The statement which is correct about the lighter dart leaves the spring moving faster than the heavy dart. Option B is correct.
This is because both darts are launched with the same initial elastic potential energy from the compressed springs, but the lighter dart has less mass than the heavier dart. According to the law of conservation of energy, the lighter dart must move faster than the heavier dart in order to have the same amount of kinetic energy as the heavier dart once it leaves the spring.
The initial potential energy is the same for both darts, and since the potential energy is converted to kinetic energy, the lighter dart must have a higher velocity than the heavier dart in order to have the same amount of kinetic energy.
Therefore, option B is correct, while options A, C, D, and E are not, as they do not accurately describe the behavior of the darts in this scenario.
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--The complete question is, A heavy dart and a light dart are launched horizontally on a frictionless table by identical ideal springs. Both springs were initially compressed by the same amount. Which of the following statements about these darts are correct?
A) The darts both have the same kinetic energy just as they move free of the spring.
B) The lighter dart leaves the spring moving faster than the heavy dart.
C) The heavy dart had more initial elastic potential energy than the light dart.
D) Both darts move free of the spring with the same speed. E) Both darts had the same initial elastic potential energy.--
The equivalent resistance of 2.0 Ω, 3.0 Ω, 5.0 Ω, and 6.0 Ω resistors connected in parallel is ________.
A) 1.2 Ω
B) 7.2 Ω
C) 0.83 Ω
D) 9.3 Ω
Answer:
C) 0.83 Ω
Explanation:
two tennis balls fall through the air from a tall building. one of them is filled with lead pellets. the ball to reach the ground first is the
From a towering building, 2 tennis balls fall into the air. Lead pellets are contained within one of them. The lead-filled ball becomes the first to touch the ground.
What do you call air?The invisible atmospheric mixture that envelops Earth is called air. Most organisms depend on vital elements like oxygen and nitrogen to thrive, which are found in air. Of course, a member of this species is human people (Homo sapiens). In some cases, "atmosphere" is substituted in place of "air."
What purpose does air serve?Respiration is a procedure that includes breathing. A living organism breathes by taking intake oxygen from the environment and exhaling carbon dioxide. This process provides the energy necessary for plants and animals to absorb, grow, and sustain life.
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What is a wave function?
During a football match, the ball kicked at 45° angle of elevation went just over the goal post, height 2.4m. Assuming the goal post height is the greatest, calculate: The speed at which the ball was projected, The time taken to reach the greatest height
the horizontal distance between the point of kick and foot of the goal post bar (neglect the thickness of the bar)
Answer:
see below
Explanation:
We are here given that ,
maximum height of projectile= 2.4m (h)angle at which it is kicked = 45° speed of projection= ? (u)As we know that,
[tex]\implies h =\dfrac{u^2\sin^2\theta}{2g} \\[/tex]
substitute the respective values,
[tex]\implies 2.4 m =\dfrac{u^2\sin^245^\circ}{2\times 10} \\[/tex]
[tex]\implies 2.4m =\dfrac{u^2\times \bigg(\dfrac{1}{\sqrt2}\bigg)^2}{20}\\[/tex]
[tex]\implies u^2 = 40 \times 2.4 = 96 \\[/tex]
[tex]\implies u^2 =\sqrt{96}\\[/tex]
[tex]\implies \underline{\underline{ u \approx 9.79 \ m/s }}\\[/tex]
secondly we know that,
[tex]\implies t = \dfrac{u\sin\theta}{g}\\[/tex]
[tex]\implies t =\dfrac{9.79\times \sin45^\circ}{10} \\[/tex]
[tex]\implies t =\dfrac{9.79\times \dfrac{1}{\sqrt2}}{10} \\[/tex]
[tex]\implies \underline{\underline{ t \approx 0.69 \ s }}\\[/tex]
and we are done!
Find the number of kilometers in a light year. A light year is the distance that light travels in one year. Light travels at the rate of 3.0×10^5 km/s.Assume a year is 365 days
The light year is an unit of measure for distance. It is defined as the distance travelled by light in a vacuum over the course of a year.
Define a vacuum?A vacuum is a space area that is either devoid of matter or has a pressure so minimal that any particles there have no bearing on any processes occurring there. It is a condition that has a pressure that is measured in units of pressure and is much lower than the mean air pressure.
What is the term pressure?The quantity of force applied to a certain region is referred to as pressure. So either a strong force or a strong force applied over a short area can cause a lot of pressure (or do both).
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a pulley system has a mechanical advantage of 3, and an object weighing 9 newtons must be lifted 15 meters. how much force must be applied to lift the object? use the following equation to find the answer: ma=fo/fi
To lift the object, you must apply a force of 27 Newtons (9 Newtons divided by 3, the mechanical advantage).
The equation you can use to find the answer is MA = F0/Fi, where MA is the mechanical advantage, F0 is the input force and Fi is the output force.
MA is the mechanical advantage of a machine and is the ratio of output force to input force. For example, if an object needs to be lifted but the force required to lift it is too great, a machine such as a pulley system can be used to reduce the force needed. A pulley system has a mechanical advantage of 3, meaning that the output force is three times greater than the input force.
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A material has a stress–strain relationship that can be approximated by the equation
ε=0.3x10-16xσ3
where the stress is in psi. Find the secant modulus and the tangent modulus for the stress level of 50,000 psi.
The secant modulus and the tangent modulus for the stress level of 50,000 psi are both 4.5x10-9 psi-1.
What is secant modulus?Secant modulus is a measure of a material's ability to resist deformation under stress. It is the ratio of stress to strain in a material and is equal to the slope of a line drawn between two points on a stress-strain curve.
The secant modulus is the slope of the line connecting two points on the stress-strain curve. In this case, the two points we need to consider are (50,000 psi, ε) and (0 psi, 0).
Therefore, the secant modulus is given by:
secant modulus = (ε - 0) / (50,000 psi - 0 psi)
Plugging in the equation for ε, we get:
secant modulus = (0.3x10-16x50,0003 - 0) / (50,000 psi - 0 psi)
secant modulus = 4.5x10-9 psi-1
The tangent modulus is the slope of the tangent line to the stress-strain curve at a given point. In this case, the point is (50,000 psi, ε).
Therefore, the tangent modulus is given by:
tangent modulus = dε/dσ
Plugging in the equation for ε, we get:
tangent modulus = (3x10-16x50,0002) / (1 psi)
tangent modulus = 4.5x10-9 psi-1
Therefore, the secant modulus and the tangent modulus for the stress level of 50,000 psi are both 4.5x10-9 psi-1.
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he circular orbits of satellites 1 and 2 coincide. Satellite 2 has twice the mass of satellite 1. Compare their accelerations. A) 1's acceleration is half as much. B) 1's acceleration is the same as 2's C) 1's acceleration is twice as much as 2's D) It depends on the periods of their orbits.
The correct answer is (a): satellite 1's acceleration is half as much as satellite 2's.
This is due to the fact that the acceleration of two satellites in a circular orbit depends on their masses and orbital periods. Satellite 2 accelerates more quickly because it has twice as much mass as satellite 1. As a result, satellite 1 accelerates at a rate that is half that of satellite 2.
This results in a divergence in the orbits of the two spacecraft since satellite 1's speed will rise more slowly than satellite 2's. Over time, this difference will become more obvious, with satellite 1's orbit straying from a circular form more so than satellite 2's.
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the acceleration of the system shown above is? please answer ASAP
Answer:
3.92 m/s²
Explanation:
It's hard to read your sketch, but it looks like m2 = 30 kg? If so, here's the answer:
m1 = 20 kg
m2 = 30 kg
a = (m2·g) - (m1·g·sin∅) / (m1 + m2) you can see how this equation is derived from Newton's 2nd Law in any physics textbook or website
a = ((30 kg)(9.8 m/s²) - (20 kg)(9.8 m/s²)(sin30)) / (20 kg + 30 kg)
a = (294 kg·m/s² - 98 kg·m/s²) / (50 kg) = 3.92 m/s²
the block has a weight of 20 lb and is being hoisted at uniform velocity. determine the angle u for equilibrium and the force in cord ab.
The force in the cord ab is 37.6 lb when being lifted at a constant speed, and the angle u for balance.
Describe uniform velocity using an illustration.The rotation of the earth is an example of a body that is moving with uniform velocity when its speed is increasing throughout an interval of time.
The sum of the forces in each direction must be zero in order to lift the block at a steady speed.
XFx = 0 : F sin θ − T sin 20° = 0
XFy = 0 : T cos 20° − F cos θ − 20 = 0
The tension in cord CAD stays constant throughout because there is no friction on the pulley: F = 20 lb.
20 sin θ − T sin 20° = 0......... (1)
T cos 20° − 20 cos θ − 20 = 0 ........(2)
Solve equation (1) for T
T = 20 sin θ/sin 20
and substitute it into equation (2).
(20 sin θ/sin 20°)cos 20° − 20 cos θ − 20 = 0
cot 20°sin θ − cos θ − 1 = 0
cot 20°sin θ − 1 = cos θ
cot 20°sin θ − 1 = √1 − sin2θ
cot²20°sin²θ − 2 cot 20°sin θ + 1 = 1 − sin²θ
(cot²20° + 1) sin²θ − 2 cot 20°sin θ = 0
csc²20°sin²θ − 2 cot 20°sin θ = 0
(csc²20°sin θ − 2 cot 20°) sin θ = 0
csc²20°sin θ − 2 cot 20° = 0 or sin θ = 0
sin θ = 2 cot 20°/csc² 20°
= 2 cos 20°sin 20° = sin 40° or sin θ = 0
θ = 40° or θ ≠ 0°.
Substitute this nonzero value for θ into the formula for T.
T =20 sin θ/sin 20°
≈ 37.6 lb
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Do the following factors increase or decrease as one moves to higher magnifications with the microscope?a. resolutionb. amount of light neededc. working distanced. depth of field
The following factors change as one moves to higher magnifications with a microscope:
What is magnification?
Magnification is a measure of how much an image is enlarged or increased in size compared to the original object. It is commonly used in optics, such as microscopes and telescopes, to describe the level of enlargement achieved by the instrument. The magnification is usually expressed as a ratio or a multiple of the original size.
a. Resolution: Resolution refers to the ability of a microscope to distinguish two separate points as separate entities. As one moves to higher magnifications, the resolution of the microscope increases, meaning that smaller and finer details can be seen.
b. Amount of light needed: As magnification increases, the amount of light needed to illuminate the specimen also increases. This is because the increased magnification reduces the amount of light that reaches the specimen and the observer.
c. Working distance: Working distance refers to the space between the lens and the specimen. As one moves to higher magnifications, the working distance decreases, meaning that the lens must be positioned closer to the specimen.
d. Depth of field: Depth of field refers to the range of distances from the lens that are in focus at any given time. As one moves to higher magnifications, the depth of field decreases, meaning that only a very small portion of the specimen will be in focus at any given time.
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A 6.0-kg rock is dropped from a height of 9.0 m. At what height is the rock's kinetic energy twice its potential energy?
At a height of 4.48 meters, a rock's kinetic energy is twice its potential energy.
What are kinetic energy and potential energy?Potential energy is the energy stored in any object or system due to the position or arrangement of its parts. It is, however, unaffected by factors outside of the object or system, such as air or height. Kinetic energy, on the other hand, is the energy of moving particles in an object or system.
Given that a 6.0-kg rock is dropped from a height of 9.0 m.
Calculate the total potential energy at the initial point,
PE = mgh
PE = 6 x 9.81 x 9
PE = 530.74 J
At the zero height, the kinetic energy will be maximum and is equal to the total energy,
KE = 530.75 J
1/2 mv² = 530.75
v² = 175.85
The height at which the kinetic energy is two times the potential energy is calculated as:-
1 /2 x mv² = 2 x mgh
h = ( 4 v²) / ( 4 x 9.81 )
h = 4 ( 175.82 ) / ( 4 x 9.81 )
h = 4.48 meters
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Question 10 0.5 pts What is the diffusion coefficient b) for iron at 700°C, with an activation energy (Q) of 18,300 cal/mol, and D.=0.0047cm/s: 2.43E3 cm2/s O 9.08E-9 cm2/s O 3.64E-7 cm2/s 60.66 cm2/s
The diffusion coefficient based on the provided data is 3.651 x 10^(-5) cm^2/s. (Option C)
The diffusion coefficient refers to the ratio of flux density to the negative of the concentration gradient in direction of diffusion. The diffusion coefficient in solids at different temperatures is generally found to be well predicted by the Arrhenius equation:
D=Do exp (-E/RT)
Where D is the diffusion coefficient (in m2/s), Do is the maximal diffusion coefficient (at infinite temperature; in m2/s), E is the activation energy for diffusion (in J/mol), T is the absolute temperature (in K), and R ≈ 8.31446 J/(mol⋅K) is the universal gas constant.
In the given case,
Do = 0.0047 cm/s = 4.7 x 10^-5 m/s
E = 18300 cal/mol = 76567.2 J/mol
T = 700°C = 973.15 K
Hence,
D=(4.7 x 10^(-5)) exp (-76567.2/(8.31446*973.15))
D=(4.7 x 10^(-5)) exp (-9.463)
D=3.651 x 10^(-9) m^2/s or 3.651 x 10^(-5) cm^2/s
Note: The question is incomplete. The complete question probably is: What is the diffusion coefficient (D) for iron at 700°C, with an activation energy (E) of 18,300 cal/mol, and Do = 0.0047cm/s. A) 2.43E3 cm2/s B) 9.08E-9 cm2/s C) 3.64E-5 cm2/s D) 60.66 cm2/s.
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Energy Essay Question 1
You do work on something when you lift it against gravity. How does this work relate to gravitational potential
energy? If the lifted object is released, what becomes of this energy? Be sure to define all terms that you use.
Posted Mon Jan 30, 2023 at 1:16 pm
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DS Immersive Reader Grade: N/A O
As the object is raised, the gravitational potential energy of the system grows. When you drop something, the potential energy of the object is transformed into kinetic energy, which is the energy of the moving object, when it strikes the ground.
What is kinetic and potential energy?
Potential energy is the energy stored in an object or system due to its position or arrangement of elements. It is unaffected by the environment outside the installation or system, such as air or altitude. Conversely, kinetic energy refers to the energy of moving particles in a system or object.
An object's kinetic energy, unlike potential energy, relates to other stationary and moving objects in its immediate vicinity. Thus, the lifted object is in kinetic motion when released.
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A 67 kg high jumper leaves the ground with a
vertical velocity of 6.4 m/s.
How high can he jump? The acceleration
of gravity is 9.8 m/s².
Answer in units of m. Answer in units of m.
The height of the jump having a mass of 67kg with the vertical velocity of 6.4m/s is 2.089m.
What is Kinetic and Potential energy?Potential energy is defined as the energy stored in an object or system by virtue of its position or arrangement of parts while kinetic energy is defined as the energy of the moving particles of an object or system.
Potential energy is represented as :
P.E.= mgh
Kinetic energy is represented as :
[tex]K.E.= 1/2mv^2[/tex]
where, m = mass of the object
h= height
v= velocity
g= acceleration due to gravity which is [tex]9.8m/s^2[/tex]
For above given example,
m= 67kg, v= 6.4m/s
we first find out Kinetic energy,
K.E.=[tex]\frac{1}{2} 67* (6.4)^2[/tex]= 2744.32/2= 1372.16 J
As we know, K.E.= P.E.
So, P.E.= 1372.16J = mgh
1372.16= 67* 9.8* h
height= 2.089 m
Thus, the height of the jump having a mass of 67kg with the vertical velocity of 6.4m/s is 2.089m.
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how much work w is done in lifting a 35-kg sandbag to a height of 4.5 m? (use 9.8 m/s2 for g. round your answer to the nearest integer.)
After applying the gravitational potential energy, the amount work done in lifting a 35 kg sandbag to a height of 4.5 m would be 1,544 Joule
Gravitational potential energy is another name for work done against gravity. Because of this, if a mass (m) object is lifted through a height (h), the work done on it will be [m × g × h], and this energy will be stored as gravitational potential energy in the body.
Thus, the amount work done would be:
Work = m × g × h
= 35 kg × 9.8 m/s² × 4.5 m
= 1,543.5 Nm
= 1,543.5 Joule
= 1,544 Joule
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When connected to a 12V battery, the current in a car headlight is 4.0 A.
When the lamp is lit, what is its resistance?
A) 3.0 ohms
B) 16 ohms
C) 48 ohms
D) 0.33 ohms
Answer:
3Ω
Explanation:
we are here given that,
voltage= 12V current= 4A resistance= ?From Ohm's law , we know that,
[tex]\implies V = iR \\[/tex]
where ,
v is potential differencei is currentR is resistanceon substituting the respective values, we have,
[tex]\implies 12V = 4A(R) \\[/tex]
[tex]\implies R =\dfrac{12V}{4A} \\[/tex]
[tex]\implies \underline{\underline{ R = 3\Omega}} \\[/tex]
and we are done!
(4 points) determine which of the following pairs of functions are linearly independent. linearly independent 1. f(t)
If there is a non-trivial linear combination of the vectors that equals 0, then a set of vectors is said to be linearly dependent.
What purposes do vectors serve in physics?Physical quantities can be represented using vectors. Vectors are most frequently employed in physics to describe displacement, velocity, and acceleration. Vectors are depicted as arrows and combine magnitude and direction.
Because they may visually depict position, displacement, velocity, and acceleration, vectors are useful. It is crucial to indicate where the scale is being drawn at when drawing.
|v| =(x2 + y2) is the formula to calculate the magnitude of a vector in two dimensions, where v = (x, y). The equation |V| = (x2 + y2 + z2) can be used to calculate the magnitude of a vector in three dimensions, where V = (x, y, z).
Therefore, vectors because you frequently do not have enough room to draw them at the scale they represent.
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The probability that a baseball player hits a home run is greater than the probability that he gets a successful hit. (Select all that apply.) A.) A home run is the only type of successful hit, so the probabilities of each must be equal. B.)The probability that he hits a home run and the probability that he gets a successful hit must add up to 1. C.)The probability that he gets a successful hit must be 1, since a successful hit is always possible, and therefore the probability that he hits a home run cannot be greater. D.)A home run by definition is a successful hit, so the probability that he gets a successful hit must be greater than, or at least equal to, the probability that he hits a home run. E.)These probabilities cannot be calculated, so it is impossible to say which one is greater.
A and D are correct. A home run is the only type of successful hit, so the probabilities of each must be equal.
Additionally, a home run by definition is a successful hit, so the probability that he gets a successful hit must be greater than, or at least equal to, the probability that he hits a home run. B, C and E are incorrect since these probabilities can be calculated and it is possible to say which one is greater.
The probability is a measure of how likely an event is to occur. It is a number between 0 and 1, where 0 indicates that the event is impossible and 1 indicates that the event is certain. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of potential outcomes. For example, if the probability of flipping a coin and getting heads is 0.5, it means that there is a 50% chance of getting heads when flipping the coin.
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A container with volume 1.62 L is initially evacuated. Then it is filled with 0.293g of N2. Assume that the pressure of the gas is low enough for the gas to obey the ideal-gas law to a high degree of accuracy. If the root-mean-square speed of the gas molecules is 178 m/s, what is the pressure of the gas?
The pressure of the gas is 0.970 atm.
The pressure of a gas can be calculated using the ideal gas law, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature in Kelvin.
First, we need to find the number of moles of N2, which can be calculated using the molar mass of N2 and the mass of N2 in the container:
n = m/M
n = 0.293g / 28.02 g/mol
n = 0.0104 mol
Next, we need to find the temperature in Kelvin, which can be calculated using the root-mean-square speed of the gas molecules:
T = (2 * k * m / (3 * R))
T = (2 * 1.38 x 10^-23 J/K * 6.63 x 10^-27 kg * (178 m/s)^2 / (3 * 8.31 J/mol/K))
T = 298.15 K
Finally, we can use the ideal gas law to find the pressure:
P = nRT / V
P = (0.0104 mol * 8.31 J/mol/K * 298.15 K) / (1.62 L)
P = 0.970 atm
So the pressure of the gas is 0.970 atm.
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Two weights are connected by a massless wire and pulled upward with a constantspeed of 1.50 m/s by a vertical pull P. The tension in the wire is T(see figure). Whichone of the following relationships between Tand Pmust be true?
A)T
B)T=P
C)P+T=125N
D)P=T+25N
The correct relationship between T and P is represented by option B)
T = P.
The net force operating on the system is represented by the tension in the wire T, which is equal to the total of the forces acting on each weight. Because only the gravitational force and the tension force are operating on each weight in this situation, the net force exerted on each weight is equal to the difference between the tension and the weight. T must therefore equal the sum of the gravitational pull P and the forces acting on each weight.
Since m represents the mass of each weight and g is the acceleration brought on by gravity, the equation for the relationship between T and P must be T = P + m * g.
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When a stone is projected, its horizontal range is 24m and greatest height 6m. Find its velocity of projection.
Answer:
15.33 m/s
Explanation:
We are here given that ,
Range = 24m (R)Maximum height= 6m (h)velocity of projection= ? (u)As we know that,
[tex]\longrightarrow R = \dfrac{u^2\sin2\theta}{g} \dots (1)\\[/tex]
And ,
[tex]\longrightarrow h =\dfrac{u^2\sin^2\theta}{2g} \dots (2)\\[/tex]
Divide equation 1 and 2 ,
[tex]\longrightarrow \dfrac{R}{h}=\dfrac{4 \cos\theta}{\sin\theta} \\[/tex]
[tex]\longrightarrow \dfrac{24m}{6m}=4 \cot\theta \\[/tex]
[tex]\longrightarrow \cot\theta = 1 \\[/tex]
[tex]\longrightarrow \theta = \cot^{-1}(1) \\[/tex]
[tex]\longrightarrow \underline{\underline{\theta = 45^{\circ}}}\\[/tex]
Now we may substitute this value in equation 1 as ,
[tex]\longrightarrow 24 =\dfrac{ u^2\sin(2\times 45^{\circ} )}{g} \\[/tex]
[tex]\longrightarrow 24g = u^2\sin90^\circ \\[/tex]
[tex]\longrightarrow u^2 = 24 \times 9.8 \\[/tex]
[tex]\longrightarrow u =\sqrt{235.2} m/s \\[/tex]
[tex]\longrightarrow \underline{\underline{ u \approx 15.33 \ m/s }}\\[/tex]
and we are done!
The following circuit diagram is partially incomplete. A device is added to the electrical circuit to vary the current in Lamp 2 only. Which of the following circuit symbols should be included in the diagram to represent this device?
The device used to vary the current in a circuit is a variable resistor. The symbol of a variable resistor is option d. The symbol with a rectangle and an arrow.
What is a variable resistor ?A variable resistor also called a rheostat is a resistor of which the electric resistance value can be adjusted. A variable resistor is in essence an electro-mechanical transducer and normally works by sliding a contact (wiper) over a resistive element.
When a variable resistor is used as a potential divider by using 3 terminals it is called a potentiometer.
When only two terminals are used, it functions as a variable resistance and is called a rheostat. Electronically controlled variable resistors exist, which can be controlled electronically instead of by mechanical action. These resistors are called digital potentiometers.
Here, the resistance thereby the current through the lamp 2 can be varied by placing a resistor. Hence, option d is correct.
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The symbol used in diagram to represent the device is rheostat's symbol.
Correct option is D.
What is electric current?Electric current is defined as the rate of flow of electrons in a conductor. The SI Unit of electric current is the Ampere.
In given circuit,
A device is added to the electrical circuit to vary the current in Lamp 2 only,
Electrical current is varied by applying variable resistance,
The device used to apply variable resistance is rheostat, which has symbol of box with an arrow through it.
Hence, rheostat's symbol will be used in diagram to represent the device.
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a golf ball is suit from a ship which is at a height 46 m above water surface the horizontal distance covered by Golf is
The horizontal distance travelled by the golf is 7.75 m.
What is the height of fall of the golf?The time taken for the golf to fall from the given height is calculated by applying the following equation.
t = √ ( 2h / g )
where;
h is the height of fall of the golfg is acceleration due to gravityt = √ ( 2 x 46 / 9.8 )
t = 3.1 seconds
The horizontal distance travelled by the golf is calculated as follows;
d = vt
where;
v is the horizontal velocityd = 2.5 m/s x 3.1 s
d = 7.75 m
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The complete question is below:
a golf ball is suit from a ship which is at a height 46 m above water surface the horizontal distance covered by Golf is if the horizontal velocity is 2.5 m/s.
what is the value of gravity on moon?
Answer:
The gravitational force on the moon is approximately 1/6th of the gravitational force on Earth. This means that the value of gravity on the moon is 1.62 m/s2.
Answer:
on earth the value of gravity on moon is 1.625 m/s2
Explanation:
1.625 m/s2
3. A stopped roller coaster cart (velocity = 0 m/s) with a mass of 12,000 kg starts from the top of
the track at a height of 35 meters. It begins to roll down to the bottom (where height will be 0
meters).
(a.)What is the kinetic energy of the roller coaster cart at the bottom? KE PE
(b.)What is the velocity of the cart at the bottom?
bottom
top
A stopped roller coaster cart (velocity = 0 m/s) with a mass of 12,000 kg starts from the top of
the track at a height of 35 meters. It begins to roll down to the bottom (where height will be 0 meters).
KE = PE = mgh
KE = (12,000)(9.8)(35)
= 4,116,000
What is height?
Despite the fact that height is typically measured in relation to a plane of reference, most height measurements in the real world are based on sea level, which is a zero surface. The position of a point above mean sea level is typically used to define altitude and elevation, two synonyms for height. The sea-level surface beneath the continents can be extended; naively, one might picture a large number of little canals running through the continents. In reality, gravity measurements must be used to calculate the sea level beneath a continent; various computing techniques are available; see Geodesy, heights.To know more about heights, click the link given below:
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how matter is identified.
Answer:
Explanation:
Matter is identified based on its physical and chemical properties.
Physical properties, such as color, texture, density, melting point, and boiling point, can be used to identify matter without changing its composition. For example, a solid object with a high density and a high melting point is likely to be a metal, while a lighter, less dense material with a low melting point is likely to be a plastic.
Chemical properties, such as reactivity, flammability, and acidity, are also used to identify matter. For example, the reaction of a substance with a strong acid or base can provide information about its chemical composition.
In addition to physical and chemical properties, matter can also be identified based on its molecular structure and composition. This can be done using techniques such as X-ray diffraction, spectroscopy, and microscopy, which allow scientists to examine the atomic and molecular structure of matter.
Finally, the chemical formula of a substance can also be used to identify it. The chemical formula specifies the types and numbers of atoms present in the substance, which can be used to determine its chemical properties and behavior.
Four small spheres, each charged to +15 nC, form a square 2.0 cm on each side. From far away, a proton is shot toward the square along a line perpendicular to the square and passing through its center. What minimum initial speed does the proton need to pass through the square of charges
The speed of the charged particles or proton or electron will be 2.75 × 10⁵ m/s.
What is Kinetic energy?The kinetic energy of an object is the energy which it possesses due to its motion. Kinetic energy is defined as the work needed to accelerate an object of a given mass from the state of rest to its stated velocity.
At the center of the square, all the kinetic energy of the proton is converted to potential energy of the proton. Therefore, far away the kinetic energy of proton must be equal to the potential energy of the person at the center.
Speed of the electron far away from the square, v = 2.75 × 10⁵ m/s
Given, that the charge, q = 15 × 10⁻⁹C
Each side of square, l = 0.02m
Distance of center of square from any charge r = √2l/2 = r= √2 × 0.02/ 2
r = 0.014m
q = 15nC
q = 15nC
I = 0.02m
q = 15nC
q = 15nC
Electric potential at the center of the square is given by:
Vc = 4 × (kq/r)
Electric potential at point far away is V∞ = 0
Potential Energy difference between the two point is
ΔV = Ve - V∞
ΔV = 4×(kq/r)
For the proton to pass through the center of square the proton must have kinetic energy equal to the potential energy at the center of the square.
The kinetic energy of the proton K = mv²
The potential energy of the proton U = eΔV
For the proton to pass through
K(at ∞) = U(Center)
1/2 mv² = 4kqe/ r
v = [tex]\sqrt{(8kq)/(mr)}[/tex]
v = √(8 × 9 × 10⁹ × 15 × 10⁻⁹ × 1.6 × 10⁻¹⁹)/ (1.67 × 10⁻²⁷ × 0.014) m/s
v = 2.75 × 10⁵ m/s
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What is the magnitude of your total displacement if you have traveled due west with a speed of 23 m/s m / s for 155 s s , then due south at 12 m/s m / s for 235 s s ?
The magnitude of your total displacement is 745 m.
What is the total displacement?
The total displacement of the your motion is calculated by applying the following formula as shown below;
Δx = x₂ - x₁
where;
x₂ is the final positionx₁ is the initial positionThe magnitude of your total displacement is calculated as follows;
Δx = ( 23 m/s x 155 s ) - ( 12 m/s x 235 s )
Δx = 745 m
Thus, the magnitude of your total displacement is based on the change of your position.
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. a body of mass m and negligible size starts from rest and slides down the surface of a frictionless solid sphere of radius r. (see below.) prove that the body leaves the sphere when
It has been demonstrated that the angle when the body exits the sphere is θ = cos⁻¹(2/3)
Between two surfaces that are sliding or attempting to slide over one another, there is a force called friction. For instance, friction makes it challenging to push a book down the floor. Every time an object moves or attempts to move, friction always acts in the direction opposing to that movement.
Force acting on a stationary particle
The following formula is used to compute the particle's force while it is stationary;
Rgcos = mgcos = mv2/R v2 —- (1)
power-saving measures
Utilizing the principle of energy conservation, one may calculate the object's ultimate speed once it begins to slide.
v2 = 1/2mR(1 - cos) = 2gR(R - Rcos) ---(2) reconcile (1) and (2)
Rgcos = 2gR (cos - 1);
cos = 2 - cos 2.
Cos1(2/3) = 3cos = 2cos = 2/3
As a result, the body exits the sphere at an angle of θ = cos⁻¹(2/3) , proved.
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The complete question is
A body of mass m and negligible size starts from rest and slides down the surface of a frictionless solid sphere of radius R. Prove that the body leaves the sphere when 0 = cos(2/3).