Force 2.47×103 N is required to stop a 950 kg automobile traveling at 90.0 km/h over a distance of 120 m.
What is the easiest way to define a force?An external force is a substance that has the power to alter a body's resting or motion state. It has a direction and a magnitude. The application of force is the location where it occurs, and the force's direction is the direction in which it occurs.
What is a force unit?The newton, represented by the letter N,
is the SI unit of force.
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you are riding a bicycle into a strong head wind, but manage to keep moving in a straight line at a constant speed. the net force on you is
You are riding a bicycle into a strong headwind, but manage to keep moving in a straight line at a constant speed net force on you is zero.
The force of the wind pushing against you is balanced by the force of your pedaling, allowing you to maintain a constant speed and stay in a straight line. This means that the forward force of your pedaling is equal in magnitude but opposite in direction to the backward force of the wind.
The net force is the vector sum of these two forces, which is zero. This is similar to the concept of action and reaction in Newton's Third Law of Motion, where for every action there is an equal and opposite reaction.
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The flux is unchanged becauYou hold a wire coil so that the plane of the coil is perpendicular to a magnetic field B⃗ .
a)If the magnitude of B⃗ increases while its direction remains unchanged, how will the magnetic flux through the coil change?
se the position of the coil with respect to B is unchanged l The flux increases because the magnitude of B increases The flux decreases because the magnitude of B increases The flux is unchanged because the surface area of the co is unchanged
The magnitude of b increases, which is the correct response, so the flux increases.
When does magnetic flux differ from magnetic field?In contrast to magnetic field, which is the region in space where the magnetic effect of the field is observed, magnetic flux is a measure of the amount of magnetic field passing through a given area. A moving charged particle creates a magnetic field that can exert a magnetic force.
ФB = BAcosθ
The magnetic flux is actually given by where B is the magnetic field's strength, A is the coil's circumference, and is the angle formed by the direction of B and the area A's perpendicular.
We can see that since B's intensity is increasing while its direction is staying the same in the problem, the magnetic flux is also increasing.
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in the sequence of steps in which a black hole is formed, a supernova occurs during the first two steps T/F
In the sequence of steps in which a black hole is formed, a supernova occurs during the first two steps this statement is false.
What is a black hole?Even light cannot escape from a black hole because of its intense gravitational pull. Gravity is quite strong because there is so much packed into a small space. This could happen when a star is dying. Since light cannot escape black holes, they are invisible to humans.
How does a black hole develop?In the initial phase of the inspiral, two black holes orbit one another and slowly approach. The second black hole is created when the two black holes combine and deform. The black hole eventually takes on its definitive shape.
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When is an object acceleration? a. change in direction velocity stays the same b. change in speed change in color objects are always accelerating
Answer:
A
Explanation:
change in direction ,velocity stays the same
two parallel long, straight wires are 0.0040 m apart and carry currents of 5.0 a and 10 a, respectively. determine the net magnetic field midway between the wires. take b as positive if it is going into the page. group of answer choices 5.0 x 10-4 t -1.0 x 10-3 t 1.0 x 10-3 t -5.0 x 10-4 t
The net magnetic field midway between the wires is 0.16 mT
What is a magnetic field?The area around with a magnet in which the properties of magnetism are felt is known as the magnetic field. To explain how the magnetic force is dispersed in the area around and inside anything electromagnetic in nature, we utilize the magnetism as a tool.
Given ,
I(1)=3A
I(2)=5A
Wkt
B= µ0I/2πr
B(1) = µ0I(1)/2πr(1)
= 4π×10^-7×3A/2π(0.25)×10^-2
=2.4×10^-4 T
B(2) = µ0I(2)/2πr(2)
=4π×10^-7×5A/2π(0.25)×10^-2
=4×10^-4 T
B(net) = (4×10^-4)
= 0.16mT
direction paralel to the wire
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Are the data from this experiment alone sufficient to conclude that the allele for smooth seeds is dominant over the allele for wrinkled seeds?
If Mendel knew that the allele for smooth (R) seeds was dominant over the allele for wrinkled (r) seeds, and the cross was Rr × rr, the middle column of the Punnett square would be filled with all Rr, because R is dominant over r.
If Mendel knew that the allele for smooth (R) seeds was dominant over the allele for wrinkled (r) seeds, and the cross was Rr × rr, the numbers that would fill the middle column of the Punnett square would be all Rr because the dominant allele R masks the recessive allele r.
The Punnett square for this cross would look like this:
R r
r Rr
r Rr
Each box in the middle column represents the genotype of an individual offspring produced by the cross, and since R is dominant over r, the genotype of all the offspring will be Rr, which results in a smooth seeds phenotype.
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question the work that must be done by an external agent to move a point charge of 2 mc from the origin to a point 3 m away is 5 j. what is the potential difference between the two points?
1.5 × 10³V is the potential difference between the two points where work done by external agent to move a point charge of 2 mc from the origin to a point 3 m away is 5 J.
What is potential difference?The quantity of current times the resistance equals the potential difference (also known as voltage), which is equal to that. When a charge travels between two locations in a circuit, a potential difference of one Volt is equivalent to one Joule of energy being used by that charge.
W = 5J, the amount of work required to move the point charge by the external agent.
q = 2 mC, is the point charge.
Description of the work is,
W = Vq
V=W/q
Replace the values listed,
V = 5J / 2mC
V = 5J / 2 × 10 ⁻³C
V = 2.5 × 10³ V
Consequently, the possible discrepancy between the points is 1.5 × 10³V
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suppose the mass is pulled down to where the spring's length is 56 cm . when it is released, it begins to oscillate. what is the amplitude of the oscillation?
The amplitude of the oscillation is the maximum displacement of the mass from its equilibrium position, which is the position where the spring is at its natural length.
What is Amplitude of an oscillation?It is a scalar quantity and is typically represented by the letter A. In simple harmonic motion, like the oscillation of a mass on a spring, the amplitude is the maximum distance that the oscillating object (in this case the mass) is displaced from its rest position. The amplitude can also be used to describe the maximum intensity of a wave, such as the amplitude of a sound wave, which corresponds to the loudness of the sound.
It is also important to note that amplitude is directly proportional to the energy of the oscillation.
In this case, the amplitude would be the difference between the position where the mass is pulled down (56 cm) and the natural length of the spring. Without more information about the spring's natural length, it is impossible to determine the amplitude of the oscillation.
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fill in the blank. A 0.50-kg sphere at the top of an incline has a potential energy of 8.0 joules relative to the base of the incline. Rolling halfway down the incline will cause the sphere's potential energy to be ______________.
Answer:
The gravitational potential energy of the sphere would be reduced to [tex](1/2)[/tex] of the initial value.
Explanation:
Near the surface of the Earth, the gravitational field is approximately uniform. The gravitational field strength is approximately [tex]g \approx 9.81\; {\rm N \cdot kg^{-1}}[/tex].
In a uniform gravitational field, the gravitational potential energy (GPE) of an object relative to the ground is proportional to height. For example, if an object of mass [tex]m[/tex] is at a height [tex]h[/tex] above the ground, the GPE of this object would be [tex]m\, g\, h[/tex] relative to the ground.
In this example, the height of the sphere is reduced to [tex](1/2)[/tex] of its initial value. As a result, the GPE of this sphere relative to the ground would also be reduced to [tex](1/2)\![/tex] of the initial value.
What is free-fall acceleration toward the sun at the distance of the earth's orbit? Express your answer to two significant figures and Include the appropriate units
The free-fall acceleration toward the sun at the distance of the earth's orbit is 5.93x 10⁻³ m/s².
What does acceleration mean when in free fall?Free fall acceleration is the speed at which a body falls while only being pulled by the gravitational pull of the earth. On the surface of the earth, it has a value of 9.8 ms² and is represented by the symbol g.
The expression for free fall acceleration
towards sun is,
a = GM/R
Mass of the Sun is, M = 1.989x 10³⁰ kg
Distance between sun and earth, R = 1496 x10¹¹ m
The value of G is, G = 6.67 x 10⁻¹¹ Nm²/kg²
Calculate the free fall acceleration
towards sun at a distance of earth's orbit is,
a = GM/R
a = (6.67x10⁻¹¹ Nm²k)(1.989 x10³⁰)/(1.496 x10¹¹ m)²
a = 5.93x 10⁻³ m/s².
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the length of the displacement vector represents how far an object is what?
The length of the displacement vector represents how far an object is traveled in one direction and is therefore denoted as option C.
What is a Displacement vector?This is used in geometry and mechanics and it helps to tell how much the position of an object has changed and also includes how far you have traveled and in which direction which may be eastwards, westward etc.
It talks about both a displacement and a direction of the object and is the reason why it is regarded as a vector quantity which is often measured in meters and the value depends on how far the object is . However, it doesn't signify visibility or how it is thrown but also depicts that it travels in one direction and is therefore the reason why option C was chosen as the most appropriate choice.
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The options are:
A) is visible
B) can be stretched
C) traveled in one direction
D) can be thrown
the exhaust temperature of a carnot heat engine is 300 celsius what is the intake temperature if the efficiency of the engine is 30
A carnot heat engine's intake temperature will be 818.5 K if the engine efficiency is 30 and the exhaust temperature is 300 °C. The ability to avoid material waste, which is frequently quantitative, is efficiency.
Putting in the necessary amount of time, money, energy, and effort into a task or project in order to get the results you want. In a broader sense, it is the ability to complete activities in an effective, efficient, and time-free manner. in terms that are more arithmetical or scientific. Using the Carnot cycle, a heat engine is referred to as a Carnot heat engine.
Carnot engines have an exhaust temperature of 573 k.
Engine performance is similar to E = 1 - T2/T1 0.3 = 1- 573/T1 -0.7 = -573/t1 T1 = 573/0.7 t1 = 818.5K
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The current in a wire varies with time according to the relation I=55A?(0.65A/s2)t2.
How many coulombs of charge pass a cross section of the wire in the time interval between t=0 and t = 8.5s ?
Express your answer using two significant figures.
What constant current would transport the same charge in the same time interval?
Express your answer using two significant figures.
The constant current that transports the same charge in the same time interval is 55A?(0.65A/s2).
What is current?Current is the movement of electricity, or the flow of electrons, through a conductor. It can also refer to a trend or state of affairs that is happening now, such as a news story or the current political climate. Current can also mean a stream of water, air, or other fluid, or the speed of such a stream.
The amount of charge that passes through a cross section of the wire in the time interval from t=0 and t=8.5s is calculated by integrating the current with respect to time.
Integrating the current, I, with respect to time gives the charge, Q, as:
Q = ∫I dt = ∫ 55A?(0.65A/s2)t2 dt
Integrating yields:
Q = 55A?(0.65A/s2)t3/3
Evaluating the integral from t=0 to t=8.5s yields:
Q = 55A?(0.65A/s2)(8.5s)3/3 = 456.9A?s
Therefore, 456.9A?s of charge pass through a cross section of the wire in the time interval from t=0 and t=8.5s.
The constant current, I, that transports the same charge in the same time interval can be calculated by rearranging the above equation and solving for I.
I = Q/∫ dt = 456.9A?s/(8.5s)3/3 = 55A?(0.65A/s2)
Therefore, the constant current that transports the same charge in the same time interval is 55A?(0.65A/s2).
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Two 2.70 cm × 2.70 cm plates that form a parallel-plate capacitor are charged to ± 0.708 nC .Part AWhat is the electric field strength inside the capacitor if the spacing between the plates is 1.20 mm? E = ...?Part BWhat is potential difference across the capacitor if the spacing between the plates is 1.20 mm? V = ... ?Part CWhat is the electric field strength inside the capacitor if the spacing between the plates is 2.40 mm? E = ...?Part DWhat is the potential difference across the capacitor if the spacing between the plates is 240 mm?V = ...?
The electric field strength inside the capacitor does not depend on the distance between plates. Hence, Potential difference and Electric field strength is -130V and -1.09 x 10^5 V/m respectively.
What does "permittivity of open space" mean?The ability of electrical fields to pass through a conventional vacuum is represented by the physical constant known as the permittivity of free space. The constant has a relative standard uncertainty of 1.5 x 10-10 and is equal to around 8.854 x 10-12 F/m (farad per metre).
Q= charge => ± 0.708 nC
E => electric field strength = Q/Aεο
A=> area of plates 2.7 x 2.7 cm2.
εο = > 8.854 x 10-12 F/m.
E= -0.708 x10^-9/ (2.7x2.7 x 8.854 x 10^-4 x 10^-12)
= -1.09 x 10^5 V/m.
Potential difference = Ed => -1.09 x 10^5x 1.2x 10^-3 => -1.30x 10^2V
=> -130V.
How strong is the electric field?The intensity of an electric field at a specific location is expressed quantitatively as "electric field strength." The volt per metre (V/m or Vm-1) is the common unit.
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What is the magnitude of the emf induced between the two sides of the shark's head?
Express your answer using two significant figures.
= mV
The magnitude of the emf induced between the two sides of the shark's head is 0.0448 mV.
What is Induced emf?It is defined as the generation of a potential difference in a coil as a result of changes in the magnetic flux through it. In simpler terms, electromotive force (EMF) is said to be induced when the flux linking with such a conductor or coil changes.
Electromotive forces can be produced in two ways.
The first method entails placing an electric conductor in a varying magnetic field.The second method involves placing a constantly moving conductor in a static magnetic field.The following are some examples of induced emf applications:
It is used in generators.It is used in galvanometers.It can be found in transformers.Magnetic field B = 56 × 10-6T
speed v = 1.0 m/s,
length l = 80 cm = 0.8 m
Induced emf is e = - B l v
= 56 × 10-6 T × 0.80 m × 1.0 m/s
= 0.0448 mV
Thus, the magnitude of the emf induced between the two sides of the shark's head is 0.0448 mV.
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Full question:
A scalloped hammerhead shark swims at a steady speed of 1.0 m/s with its 80 -cm-wide head perpendicular to the earth's 56µT magnetic field?
What is the magnitude of the emf induced between the two sides of the shark's head?
Express your answer using two significant figures.
= mV
Two 2.10 cm × 2.10 cm plates that form a parallel-plate capacitor are charged to ± 0.708 nC .
Part A
What is the electric field strength inside the capacitor if the spacing between the plates is 1.30 mm ?
Part B
What is potential difference across the capacitor if the spacing between the plates is 1.30 mm ?
Part C
What is the electric field strength inside the capacitor if the spacing between the plates is 2.60 mm ?
Part D
What is the potential difference across the capacitor if the spacing between the plates is 2.60 mm ?
The electric field strength inside the capacitor does not depend on the distance between plates. Hence, Potential difference and Electric field strength is -234V and -1.8 x 10^5 V/m respectively.
What does "permittivity of open space" mean?The ability of electrical fields to pass through a conventional vacuum is represented by the physical constant known as the permittivity of free space. The constant has a relative standard uncertainty of 1.5 x 10-10 and is equal to around 8.854 x 10-12 F/m (farad per metre).
Q= charge => ± 0.708 nC
E => electric field strength = Q/Aεο
A=> area of plates 2.10x 2.10 cm2.
εο = > 8.854 x 10-12 F/m.
E= -0.708 x10^-9/ (2.1 x 2.1 x 8.854 x 10^-4 x 10^-12)
= -1.8 x 10^5 V/m.
Potential difference = Ed => -1.8 x 10^5 x 1.3 x 10^-3 => -2.34 x 10^2V
=> -234V.
How strong is the electric field?
The intensity of an electric field at a specific location is expressed quantitatively as "electric field strength." The volt per metre (V/m or Vm-1) is the common unit.
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find the capacitance of a parallel plate capacitor having plates of area 5.00 m2 that are separated by 0.100 mm of teflon.
The capacitance of a parallel plate capacitor with 5.00 m² plates separated by 0.100 mm of Teflon is 0.0427 μF.
Given,
C=ε₀A/D
C=(8.854×10⁻¹²)(5)/0.1×10⁻³
C=4.427×10⁻⁸=0.0427 μF
Capacitance is the property of an electric conductor or set of conductors measured by the amount of separated electric charge that can be stored on it per unit change in electrical potential. Capacitance also implies electrical energy storage. When an electric charge is transferred between two initially uncharged conductors, both become equally charged, one positively, the other negatively, and a potential difference between them is established. The capacitance C is defined as the ratio of the amount of charge q on either conductor to the potential difference V between them, or C = q/V.
The coulomb is the unit of electric charge in both practical and scientific systems, and the volt is the unit of potential difference.
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Sodium and potassium are in the same group in the periodic table. Sodium is in the 11th position. How many valence electrons does potassium have?
a capacitor of capacitance c0 is fully charged by a battery of voltage v0, then disconnected from the battery. how much work is required to pull the plates of the charged capacitor apart to three times their original separation?
The amount of work required to pull the plates of the charged capacitor apart to three times their original separation is equal to the change in electrical potential energy between the initial and final states,or (c0)(3v0)^2.
What is the capacitor ?
A capacitor is an electrical component that stores energy in an electric field and is often used to regulate voltage in a circuit. It consists of two conductive plates separated by a dielectric material. When a voltage is applied to the capacitor, the electric field created around the plates stores energy. When the voltage is removed, the capacitor can discharge the stored energy. Capacitors are used in a wide range of electronic applications, such as filtering signals, storing energy, and providing a timing reference. They can also be used to smooth out power surges or provide a reserve of energy when a sudden increase in current is required.
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what is the breakdown for the composition of the universe by element
Answer:
Explanation: earth water fire space thats are the breakdown for the composition of the universe by element
About how much of the solar energy that reaches earth’s atmosphere is absorbed by the atmosphere?
"About three-fourth's of the solar energy that reaches earth’s atmosphere is absorbed by the atmosphere."
Solar energy is defined as the energy produced by the sun and is the major source of energy on earth. The ecosystem's plants benefit from it. The solar energy is absorbed by the atmosphere through compounds such as, water vapour, dust, ozone. These substances absorb about 71 percent of the solar energy which is approximately equivalent to three-fourths of it.
In total approximately 71% of incoming radiation is absorbed by the atmosphere and the Earth's surface while around 29% is reflected back to space and does not heat the surface.
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an object has velocity relative to the ground. an observer moving past with a constant velocity relative to the ground measures the velocity of the object to be (relative to the observer). the magnitudes of these velocities are related by (a) (b) (c) (d) all the above are true. 17. (a) a boy sitting in a railroad car moving at constant vel
The right answer is (C). These velocities' magnitudes are connected by the formula v(2)v(o)+ v (1)
What is speed?The direction of a body or object's movement is defined by its velocity. Through its basic form, speed is just a scalar quantity. In essence, velocity is a vector quantity. It refers to the speed at which distance changes. It is the migration change rate.
Why is velocity a vector unit?Velocity is a vector quantity because it has alike magnitude and direction. Speed is a scalar quantity because it just has magnitude and no direction.Velocity (v) is a vector quantity that measures displacement (or change in position, Δs) over the change in time (Δt), represented by the equation v = Δs/Δt.
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the complete question is -
An object has velocity v(1) relative to the ground.An observer moving with a constant velocity v(o) relative to the ground measure the velocity of the object tov(2) be (relative to the observer). The magnitudes of these velocities are related by
(a) v(o)≤v(1)+v(2)
(b) v(1)≤v(2)+v(o)
(c) v(2)≤v(o)+v(1)
(d) All of the above are true
If a wave traveling along a string bounces off an object and returns on the opposite side of the equilibrium, what type of boundary did the wave run into
The wave encountered a reflective boundary. A reflective boundary occurs when a wave reaches the end of a medium and then reverses its direction.
In this case, the wave started on one side of a string and, when it reached the object, it reversed direction and traveled back on the opposite side of the equilibrium.
Reflective boundaries usually occur when a wave reaches the end of a medium, but they can also be caused by an obstacle or an abrupt change in the medium's properties. In this case, the object acted as a barrier and reflected the wave, causing it to reverse direction.
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a 1.8 kg book has been dropped from the top of the football stadium. its speed is 4.8 m/sec when it is 2.9 m above the ground. a. what is its total mechanical energy? b. how fast will it be moving when it hits the ground? c. how far above the ground was the book released from rest?
The mechanical energy of the book dropped from the top of the football stadium is 71.89 Joules.
What does it mean to be mechanical?adjective. A person is said to be mechanic if they have a natural aptitude for knowing how machines operate. He was a highly mechanical guy who had a deep understanding of sound. adverb mechanically [ADV -ed]
Given the data in the question;
Mass of the book; m=1.8kg
Speed; v=4.8/s
Height; h=2.9
Mechanical energy; Emcchanical =?
Mechanical energy is energy due to the position or movement of a particle or object. It is expressed as;
Emcchanical= Kinetic energy+ Potential energy
Emcchanical=[tex]\frac{1}{2}mv2[/tex] +mgh
Where m is mass of object, v is velocity, h is height and g is acceleration due to gravity { On earth, acceleration due to gravity }
We substitute our values into the equation
Emcchanical=[tex]\frac{1}{2}*1.8kg*(4.8m/s)2]+[1.8kg*9.8m82*2.9m][/tex]
Emcchanical=20.736kg.m2/82
Emcchanical=71.89.m2/82
Emcchanical=71.89.j
Therefore, the mechanical energy of the book dropped from the top of the football stadium is 71.89 Joules.
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Suppose you throw a football. At some instant, when the ball is in contact with your hand, your hand exerts a force of 600 N on the ball in the x direction. What is the force of the ball on your hand
The force of the ball on your hand is 600 N.
What is Newton's third law of motion?Newton's third law of motion states that, for every action force, there is an equal and opposite reaction force. That is action force and reaction force are equal in magnitude but opposite in direction.
Mathematically, the formula for Newton's third law of motion is given as;
Fa = - Fb
where;
Fa is the force exerted by AFb is the reaction of BIf your exert a certain amount of force on a ball, the ball will exert the same equal amount of force back to your hand but in opposite direction.
Thus, the force of the ball is equal to 600 N.
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determine the minimum speed necessary for a roller coaster car to pass the top of a 12 m radius loop without falling.
The centripetal acceleration must be equal to and in opposition to gravity in order for there to be a net force of zero g's at the top of the loop. the minimum speed required for a roller coaster car is 10.844m/s.
V²/12m = 9.8 m/s²
V = √(12)(9.8) m/s =10.844 m/s.
Acceleration is the rate at which velocity changes with time in terms of both speed and direction. A straight-line moving point or object is accelerated if it speeds up or slows down. Motion on a circle is accelerated even if the speed is constant because the direction is constantly changing. For all other types of motion, both effects contribute to acceleration.
Because acceleration has both a magnitude and a direction, it is a vector quantity. Velocity is also a vector quantity. Acceleration is defined as the change in the velocity vector over a time interval divided by the time interval. The limit of the ratio of the change in velocity gives the instantaneous acceleration (at a specific moment and location).
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The change in the viscosity of a melt is directly proportional to the change in Choose one or more:
A.silica content.
B.carbon dioxide.
C.water content.
D. temperature
All of the options are valid; a melt's viscosity changes in a direct relationship with its silica content, carbon dioxide content, water content, and temperature.
What is a simple explanation of viscosity?Low viscous fluids flow easily because thier molecular structure causes minimal to no friction when they are in action. Viscosity also exists in gasses, however it is less obvious in typical situations.
Is viscosity a liquid or a solid?Another form of bulk attribute called viscosity is the resistance of a liquid to flow. A liquid has a higher viscosity when the forces of attraction within it are strong. Imagine two liquids competing for the first place in a race down a windshield to understand this phenomenon.
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a 500 kgkg horse can provide a steady output power of 750 ww (that is, 1 horsepower) when pulling a load. how about a 38 kgkg sled dog? data show that a 38 kgkg dog can pull a sled that requires a pulling force of 70 nn at a steady 2.4 m/sm/s.
this translates to a power output of 167 ww (70 nn x 2.4 m/sm/s). horse can provide a steady output power when pulling a load.
what is power ?
Power is the ability to influence people, events, or outcomes. It is an important concept in many fields, including politics, business, and psychology. Power is often seen as an abstract concept, but it can be described in terms of tangible resources such as money, authority, and control.
People often use power to achieve their goals and objectives, but it can also be used to limit the freedom and choices of others. Positive power is used to create or support something, while negative power is used to control or manipulate people or situations.
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a 22 cm diameter bowling ball has a terminal speed of 77 m/s. Answer in kg.
The mass of a bowling ball whose diameter is 22 cm and has a terminal speed of 77 m/s is 6.62 kg.
What is terminal speed?The maximum speed (terminal velocity) that an object can reach while falling throughout a liquid. The speed wherein the drag force equivalent to the gravitational force is known as the terminal velocity. The object's mass, cross-sectional area, drag coefficient, the density of the fluid it is falling through, and gravitational acceleration will all affect its terminal velocity.
By using the equation of terminal speed-
Vt = √2mg/ρADc
77 = √2(9.8)m / (1.225) (π(0.11)∧2 (0.47)
m = 77∧2[(1.225)(π(0.11)∧2(0.47)] / 2(9.8)
m = 6.62 kg
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would it be more fuel efficient to drive to the top of a hill along a steeply inclined road or a gradually inclined road
It can be concluded that both paths will require same amount of energy to reach the top.
What is work done?The work done by a force on a body that displaces it from its initial location (x{i}) to a new location (x{f}) can be calculated using the formula given by -
dW = Fdx → ∫dW = F∫dx {integral form}W = F × d × cosθ {normal form}W = F{x}d{x} + F{y}d{y} + F{z}d{z} {unit vector form}Given is to drive to the top of a hill along a steeply inclined road and a gradually inclined road.
Greater the amount of work done by burning the fuel on the car, lesser fuel efficient the car will be. The least steep incline will require the least amount of force while the most steep incline will require the greatest amount of force. Force is not the only variable affecting the amount of work done by the car in ascending to a certain elevation. Another variable is the displacement which is caused by this force. the least steep incline would correspond to the largest displacement and the most steep incline would correspond to the smallest displacement. The final variable is θ. The angle between the force and the displacement vector. Theta is 0° in both situations. So when the force is greatest (on steep incline) the displacement is smallest and when the force is smallest (on least steep incline) the displacement is largest. Subsequently, each path happens to require the same amount of work to elevate the object from the base to the same summit elevation.Therefore, it can be concluded that both paths will require same amount of energy to reach the top.
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