) = 9.5°
Next, we need to convert the station notation to feet.
PI Sta. 13+00 = 1300 ft
Now, we can calculate the radius of curvature (R) using the formula:
R = 50,000 / (Da in decimal degrees)
R = 50,000 / 9.5° = 5263.16 ft
Next, we need to calculate the superelevation (e). The superelevation is the ratio of the difference in elevation between the inside and outside of the curve to the width of the lane (12 ft).
e = (wall distance) / (lane width)
e = 25.6 ft / 12 ft = 2.13
The friction factor (f) typically ranges from 0.1 to 0.3, depending on the road conditions. For this calculation, let's assume a friction factor of 0.15.
Now, we can plug the values into the design speed formula:
V = \(\sqrt {((32.2 * 5263.16 * 2.13) / 0.15)\)
Simplifying the equation:
V ≈\(\sqrt {(1497801.04 / 0.15)\)
V ≈ \(\sqrt {(9985336.93)\)
V ≈ 3160.54 ft/s
Convert the design speed to miles per hour (mph), we can multiply by the conversion factor of 0.6818:
\(V_mph\) ≈ 3160.54 ft/s * 0.6818
\(V_mph\) ≈ 2157.93 mph
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At which position would the electric force be greatest?
CI
The image shows the electric field lines around two
charged particles
O 1
02
1
2
O 3
O 4
3
*4
Helps pls
Explanation:
F = qE
where E is an electric field.
The denser lines of electric force are, the stronger electric field will be.
Since 4 is densest part, electric force on 4 is would be greatest.
The electric field would be stronger the denser the lines with electric force are. Since part 4 is the densest, its electric force would be greatest. Therefore, the correct option is option 4.
The force acting on the items is referred to as the electric force. When two electrons and two protons are put at equal distances, the electric force that separates them is equivalent to the electrostatic charge between the two.
The electric force primarily reliant on the quantity known as electric charge rather than the object's mass. Forces involving charges are the subject of electrostatics. Static refers to charges that aren't moving, or are moving very slowly. The electric field would be stronger the denser the lines with electric force are. Since part 4 is the densest, its electric force would be greatest.
Therefore, the correct option is option 4.
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A ball has an initial velocity of 1m/s and a final velocity of 15m/s. The ball travels at an acceleration
of 6m/s².
What was the distance the ball travelled?
Give your answer to 1 decimal place.
The ball travelled approximately 18.7 meters.
How to calculate the distance the ball travelled ?We can use the following kinematic equation to calculate the distance the ball travelled:
v² = u² + 2as
Where
v is the final velocity u is the initial velocitya is the acceleration s is the distance travelledSubstituting the given values, we get:
15² = 1² + 2(6)s
225 = 1 + 12s
224 = 12s
s = 224/12
s ≈ 18.7
Therefore, the ball travelled approximately 18.7 meters.
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what will be the magnitude of work if a force of 25N pulls a stone through a distance of 5m in its direction?
Explanation:
125 is your answer........
Ren runs a hamburger stand and needs to clean up a season’s worth of grease buildup on the range hood over his griddle. explain what he should look for in a cleaning product that can handle a layer of grease
Answer:
A cleaning product that contains a base.
Explanation:
Ren should use a cleaning product that contains a base. This is because bases readily react with lipids (fats), the kind of compound that makes up grease. A base would break down the grease, forming soap, which would then easily wash away.
The Rock drops from a cliff for 5 seconds. It has an initial velocity of Om/s. It has a final velocity of 50m/s.
Answer:
500j i got it right on a test
Explanation:
A person pushes a lawnmower across 20 meters of grass. If the person pushes with 37 Newtons of force while pushing downward at an angle of 15 degrees below the horizontal, what is the amount of work the person does on the lawnmower?
Therefore, the amount of work done on the lawnmower is: W=Fdcosθ=(37 N)(20 m)cos15∘≈710J if is the amount of work the person.
What is the simple definition of work?Work is force applied over distance. Examples of work include lifting an object against the Earth's gravitation, driving a car up a hill, and pulling down a captive helium balloon. Work is a mechanical manifestation of energy. The standard unit of work is the joule (J), equivalent to a newton - meter.
What is work and energy?Work is defined as transferring energy into an object so that there is some displacement. Energy is defined as the ability to do work. Work done is always the same. Energy can be of different types such as kinetic and potential energy.
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What has an ionised atom lost or gained?
Protons
Gamma Rays
Electrons
Neutrons
Answer:
Electrons
Explanation:
Ionised atoms loose and gain electrons.
hope it helps!
A ball is dropped from a 10 story building (30.0 m). How long does it take to hit the ground?
I NEED HELP PLEASE, THANKS! :)
What is electrical power in terms of current and potential difference? Explain.
Answer:
Read the explanations ●
Explanation:
Electric power is the rate which energy is transformed to or from a part of an electrical circuit. A battery can deliver energy or a circuit element , the power is equal to the voltage difference across the element multiplied but the current...
Answer:
See explanation below -
Explanation:
Electrical power is, by definition, the rate at which electrical energy is absorbed in a circuit. However, we are asked the electrical power with respect to current.
This is a perfect example of Ohm's law, or the formula of power. It defines the relationship between power, voltage and current, as such -
P = VI
As you can see, electrical power is directly proportional to the current.
Now the potential difference is also recognized as the voltage, and is similarly directly proportional to the electrical power.
Hope that helps!
A system has 4 independent and identical motors, in order for the system to work, at least one of the motors must operate. Each motor's failure rate is 0.002 failures per hour. What is the system's Mean Time to Failure (MTTF)?
Answer:
The system's Mean Time to Failure is 1,041.\(\bar 6\) hours
Explanation:
The number of independent identical motors = 4
The failure rate of each motor, λ = 0.002 failures per hour
Given that in order for the system to work, at least one of the motors must operate, therefore, the system are in parallel
The Mean Time to Failure for a parallel system of four identical components is given as follows;
\(MTTF = \dfrac{1 }{\lambda} \times \left (1 + \dfrac{1}{2} + \dfrac{1}{3} + \dfrac{1}{4} \right)\)
Which gives;
\(MTTF = \dfrac{1 }{0.002} \times \left (1 + \dfrac{1}{2} + \dfrac{1}{3} + \dfrac{1}{4} \right) = 1,041.\bar 6\)
The system's Mean Time to Failure = 1,041.\(\bar 6\) hours.
What is the difference between centripetal force and centrifugal force???
Answer:
While centripetal force focuses towards the centre of a rotating path, the centrifugal force is just opposite to this, meaning it exerts a force to liberate a body from ...
Centripetal force is an inward force and centrifugal force is an outward force.
Centrifugal force is often referred to as inertial force or fictitious force.
More items...
Explanation:
A box has a mass of 75 g. It has a length of 2.0 cm, a width of 2.0 cm and a height of 3.0 cm. What is the density?
Answer:
6.25 g/cm³
Explanation:
2 cm * 2 cm * 3 cm = 12 cm³ (volume)
75 g / 12 cm³ = 6.25 g/cm³
FILL IN THE BLANK. immediately following the arrival of the stimulus at a skeletal muscle cell there is a short period called the __ period during which the events of excitation-contraction coupling occur.
Immediately following the arrival of the stimulus at a skeletal muscle cell, there is a short period called the latent period during which the events of excitation-contraction coupling occur.
This process is a connection between transduction in the sarcolemma and the initiation of muscle contraction. Sarcolemma is nothing but the cell membrane of skeletal muscle.
A single muscle twitch has a latent period, a contraction phase when tension increases and a relaxation phase when tension decreases.
The period of incubation, the interval preceding exposure to a pathogen toxin or radiation, and when effects occur. Muscle contracting, the time between a nerve stimulus and muscle contraction.
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Earth's ________ is the pattern of slow changes in rocks from one kind to another.
a
rock cycle
b
rock
c
mineral
d
weat
Answer:
A. Rock cycle
Explanation:
Because it really is the change of a rock from another, like ingenuous, sedimentary rock..
Which of the following situations describes a non-contact force acting on an object?
I think its "a dropped penny sinks at the bottom of a pond". Because, non-contact force is a force that you don't touch, like gravity or weight, that falls but you didn't drop it on purpose nature did or gravity itself did.
Two airplanes leave an airport at the same time. The velocity of the first airplane is 650 m/h at a heading of 16.9 ◦ . The velocity of the second is 590 m/h at a heading of 161◦ . How far apart are they after 1.8 h? Answer in units of m.
Distance of train after 1.8 h is 485.099 m
Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. Distance can refer to a physical length in physics or to an estimate based on other factors in ordinary language.
Distance of the first plane = 650 x 1.8 = 1170 m
Distance of the second plane = 590 x 1.8 = 1062m
The angle between 2 planes
161◦ - 16.9◦ = 144.1°
Using the law of cosine
d^2 = (1170)^2 + (1062)^2 - 2*1170*1062*cos 144.1°
d = 485.099 m
Hence, distance of train after 1.8 h is 485.099 m
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The more __________ energy being used, the ___________ the roller coaster will go. Question
A:Kinetic, slower
B:Potential, faster
C:Kinetic, faster
D:Potential, slower
Answer: b
Explanation:
Answer:
C.
The More Kinetic Energy being used, the Faster, the Roller Coaster will go.
Explanation:
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Length is to meter as _____ is to ____
A
Weight is to mass
B
Mass is to gram
C
Liter is to distance
D
Cubic centimeters is to distance
Answer:
Mass is to gram
Explanation:
I have this bigfoot worksheet for science. It says, "When designing an experiment, which two groups must be involved?" Can you help me?
Answer:
control group and experimental group
a) For a motorcycle traveling at speed v (in mph), when the brakes are applied, the distance (in feet) required to stop the motorcycle may be approximated by the formula d = 0.05^2
. Find the instantaneous rate of change of distance with respect to velocity when the speed is 41 mph.
A. 10.2 mph
B. 5.1 mph
C. 4.1 mph
D. 42 mph
Taking the data into consideration the instantaneous rate of alteration of distance with concerning velocity in the event the speed is 41 mph is approximately 4.1 mph. The answer is C.
To evaluate the instantaneous rate of change of distance with concerning velocity in the evebt the speed is 41 mph for a motorcycle traveling at speed v (in mph), after the brakes are applied, we have to evaluate the derivative of the distance formula with respect to velocity:
\(d = 0.05v^2 + v\)
Projecting the derivative concerning v, we get:
\(dd/dv = 0.1v + 1\)
Applying substitution of the given value of v = 41 mph, we get:
\(dd/dv = 0.1(41) + 1\)
\(dd/dv = 4.1 mph\)
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What happens to distance and velocity if the time to fall increases or decreases?
In free-fall motion the velocity is given by the following equation of motion:
\(v=v_0-gt\)Where:
\(\begin{gathered} v=\text{ velocity} \\ g=\text{ acceleration of gravity} \\ t=\text{ time} \end{gathered}\)Therefore, the velocity increases linearly with time. This happens if the object encounters no air resistance. In the case that there is air resistance the object will reach a terminal velocity.
In the case of distance, this is given by the following equation:
\(s=v_0t-\frac{1}{2}gt^2_{}\)This means that the distance increases with time following a parabolic function.
Calculate the minimum height that 7.0 kg of water must fall to gain 1300 J of kinetic energy.
Explanation:
K=mgh\\1300=(7)(9.8)h\\h=19\ mK=mgh
1300=(7)(9.8)h
h=19 m
Can the sun explain global warming? ( 2 points) Suppose that the Earth has warmed up by 1 K in the last hundred years. i) How much would the solar constant have to increase to explain this? ii) Compare this to the observed fluctuation of the solar constant over the past 400 years (shown in class) For part (i), begin with the standard 'blackbody' calculation from class, that is: set α=0.30, and assume that the Earth acts as a blackbody in the infrared.
No, the sun cannot explain global warming. Global warming is a phenomenon in which the temperature of the Earth's surface and atmosphere is rising continuously due to human activities such as deforestation, burning of fossil fuels, and industrialization.
This increase in temperature cannot be explained only by an increase in solar radiation.There are several factors which contribute to global warming, including greenhouse gases such as carbon dioxide, methane, and water vapor. These gases trap heat in the Earth's atmosphere, which causes the planet's temperature to rise. The sun's radiation does contribute to global warming, but it is not the main cause.
i) To calculate the increase in solar radiation that would cause the Earth to warm up by 1 K, we can use the following formula:ΔS = ΔT / αWhere ΔS is the increase in solar constant, ΔT is the increase in temperature, and α is the Earth's albedo (reflectivity).α = 0.30 is the standard value used for the Earth's albedo.ΔS = ΔT / αΔS = 1 K / 0.30ΔS = 3.33 W/m2So, to explain the increase in temperature of 1 K over the last hundred years, the solar constant would need to increase by 3.33 W/m2.
ii) The observed fluctuation of the solar constant over the past 400 years has been around 0.1% to 0.2%. This is much smaller than the 3.33 W/m2 required to explain the increase in temperature of 1 K over the last hundred years. Therefore, it is unlikely that the sun is the main cause of global warming.
The sun cannot explain global warming. While the sun's radiation does contribute to global warming, it is not the main cause. The main cause of global warming is human activities, particularly the burning of fossil fuels, which release large amounts of greenhouse gases into the atmosphere.
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The emf of a battery is E = 20 V . When the
battery delivers a current of 0.2 A to a load,
the potential difference between the terminals
of the battery is 18 V volts.
Find the internal resistance of the battery.
Answer in units of Ω.
Answer:
10 ohms
Explanation:
V = IR
2 v is the drop in the battery
2 = .2 R
R = 10 ohms