The speed of the meter stick is approximately 180,000 kilometers per second, or 0.6 times the speed of light.
To determine the speed of the meter stick, we will use the concept of length contraction from special relativity. The formula for length contraction is:
L = L0 * sqrt(1 - (v^2/c^2))
where
L is the contracted length (80 cm in this case), L0 is the original length (100 cm for a meter stick), v is the relative velocity between the observer and the meter stick, and c is the speed of light (approximately 3 * 10^8 m/s).First, convert the lengths to meters:
L = 0.8 m
L0 = 1.0 m
Now, rearrange the formula to solve for v:
v^2/c^2 = 1 - (L/L0)^2
v^2 = c^2 * (1 - (L/L0)^2)
v = sqrt(c^2 * (1 - (L/L0)^2))
Plug in the values:
v = sqrt((3 * 10^8 m/s)^2 * (1 - (0.8 m/1.0 m)^2))
Calculate the result:
v ≈ 0.6c, or about 180,000 km/s
The speed of the meter stick is approximately 180,000 kilometers per second, or 0.6 times the speed of light.
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During the "Power Lab", Andrew runs up the stairs, elevating his 79.5 kg body a vertical distance of 2.29 meters in a time of 1.32 seconds. Calculate the power generated by Andrew. (g = 9.8 m/s2)
Answer:
1351.62 Watts.
Explanation:
The following data were obtained from the question:
Mass (m) = 79.5 kg
Height (h) = 2.29 m
Time (t) = 1.32 s
Acceleration due to gravity (g) = 9.8 m/s²
Power =?
Next, we shall determine the potential energy of the boy. This can be obtained as follow:
Potential energy (PE) = mass × acceleration × height
PE = m × g × h
Mass (m) = 79.5 kg
Height (h) = 2.29 m
Acceleration due to gravity (g) = 9.8 m/s²
Potential energy (PE) =?
PE = m × g × h
PE = 79.5 × 9.8 × 2.29
PE = 1784.139 J
Finally, we shall determine the power generated by Andrew as illustrated below:
Energy (E) = 1784.139 J
Time (t) = 1.32 s
Power (P) =?
P = E/t
P = 1784.139 /1.32
P = 1351.62 watts
Therefore, the power generated by Andrew was 1351.62 watts
A baseball is thrown straight up. The drag force is proportional to v^2.
-In terms of g, what is the y-component of the ball's acceleration when its speed is half its terminal speed and it is moving up?Express your solution with three significant digits, and +y direction is upwards. Omit the unit (m/s2).
-In terms of g, what is the y-component of the ball's acceleration when its speed is half its terminal speed and it is moving back down? Express your solution with three significant digits, and +y direction is upwards. Omit the unit (m/s2).
a) The y-component of the ball's acceleration when its speed is half its terminal speed and it is moving up is calculated to be -(1/2)g.
b) The y-component of the ball's acceleration when its speed is half its terminal speed and it is moving back down is calculated to be -(3/2)g.
a) When the speed of the ball is half its terminal speed and it is moving back down, its velocity is also v = vt/2 = (1/2)mg/k.
At this moment, the drag force is positive because it opposes the direction of the velocity,
Fd = (1/2)mg
The acceleration of the ball is,
a = -g + (1/m)Fd = -g + (1/2g) = -(1/2)g
b) We can write, because the drag force is proportionate to the velocity v,
Fd = - kv
where,
k is constant
When the drag force equals the ball's weight and is directed in the opposing direction, the ball reaches its terminal velocity, which results in,
mg = k vt
where,
vt is the terminal velocity
Solving for vt, we get,
vt = mg/k
The ball's velocity is v = vt/2 = (1/2) mg/k when it is ascending at half its final speed. Currently, the pull force is
Fd = -(k/2)mg/k = -(1/2)mg
So, the acceleration of the ball is,
a = -g + (1/m) Fd = -g - (1/2)g = -(3/2)g
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Which evidence is an indication that a chemical reaction has occurred?
freezing of a substance
freezing of a substance
formation of a precipitate
formation of a precipitate
melting of a substance
melting of a substance
boiling of a substance
The evidence which is an indication that a chemical reaction has occurred is the formation of a precipitate and is denoted as option B.
What is Chemical change?This is the referred to as the type of change which occurs when a new substance is formed and it involves a chemical reaction. Physical change on the pother hand doesn't involve the production of a new substance.
Chemical change in this scenario is a precipitate forming because it depicts a new substance and chemical reactions took place before it occurred which is therefore the reason why option B was chosen as the correct choice.
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X-rays having an energy of 850 keV undergo Compton scattering from a target. The scattered rays are detected at 52.0° relative to the incident rays.
24. Find the energy of the recoiling electron in units of keV.
(A) 101 (B) 331 (C) 286 (D) 538 (E) 432
25. Find the de Broglie wavelength of the recoiling electron in units of picometers.
(A) 5.28 (B) 1.85 (C) 8.64 (D) 3.64 (E) 4.88
To find the energy of the recoiling electron in units of keV, we can use the principles of Compton scattering and conservation of energy and momentum.
The change in wavelength (Δλ) of the X-ray photon due to Compton scattering can be calculated using the formula:
Δλ = λ' - λ = h / (m_e * c) * (1 - cos(θ))
where λ' is the wavelength of the scattered X-ray photon, λ is the wavelength of the incident X-ray photon, h is the Planck's constant, m_e is the mass of the electron, c is the speed of light, and θ is the scattering angle.
Using the energy-wavelength relationship for photons:
E = h * c / λ
we can relate the change in wavelength to the change in energy:
ΔE = E' - E = h * c / λ' - h * c / λ
For Compton scattering, the change in energy is given by:
ΔE = (E * (1 - cos(θ))) / (1 + (E / (m_e * c^2)) * (1 - cos(θ)))
Given that the incident X-ray energy (E) is 850 keV and the scattering angle (θ) is 52.0°, we can substitute these values into the equation to find the change in energy.
The energy of the recoiling electron is equal to the change in energy of the X-ray photon.
For question 24, we need to find the energy of the recoiling electron in units of keV. The result will be a numerical value that needs to be rounded to the nearest whole number.
For question 25, we need to find the de Broglie wavelength of the recoiling electron in units of picometers. The de Broglie wavelength can be calculated using the formula:
λ = h / (m_e * v)
where λ is the de Broglie wavelength, h is the Planck's constant, m_e is the mass of the electron, and v is the velocity of the electron.
To find the velocity of the recoiling electron, we can use the relativistic relationship between energy and momentum:
E = √((m_e * c^2)^2 + (p * c)^2)
where E is the energy of the electron, m_e is the mass of the electron, c is the speed of light, and p is the momentum of the electron.
Using the relationship between momentum and velocity:
p = m_e * v
we can solve for the velocity and then substitute it into the de Broglie wavelength equation to find the de Broglie wavelength of the electron.
For both questions 24 and 25, the given options provide possible numerical values. By performing the calculations as described above, you can determine which option matches the calculated result.
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A 100 N force is applied to a 50 kg crate resting on a level floor. The coefficient of kinetic friction is 0.15. What is the acceleration of the crate after it begins to move
The acceleration of the crate after it begins to move is 0.5 m/s²
We'll begin by calculating the the frictional force
Mass (m) = 50 Kg
Coefficient of kinetic friction (μ) = 0.15
Acceleration due to gravity (g) = 10 m/s²
Normal reaction (N) = mg = 50 × 10 = 500 N
Frictional force (Fբ) =?Fբ = μN
Fբ = 0.15 × 500
Fբ = 75 NNext, we shall determine the net force acting on the crateFrictional force (Fբ) = 75 N
Force (F) = 100 N
Net force (Fₙ) =?Fₙ = F – Fբ
Fₙ = 100 – 75
Fₙ = 25 NFinally, we shall determine the acceleration of the crateMass (m) = 50 Kg
Net force (Fₙ) = 25 N
Acceleration (a) =?a = Fₙ / m
a = 25 / 50
a = 0.5 m/s²Therefore, the acceleration of the crate is 0.5 m/s²
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Acceleration due to gravity is stated as a constant which is given 9.8 m/s2. Many scientists have planned and design experiments to investigate if this value is true or false, and most of the results have concluded that the values of acceleration due to gravity ranges from 9.8 m/s2 to 10 m/s2.
Which is not part of an
atom?
A. Proton
B. Neutron
C. Electron
D. Carbon
Answer:D.carbon
Explanation:Protons are positively charged,neutron us nuetrally charged and electron is negatively charged and it contains a ne clues in the centre.
Answer:
Carbon
Explanation:
It is because Carbon is a relatively light element.
A car travelling at 91.0 km/h approaches the turnoff for a restaurant 30.0 m ahead. If the driver slams on the brakes with an acceleration of -6.40 m/s2
2
what will her stopping distance be?
The stopping distance of the car is 49.9 m
Data obatined from the questionThe following data were obtained from the question:
Initial velocity (u) = 91 Km/h = 91 / 3.6 = 25.28 m/sAcceleration (a) = -6.4 m/s²Final velocity (v) = 0 m//s Stopping distance (s) = ?How to determine the stopping distanceThe stopping distance can be obtained as illustrated below:
v² = u² + 2as
0² = 25.28² + (2 × -6.4 × s)
0 = 639.0784 - 12.8s
Collect like terms
-12.8s = 0 - 639.0784
-12.8s = -639.0784
Divide both sides by -12.8
s = -639.0784 / -12.8
s = 49.9 m
Thus, the stopping distance of the car is 49.9 m
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A fiber-optic rod consists of a central strand of material surrounded by an outer coating. the interior portion of the rod has an index of refraction of 1.55. if all rays striking the interior walls of the rod with incident angles greater than 59.5° are subject to total internal reflection, what is the index of refraction of the coating?
Answer:
the index of refraction of the coating is 1.33
Explanation:
Given the data in the question;
refraction index of interior portion of the rod η\(_{interior\) = 1.55
angle of incidence θ\(_i\) = 59.5°
From Snell's law, we know that;
η\(_{interior\) × sinθ\(_i\) = η\(_{coating\) × sinθ\(_r\)
where η\(_{interior\) is the index of refraction of the rod ( material 1 )
θ\(_i\) is the angle of incidence
η\(_{coating\) is the index of refraction in outer coating ( material 2 )
θ\(_r\) is the angle of refraction
so we substitute our values into the equation;
η\(_{interior\) × sinθ\(_i\) = η\(_{coating\) × sinθ\(_r\)
1.55 × sin( 59.5° ) = η\(_{coating\) × sin( 90° )
1.55 × 0.861629 = η\(_{coating\) × 1
1.3355 = η\(_{coating\) × 1
η\(_{coating\) = 1.33 { 2 decimal places }
Therefore, the index of refraction of the coating is 1.33
imagine watching a man swinging a baseball on a rope around his head. Explain how the circular motion of that object is maintained.
The balance of centripetal and centrifugal forces acting on the object enables it to continue moving along the circular path.
There are two forces that act on the object as it is being swirled by the rope above the man's head. These two forces are;
Centripetal force which acts towards the center of the circular path thereby preventing the object from being thrown outCentrifugal force which acts away from the center of the circular path and causes the object to be thrown out of the circular path.When the centripetal force and centrifugal force are exactly balanced, the object remains in the circular path.
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A student pushes a block from rest across a frictionless surface while the block is in front of a motion detector for 3 seconds. The block first speeds up for the 1st second, then moves at constant velocity for the 2nd second, and finally slows down during the final second.
Which statement best explains the motion of the block using Newton's 1st Law?
There is a net force on the block during the 2nd second as a net force keeps the motion constant.
There is a net force on the block during the 3rd second as a net force keeps the motion constant.
There is no net force on the block during the 2nd second as zero net force keeps the motion constant.
There is no net force on the block during the 3rd second as zero net force causes the motion to accelerate.
The true statement according to Newton's laws of motion is; "there is no net force on the block during the 2nd second as zero net force keeps the motion constant."
According to the Newton first law of motion, an object will continue in its state of rest or uniform motion unless it is acted upon by a net force. The action of a net force leads to an acceleration.
In the 2nd second of the journey, there is no net force on the block hence the block continues to move at constant velocity.
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A wide receiver catches the football that has 108 J of energy (work). How much force did his hands apply if he stopped it over a distance of 0.32m
Answer: \(337.5\ N\)
Explanation:
Given
Energy associated with football is \(E=108\ J\)
The receiver takes 0.32 m to stop the ball
Suppose F is the force applied
\(\therefore W=F\cdot d\\\text{Insert the values}\\\\\Rightarrow 108=F\times 0.32\\\\\Rightarrow F=\dfrac{108}{0.32}\\\\\Rightarrow F=337.5\ N\)
A ray of light strikes a plane mirror at an angle of incidence of 60°, is reflected from the mirror and then strikes a second plane mirror placed so that the angle beftween the mirrors is 45°. The angle of reflection at the second mirror, in degrees, is
A 15
B 25
C 45
D 65
E 75
plz help me guys ASAP!
Answer:
60 - 45 = A. 15
Explanation:
Subtracted because the plane mirror at an angle is incidence of 60°, so then in order to find the value it would be 60-45 and not adding it or dividing and multiplying to find the value thus the answer is 15.
60 - 45 = A. 15. Subtracted because the plane mirror at an angle is incidence of 60°, so then in order to find the value it would be 60-45 and not adding it or dividing and multiplying to find the value thus the answer is 15.
What is Plane mirror?A flat or highly polished surface called a plane mirror reflects light or waves to create an image. It is a polished, smooth surface that creates a virtual representation of the actual object.
A plane mirror is a surface on which an image can only be produced by at least two light beams. The intersection of these two beams can occur inside the mirror or appear to occur somewhere behind the mirror.
The image that follows illustrates how an object appears when viewed via a plane mirror.
Therefore, 60 - 45 = A. 15. Subtracted because the plane mirror at an angle is incidence of 60°, so then in order to find the value it would be 60-45 and not adding it or dividing and multiplying to find the value thus the answer is 15.
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Al 26.98 and S 32.06 calculate the number of formula units in 62.2 g sample of aluminum sulfide
The number of formula units would be 2.5 x \(10^2^3\)
Formular unitThis is mathematically given as: mole x Avogadro number
Molar mass of the aluminum sulfide (Al2S3) sample = 26.98 x 2 + 32.06 x 3
= 53.96 + 96.18 = 150.14 g/mole
Mole of 62.2 g aluminum sulfide = 62.2/150.14 = 0.4143 moles
Formular unit = 0.4143 x 6.023 x \(10^2^3\) = 2.5 x \(10^2^3\)
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when an object accelerates in the same direction its motion, it has _____ acceleration, And it _________.
Answer:
1.positive velocity.
2.speeding up.
Weight is proportional to but not equal to mass. In which of the following situations would a person show an increase in weight but not an increase in mass?
Group of answer choices
a Landing on a planet with more gravity.
b Traveling on the highway in a SUV.
c Living in a chamber in an underwater habitat.
d Climbing to the top of a mountain.
Answer: c living in a camber in an under water habitat
Explanation:
what observable (observable - something you can measure) stays constant in a series circuit, but in a parallel circuit?
The observable (observable - something you can measure) stays constant in a series circuit, but in a parallel circuit is the current.
In a series circuit, the current is the same at all points in the circuit. However, in a parallel circuit, the current is divided among the different branches of the circuit. In a series circuit, the total resistance is equal to the sum of the individual resistances, and the current is equal to the voltage divided by the total resistance. This means that the current is the same at all points in the circuit, regardless of the number of components or their individual resistances.
In a parallel circuit, the total resistance is equal to the inverse of the sum of the inverses of the individual resistances, and the current is divided among the different branches of the circuit. This means that the current is not the same at all points in the circuit, and will vary depending on the number of components and their individual resistances. In summary, the current stays constant in a series circuit, but not in a parallel circuit.
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I need help for this displacement question.
Answer:
577656.0
Explanation:
Which of the following is a base?
A. Lemon Juice
B. Baking Soda
C. Vinegar
A balloon clings to a wall after it is negatively charged by rubbing.(a) Does that occur because the wall is positively charged?
A balloon clings to a wall after it is negatively charged by rubbing because the wall is positively charged.
Is opposite charge attract each other?Yes, opposite charges attract each other. When a positive charge and a negative charge interact with each other, their forces act from the direction of positive to the direction of negative charge. As a result opposite charges attract each other while on the other hand, similar charges repel each other because their forces move in the opposite direction so they repel each other.
So we can conclude that a balloon clings to a wall after it is negatively charged by rubbing because the wall is positively charged.
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The geocentric model could not explain which of the following observations made by early astronomers? Select the two correct answers
Mars and Jupiter appeared to move backwards for some period of time
The planets had epicycles
The stars appeared to move
Mercury and Venus changed in appearance throughout the year
s
Owing to the fact that planets orbits the sun at different speeds, Mars and Jupiter does appear to move backwards for some period of time. The geocentric model fails to explain this.
The geocentric model of the solar system is the approach that held the earth rather than the sun as the center of the solar system. The geocentric model was favored by most of the early astronomers.
However, as popular as the geocentric model of the solar system was, it failed to explain the phenomenon of retrograde motion which includes the apparent backward movement of Mars and Jupiter for some period of time.
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Answer:
My guess is
Explanation:
C or Mars and Jupiter appeared to move backwards for some period of time
B or The stars appeared to move
Sorry if i'm wrong
Consider the causal LTI system with impulse response h(t) = u(t). Prove that this system is an integrator, i.e., the output of the system is the integral of the input. X(t) 1 2 t t(2-t) 0 h(t) 1 b 1 21 Figure 1: Input function and impulse response
Using the input and impulse response given in Fig.1, find and sketch the output calculating x(t) * h(t). You can either use the integral definition of the convolution or the Reflect-and-Shift approach.
The impulse response of the LTI system is h(t) = u(t).Let's find the output for the given input and impulse response using the integral definition of the convolution, given as follows:x(t) h(t) = ∫x(τ)h(t-τ)dτWe have to consider two cases when t < 0 and t ≥ 0.
Case 1:
When t < 0x(t) h(t) = ∫x(τ)h(t-τ)dτWhen t < 0, h(t - τ) = u(t - τ) = 0 for all τ > t. Therefore, for this range of t, x(t) h(t) = 0.Case 2:
When t ≥ 0x(t) h(t) = ∫x(τ)h(t-τ)dτ= ∫x(τ)u(t-τ)dτSince u(t - τ) = 1 for τ ≤ t and u(t - τ) = 0 for τ > t, we can split the integral into two parts:x(t) h(t) = ∫x(τ)u(t-τ)dτ= ∫x(τ)u(t-τ)dτ + ∫x(τ)u(τ-t)dt= ∫x(τ)u(t-τ)dτ + ∫x(t-τ)u(τ)dτ= ∫0tu(τ)x(t-τ)dτ + ∫t∞u(τ)x(t-τ)dτ= ∫0tx(t-τ)dτAs the function x(t) is given,we can evaluate the integral:
x(t) h(t) = ∫0tx(t-τ)dτ= ∫0t(2-τ)dτ= 2t - t²/2Let's plot the graph of the output function using the given input and impulse response:Graph of the output functionAbout Impulse ResponseIn signal processing and control theory, the impulse response, or impulse response function, of a dynamic system is its output when presented with a brief input signal, called an impulse. More generally, the impulse response is the reaction of any dynamic system in response to some external change.
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Emily is pushing a toy sand truck. She realizes it is much harder to push the truck when it is full of sand than when it is empty. What is the reason for this?
An object with a greater mass requires a smaller force to accelerate.
An object with a greater mass requires a greater force to accelerate.
An object pushed with a greater force has a greater mass.
An object pushed with a greater force has less mass.
Answer: An object with a greater mass requires a greater force to accelerate.
Explanation:
Answer:
An object with a greater mass requires a greater force to accelerate.
Explanation:
I took the test.
Which is NOT an example of evidence that shows a chemical reaction occurred?
change in color
change in temperature
change in shape
bubbles, fizzing
A rod of length 2Do and mass 2 Mo is at rest on a flat, horizontal surface. One end of the rod is connected to a pivot that the rod will rotate around if acted upon by a net torque. A sphere of mass mo is launched horizontally toward the free end of the rod with velocity to, as shown in the figure. After the sphere collides with the rod, the sphere sticks to the rod and both objects rotate around the pivot with common angular velocity. Which of the following predictions is correct about the angular momentum and rotational kinetic energy of the sphere-rod system immediately before the collision and immediately after the collision?
The correct prediction about the angular momentum and rotational kinetic energy of the sphere-rod system immediately before the collision and immediately after the collision is: Before the collision, the sphere has linear momentum (mass mo multiplied by velocity to) while the rod has zero angular momentum since it is at rest.
After the collision, the sphere and rod form a single system, and the conservation of angular momentum dictates that the final angular momentum of the system should equal the initial angular momentum of the sphere. Therefore, the sphere-rod system will have non-zero angular momentum after the collision.
Regarding rotational kinetic energy, before the collision, the sphere has linear kinetic energy (1/2 mo * to²) and the rod has zero rotational kinetic energy. After the collision, the sphere-rod system will have rotational kinetic energy (as they both rotate around the pivot with a common angular velocity). Due to the inelastic nature of the collision, some linear kinetic energy from the sphere will be converted to rotational kinetic energy in the sphere-rod system, but not all of it, as some energy will be lost as heat and sound during the collision.
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How do you format short quotations in an MLA-style document?
Answer:
To indicate short quotations (four typed lines or fewer of prose or three lines of verse) in your text, enclose the quotation within double quotation marks.
a 2.75 kg bucket is attached to a disk-shaped pulley of radius 0.101 m and mass 0.792 kg . if the bucket is allowed to fall,Part A What is its linear acceleration?a = ___ m/s^2 Part B What is the angular acceleration of the pulley? a = ___ rad/s^2
The linear acceleration of the bucket is\(-3.92 m/s^2\) and The angular acceleration of the pulley is\(-38.82 rad/s^2.\)
What do you mean by the term acceleration due to gravity?Acceleration due to gravity refers to the acceleration experienced by objects in the Earth's gravitational field. To solve this problem, we need to apply Newton's laws of motion to the system. First, we'll consider the forces acting on the bucket. Since it's falling freely, the only force acting on it is its weight, which is given by:
\(Fbucket = mbucket * g\)
where \(mbucket\) is the mass of the bucket and g is the acceleration due to gravity (\(9.81 m/s^2\)).
Next, we'll consider the forces acting on the pulley. There are two forces acting on the pulley: its weight and the tension in the rope connecting it to the bucket. Since the pulley is stationary (not accelerating in the vertical direction), the weight force is balanced by the tension force:
\(Ftension = Fweight pulley\)
\(mpulley * g = Ftension\)
where \(mpulley\) is the mass of the pulley.
The tension force is also responsible for the motion of the bucket and the pulley. The tension force causes an acceleration in the bucket, and since the rope is attached to the pulley, it also causes an angular acceleration in the pulley.
Part A:
To find the linear acceleration of the bucket, we'll use Newton's second law:
\(Ftension - Fbucket = mbucket * a\)
where a is the linear acceleration of the bucket.
Substituting\(Ftension\) and \(Fbucket\) and solving for a, we get:
\(mpulley * g - mbucket * g = mbucket * a\)
\(a = (mpulley - mbucket) * g / mbucket\)
\(a = (0.792 kg - 2.75 kg) * 9.81 m/s^2 / 2.75 kg\)
\(a = -3.92 m/s^2\) (The negative sign indicates that the bucket is accelerating downwards)
Therefore, the linear acceleration of the bucket is \(-3.92 m/s^2\).
Part B:
To find the angular acceleration of the pulley, we'll use the formula:
\(a = alpha * r\)
where a is the linear acceleration of the bucket (which we just found), alpha is the angular acceleration of the pulley, and r is the radius of the pulley.
Substituting the values and solving for alpha, we get:
\(alpha = a / r\)
\(alpha = -3.92 m/s^2 / 0.101 m\)
\(alpha = -38.82 rad/s^2\) (The negative sign indicates that the pulley is rotating clockwise)
Therefore, the angular acceleration of the pulley is\(-38.82 rad/s^2\).
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A rollercoaster cart leaves point A at a speed of 4 m/s, passes through point B on the ground, and reaches point C at a speed of 6 m/s. The total mass of the cart assembly and the passengers are 300 kg,
(a) What is the total energy of the cart at point B?
(b) What is the height of point A?
a) the total energy of the cart at point B is 2400 Joules.
b) the height of point A is approximately 1.83 meters.
(a) To find the total energy of the cart at point B, we need to consider both its kinetic energy and potential energy.
The kinetic energy (KE) of the cart can be calculated using the formula:
KE = (1/2)mv^2
where m is the mass of the cart assembly and passengers, and v is the speed of the cart.
Given:
Mass (m) = 300 kg
Speed (v) = 4 m/s
Plugging in the values, we get:
KE = (1/2) * 300 kg * (4 m/s)^2
KE = 2400 J
Next, we need to calculate the potential energy (PE) of the cart at point B. Since point B is on the ground, we can take the reference level as the ground level, where the potential energy is zero.
Therefore, at point B, the potential energy of the cart is zero.
The total energy (E) of the cart at point B is the sum of its kinetic energy and potential energy:
E = KE + PE
E = 2400 J + 0 J
E = 2400 J
Therefore, the total energy of the cart at point B is 2400 Joules.
(b) To determine the height of point A, we can use the conservation of energy principle. At point A, the cart has potential energy (PE) and kinetic energy (KE).
The total energy (E) of the cart at point A is the sum of its kinetic energy and potential energy:
E = KE + PE
Since the cart is at rest at point A (initially), its kinetic energy is zero:
KE = 0
Therefore, the total energy (E) at point A is equal to the potential energy (PE):
E = PE
Given:
Total mass (m) = 300 kg
Speed at point A (v_A) = 0 m/s
Speed at point C (v_C) = 6 m/s
Acceleration due to gravity (g) = 9.8 m/s²
Using the equation for potential energy:
PE = mgh
At point C, the cart has maximum kinetic energy and zero potential energy. Therefore, the total energy (E) at point C is equal to the kinetic energy (KE):
E = KE = (1/2)mv_C^2
Plugging in the values, we get:
E = (1/2) * 300 kg * (6 m/s)^2
E = 5400 J
Since energy is conserved, the total energy at point A is also 5400 J:
E = 5400 J
Equating the total energy at point A to the potential energy, we have:
PE = 5400 J = mgh
Rearranging the equation, we can solve for the height (h):
h = PE / (mg)
h = 5400 J / (300 kg * 9.8 m/s²)
h ≈ 1.83 meters
Therefore, the height of point A is approximately 1.83 meters.
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A certain car is capable of accelerating at a rate of 0.59 m/s2. how long does it take for this car to go from a speed of 50 mi/h to a speed of 57 mi/h?
A certain car with an accelerating rate of 0.59 m/s2 will take 5.30 s to go from a speed of 50 mi/h to a speed of 57 mi/h
The formula for Uniformly varied rectilinear motion (UVRM) and procedure we will use to solve this exercise is:
t = (vf - vi) /a
Where:
vf = final velocityvi = initial velocityt = timea = accelerationInformation about the problem:
vi= 50 mi/h vf= 57 mi/ha= 0.59 m/s2t = ?By converting the velocity from mi/h to m/s, we get:
50 mi/h * (1609.34 m / 1 mi) * (1h / 3600 s) = 22.35 m/s
57 mi/h * (1609.34 m / 1 mi) * (1h / 3600 s) = 25.48 m/s
Applying the time formula, we have:
t = (vf - vi) /a
t = ( 25.48 m/s - 22.35 m/s) / 0.59 m/s2
t = 3.13 m/s /0.59 m/s2
t = 5.30 s
What is acceleration?It is a physical quantity that indicates the variation of velocity as a function of time, it is expressed in units of distance per time squared e.g.: m/sec2 ; km/h2
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fill in the blanks
8) Kinetic energy is the energy of ________.
9)The potential energy of an object depends on its ________ and its height.
10) The law of ________ of energy states that energy can be neither created nor destroyed, but it can change its form.
Answer: Kinetic energy is the energy an object has because of its motion
(if it needs to be a one worded answer than just type motion)
The potential energy of an object depends on its mass and its height.
The law of conservation of energy states that energy can be neither created nor destroyed, but it can change its form.
Answer:Kinetic energy is the energy an object has because of its motion. If we want to accelerate an object, then we must apply a force. Applying a force requires us to do work.
As expressed by the equation, potential energy depends upon the mass and the height of the object. Any increase in these two quantities will lead to an increase in the amount of potential energy possessed by the object.
The law of conservation of energy states that energy can neither be created nor destroyed - only converted from one form of energy to another. This means that a system always has the same amount of energy, unless it's added from the outside.