Calculate the vertical component of the athlete's speed:
Vy = Vsin(θ)
Vy is the vertical component of the speed, V is the speed, and θ is the angle the athlete jumps off the ground at.
Given values:
V = 4m/s
θ = 23°
Plug in these values and solve for Vy:
Vy = 4sin(23°) = 1.563m/s
Let us use this kinematics equation for the athlete's vertical motion:
H = Vt + 0.5At²
H is the height, t is time, V is the initial vertical velocity, and A is acceleration.
Given values:
V = 1.563m/s
A = -9.81m/s² (acceleration due to gravity)
Plug in these values:
H = 1.563t - 4.905t²
We want to know the athlete's airtime, or when they reach the ground, ie calculate a time t when H = 0m. So let us substitute H = 0 and solve for t:
1.563t - 4.905t² = 0
t = 0.3187, 0
Reject t = 0s
t = 0.3187s
Choice A
find the weight density 1.00 qt. of liquid weighing 4.00 lb.
Answer:
p = 1.91722 g/cm3
Explanation:
Density is p=m/V, where density (p) is equal to mass (m) divided by volume (V).
Answer/Explanation:
I've worked out that p = 1.91722 g/cm3
Density is p=m/V, where density (p) is equal to mass (m) divided by volume (V).
Can yall help me?
A. What is the effect on the current through a circuit of steady resistance when the voltage is increased by a factor of 2? Find the ratio of the current after the change of voltage Ifinal1 and the current before the change of voltage Iinitial1.
B. What is the effect on the current if both voltage and resistance are increased by a factor of 2? Find the ratio of the current after the change of voltage and resistance Ifinal2 and the current before the change of voltage and resistance Iinitial2.
Explanation:
Ohm's law describes the relationship between voltage, current, and resistance.
V = IR
where V is voltage, I is current, and R is resistance.
A. At the original voltage:
V₁ = I₁ R₁
When the voltage is doubled and resistance stays the same:
2V₁ = I₁' R₁
Dividing the two equations:
2V₁ / V₁ = (I₁' / I₁) (R₁ / R₁)
2 = I₁' / I₁
So the new current is double the original current.
B. At the original voltage and resistance:
V₂ = I₂ R₂
When both the voltage and resistance are increased by a factor of 2:
2V₂ = I₂' (2R₂)
Dividing the two equations:
(2V₂ / V₂) = (I₂' / I₂) (2R₂ / R₂)
2 = (I₂' / I₂) (2)
1 = I₂' / I₂
So the new current is the same as the original current.
Based on Ohm's Law, if voltage in an electric circuit is doubled, the current also doubles. However, if both voltage and resistance are doubled, the current remains the same.
Explanation:The subject you're asking about is focused on how changes in voltage and resistance can affect current, according to Ohm's law. Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points, and inversely proportional to the resistance between them. It can be represented by the formula I = V/R, where I is the current through the conductor, V is the voltage, and R is the resistance.
A. Effect of Doubling VoltageIf the voltage is increased by a factor of 2, while the resistance remains constant, the current would also increase by a factor of 2. So the ratio Ifinal1/Iinitial1 would be 2/1 = 2.
B. Effect of Doubling Voltage and ResistanceIf both the voltage and resistance are increased by a factor of 2, the current would remain the same, because the increase in voltage would be offset by the increase in resistance. Thus, the ratio Ifinal2/Iinitial2 would be 2/2 = 1.
Learn more about Ohm's Law here:https://brainly.com/question/36009177
#SPJ3
Which shows the correct order of steps during the formation of an ionic bond?
Ions are attracted to each other – Electrons are transferred – An ionic compound forms
An ionic compound forms - lons are attracted to each other - Electrons are transferred
Electrons are transferred – lons form - lons are attracted to each other
lons form - Electrons are transferred – Ions are attracted to each other
Answer: Electrons are transferred → Ions form → Ions are attracted to each other
Explanation:
Answer: Option (d) is the correct answer.
Explanation:
An ionic bond is defined as the bond that is formed by transfer of electron(s) from one atom to another.
For example, Lithium has atomic number 3 and first, it will form an ion by loosing an electron.
[tex]Li \rightarrow Li^{+} + 1e^{-}[/tex]
On the other hand, chlorine has atomic number 17 and it needs one electron to form a chlorine ion. So, it will gain an electron from lithium atom.
[tex]Cl + 1e^{-} \rightarrow Cl^{-}[/tex]
Therefore, these ions will then get attracted towards each other resulting in the formation of lithium chloride compound.
Thus, we can conclude that the correct order of steps during the formation of an ionic bond is ions form - Electrons are transferred – Ions are attracted to each other.
What is a successful result of science?
a discovery
an experiment
curiosity
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\text{What s a successful result of science?}[/tex]
[tex]\huge\text{A discovery is a successfully result of science}[/tex]
[tex]\huge\text{Reason?}[/tex]
[tex]\huge\text{Well, because it known for the working or making}[/tex] [tex]\huge\text{'newer' discovers so it can tell us humans}[/tex] [tex]\huge\text{that something is theoretically correct}[/tex]
[tex]\boxed{\boxed{\huge\text{Thus the answer is A. a discovery}}}\huge\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
if an atom has 34 protons and 40 neutrons, what is the mass number?
If an atom has 34 protons and 40 neutrons, the mass number is 74.
Explanation:
Mass number is related to the protons and neutrons. It is the product of the above two subatomic particles. Hence the mass number and the atomic number are dependent upon the subatomic particles of an atom. From the given data in the question, mass number of the atom is calculated as, 34 + 40 = 74.
How are the fossils of the Precambrian eon different from the Phanerozoic eon
Answer:by carbon and oder element
Explanation:
The Precambrian eon is different from the Phanerozoic eon due to the fact that the fossil present from the Precambrian eon was of mostly microorganisms which are single cellular organisms.
Explanation:
The Phanerozoic eon was marked with eon which had the multi cellular organism that is the level of cellularity was enhanced by this eon due to the evolutionary course taken for the organisms. Phanerozoic eon and Precambrian eon had a vast difference of cellular level of organization found in the fossil remains of both times.
Precambrian eon had many primitive algae which existed mostly till the earliest Cambrian era only. Due to single cellularity of the organisms, the fossil of Precambrian eon was not much in abundance whereas the Phanerozoic eon had much abundant fossil remains.
When the ionic compound NaBr dissolves in water, Br– ions are pulled into solution by the attraction between what two particles?
Answer:
The attraction of Br⁻ to H⁺ and Na⁺ to OH⁻
Explanation:
NaBr is an ionic compound and would easily be dissociated by water in solutions.
Water is a polar covalent molecule and with a partial dipole on it. The hydrogen ions have a positive charge and the hydroxyl ions are negatively charged.
In solutions with water, NaBr dissolves. This releases the sodium and bromide ion into the solution. The Bromide ion becomes hydrated and surrounded by the water molecules. The negatively charged end of the water molecule bonds with the Na ion and the positive end bonds with the negative part of the water molecule. This bonding provides the NaBr an ease of movement in its lattice structure.
This procedure leads to the solubility of NaBr in water.
9. At the amusement park, a blue bumper car crashes into a red bumper car. Which of the
following statements about their momentum is accurate?
A. There is less overall momentum after the collision.
B. The momentum of the red car is destroyed as it is hit.
C. There is greater overall momentum after the collision.
D. The overall momentum stavs the same before and after the collision
Answer:A)
Explanation:
Well It makes the Most sense. The momentum of the Cars were lessened due to the hit.
B is wrong because not only did the red car crash but so did the blue so the real answer should be both.
C makes no sense at all.
D The momentum is lost after collision so it is not the same, so this is false also.
HOPE THIS HELPS! :)
A man of 60kg moves in a lift of constant velocity 5m/s .What is the reactive force acting on the man by the elevator?
Answer:
588 N
Explanation:
Since the 60 kg is moving at a constant velocity there is no acceleration. In order for the system to be balanced, both the normal force and the force of gravity must be equal. In this case the man has a mass of 60 kg. So to find the force you multiply mass by gravitys constant (9.81). And you end up with an answer of 588.6 but I rounded to 588.
The reactive force acting on the man by the elevator is about 588 Newton
Further explanationNewton's second law of motion states that the resultant force applied to an object is directly proportional to the mass and acceleration of the object.
[tex]\large {\boxed {F = ma }[/tex]
F = Force ( Newton )
m = Object's Mass ( kg )
a = Acceleration ( m )
Let us now tackle the problem !
Given:
mass of the man = 60 kg
velocity of the lift = 5 m/s
Unknown:
reactive force = N = ?
Solution:
We will use Newton's 2nd law formula for this problem.
[tex]\Sigma F = ma[/tex]
[tex]N - w = ma[/tex]
[tex]N - mg = ma[/tex]
[tex]N - 60(9.8) = 60(0)[/tex] → constant velocity ⇒ a = 0
[tex]N = 0 + 588[/tex]
[tex]N = 588 ~ Newton[/tex]
Learn moreImpacts of Gravity : https://brainly.com/question/5330244Effect of Earth’s Gravity on Objects : https://brainly.com/question/8844454The Acceleration Due To Gravity : https://brainly.com/question/4189441Newton's Law of Motion: https://brainly.com/question/10431582Example of Newton's Law: https://brainly.com/question/498822Answer detailsGrade: High School
Subject: Physics
Chapter: Dynamics
Keywords: Gravity , Unit , Magnitude , Attraction , Distance , Mass , Newton , Law , Gravitational , Constant
A ball rolls horizontally off a table and a height of 1.4 m with a speed of 4 m/s. How long does it take the ball to reach the ground
For vertical motion, use the following kinematics equation:
H(t) = X + Vt + 0.5At²
H(t) is the height of the ball at any point in time t for t ≥ 0s
X is the initial height
V is the initial vertical velocity
A is the constant vertical acceleration
Given values:
X = 1.4m
V = 0m/s (starting from free fall)
A = -9.81m/s² (downward acceleration due to gravity near the earth's surface)
Plug in these values to get H(t):
H(t) = 1.4 + 0t - 4.905t²
H(t) = 1.4 - 4.905t²
We want to calculate when the ball hits the ground, i.e. find a time t when H(t) = 0m, so let us substitute H(t) = 0 into the equation and solve for t:
1.4 - 4.905t² = 0
4.905t² = 1.4
t² = 0.2854
t = ±0.5342s
Reject t = -0.5342s because this doesn't make sense within the context of the problem (we only let t ≥ 0s for the ball's motion H(t))
t = 0.53s
Final answer:
In the Physics topic of projectile motion, it takes approximately 0.5345 seconds for a ball to reach the ground after rolling off a 1.4-meter high table horizontally at a speed of 4 m/s. This calculation is based on the free fall motion equation considering a gravitational acceleration of 9.8 m/s².
Explanation:
The subject of this question is Physics, particularly the topic of projectile motion. To determine how long it takes for a ball to reach the ground when it is rolled off a table, we need to use the equations of motion for objects in free fall. Since the horizontal motion and vertical motion are independent of each other, we only need to consider the vertical motion to answer this question.
Step-by-Step Calculation:
Identify the known variables: the height of the table (h) is 1.4 meters, and the acceleration due to gravity (g) is 9.8 m/s² (assuming earth's gravity).
The initial vertical velocity (vi) is 0 m/s since the ball is rolling off horizontally.
Use the equation for the vertical motion in free fall: h = vi * t + (1/2) * g * t², where t is the time in seconds.
Plugging in the known values, we get 1.4 = 0 * t + (1/2) * 9.8 * t².
Simplifying, we have 1.4 = 4.9 * t², which gives us t² = 1.4 / 4.9.
Calculating t², we find it equals approximately 0.2857.
Take the square root of both sides to find the time (t), which is roughly 0.5345 seconds.
Therefore, the ball takes approximately 0.5345 seconds to reach the ground after rolling off the table.
if you break a magnet in two you get
Breaking a bar magnet in half results in two smaller magnets each with a north and south pole, illustrating that magnets always have two poles and magnetic 'monopoles' do not exist in isolation.
Explanation:If you break a bar magnet in half, the result is not a separation of magnetic poles, but rather the creation of two smaller magnets, each with its own north and south pole. This outcome underscores a fundamental principle of magnetism: magnets are always dipolar, meaning they have two poles. The behavior of magnets when broken can be traced to the atomic level, where even the tiniest particles that exhibit magnetism possess a north and south pole.
Unlike electric charges, which can exist in isolation, magnetic 'monopoles' have not been observed. Instead, the magnetic properties of materials like iron derive from the orientation of electrons' rotation, offering a microscopic explanation for why severing a magnet produces smaller dipoles rather than isolated poles.
The age of the universe in seconds
Answer:
4.351968e+17 seconds
Explanation:
So I googled age of the universe and it says 13.8 billion years.
you'll have to do some conversions:
in one year, there are 365 days. in one day, there are 24 hours. in one hour, there are 3600 seconds.
[tex]\frac{1 year}{365 days} x \frac{1 day}{24 hours} x \frac{1 hour}{3600 seconds}[/tex]
so you have to add in the current age of the universe to that equation:
[tex]\frac{x seconds}{13.8 bil years} x \frac{1 year}{365 days} x \frac{1 day}{24 hours} x \frac{1 hour}{3600 seconds}[/tex]
arranged so that the proper "units" will read as "x seconds" at the end of the equation.
then you do the math to find x:
13.8 billion x 365 x 24 x 3600 = 4.351968e+17 seconds.
which would be 435,196,800,000,000,000 seconds
Hope this helps :)
Final answer:
The age of the universe is approximately 13.8 billion years, estimated using the Hubble constant. For a Hubble constant of 70 kilometers/second per million parsecs, the age of the universe is about 13.8 billion years. The age of the universe is approximately 13.799 billion years. Converting this into seconds, we get around 4.358 × 10^17 seconds with a margin of error due to uncertainty.
Explanation:
The student has asked for the age of the universe in seconds. To determine this, we use the currently accepted estimate for the age of the universe, which is approximately 13.799 billion years. To convert this age into seconds, we follow these steps:
First, convert the age in years to seconds by multiplying by the number of seconds in a year (31,536,000). Since there are ± 0.038 billion years of uncertainty, calculate the margin of error in seconds by multiplying 0.038 billion years by the number of seconds in a year. Performing the calculations, we find that the age of the universe in seconds is approximately 4.358 × 10^17 seconds, with an uncertainty of about 1.2 × 10^15 seconds. This answer provides an estimation based on the current understanding of astrophysics and cosmology.
If an object accelerates from rest, with a constant acceleration of 6.4 m/s2, what will
its velocity be after 18s?
Answer:
120 m/s
Explanation:
Acceleration = 6.4 m/s²
Initial velocity = 0 m/s
Time = 18 s
v = at + v₀
v = (6.4)(18) + 0
v = 115.2
Rounded to two significant figures, the final velocity is 120 m/s.
A boat having a length 3m and breadth 2m is floating on a
lake. The boat sinks by 1cm when a man gets on it. The mass
of the man is:
Answer:
60 kg
Explanation:
The man's weight is equal to the weight of the water he displaces.
mg = ρVg
m = ρV
m = (1000 kg/m³) (3 m × 2 m × 0.01 m)
m = 60 kg
The man's mass is 60 kg.
A helicopter is hovering at an altitude of 200m above the surface of the lake. A speaker on the helicopter is sending out sound waves which are reflected from both the surface of the water and bottom of the lake. If the differences in arrival times of the two echoes is measured to be 0.24s, what is the depth of the lake? (The atmospheric temperature is 20°C)
Explanation:
The first echo travels from the helicopter to the surface and back. The second echo travels from the helicopter to the surface to the bottom of the lake and then back.
We know the difference in time is 0.24 s, so the time it takes the sound wave to travel through only the water is 0.24 s. Since the sound wave covers the distance twice (first from the surface to the bottom, then the bottom to the surface), we only want half the time, 0.12 s.
The speed of sound in water at 20°C is 1481 m/s. Therefore:
d = 1481 m/s × 0.12 s
d = 178 m
The depth of the lake is 178 meters (round as needed).
To calculate the depth of the lake, use the speed of sound at 20°C (343 m/s) and multiply it by the time difference (0.24s) between the echoes. This product gives the total distance sound traveled, which is twice the depth of the lake. The depth is found by dividing this distance by two, resulting in 41.16 meters.
Explanation:The student is asking about determining the depth of a lake using sound waves from a hovering helicopter that are reflected from the surface of the water and the bottom of the lake. The time difference between the arrivals of the two echoes is given, and the speed of sound at 20°C needs to be used in the calculations. Since the speed of sound at this temperature is approximately 343 m/s, the total distance traveled by the sound waves is the speed of sound multiplied by the time difference between the echoes. This total distance is twice the depth of the lake, because the sound travels to the lake bottom and back up. Dividing this total distance by two gives the depth of the lake.
The formula to calculate the total distance traveled by the sound is:
Total distance = Speed of sound × Time difference
To find the depth, we divide the total distance by two:
Depth = (Speed of sound × Time difference) / 2
Depth calculation:
Speed of sound at 20°C = 343 m/sTime difference = 0.24 sTotal distance = 343 m/s × 0.24 s = 82.32 m
Depth = 82.32 m / 2 = 41.16 m
The depth of the lake is therefore 41.16 meters.
Black holes have three major parts that include:
A) The event horizon, singularity, and the chute located between the two.
B) Stars, planets, and the event horizon
C) The event horizon, singularity, and moons
D) The event horizon, a large planet, and the chute located between the two.
Answer:
A) The event horizon, singularity, and the chute located between the two.
Answer:
Black holes have three major parts that include A) The event horizon, singularity, and the chute located between the two.
Explanation:
A black hole is a celestial object that has an extremely important mass in a very small volume. They are cold remains of very old stars that contain a lot of matter in a compact space. Because of this, they have a great force of gravity.
Black holes are only formed by very massive stars. When they collapse on themselves forming a well in space: a black hole. If they are not so massive, the matter they are made of can stop the collapse and form a dying star that barely shines: a white dwarf or a neutron star.
Black holes have three main parts that include:
The event horizon: In the center of each black hole there is such a concentration of matter that it exerts a gravitational attraction so strong that not even light, the fastest phenomenon in nature, can escape. Then the event or event horizon is the point at a distance from the center of that rotating celestial object where matter or energy, when crossed, cannot escape gravity. The singularity: a singularity is a theoretical point with zero volume and infinite density. It is a place where the density of matter and the curvature of space become infinite. They are inside the horizon of a black hole. The ramp located between the two (the even horizon and singularity).When is a zero not significant?
Answer:
Not between significant digits.
Explanation:
A zero not significant when it's not between significant digits.
Answer:
Zero are not significant when indicating the decimal point position
Explanation:
The number zero has a special meaning with respect to its meaning, when it is placed to the right as a decimal, its meanings so precision measurements were made, for example 10 cm and 10.0 cm, the first one has an accuracy of one centimeter and the second has an accuracy of 0.1 cm.
In the case of being placed to the left of all numbers, the meaning is to indicate where the decimal point goes, but it does not give information about the accuracy of the measurement, in this second case the zeros are not significant, for example: 0.1 0.0001 in these two cases are not significant
Select the correct answer.
What do microwaves have in common with light waves?
O
Both are compression waves.
A.
B.
0
Both are longitudinal waves.
0
o
Both are electromagnetic waves.
0
Both are mechanical waves.
Reset
Answer:
Both are electromagnetic waves
Explanation:
Both microwaves and light waves form a part of the electromagnetic spectrum. Electromagnetic waves are produced as a result of oscillating magnetic and electric fields. when arranged in order of frequencies and wavelengths they form the electromagnetic spectrum.
A 20.0 cm tall object is placed 50.0 cm in front of a convex mirror with a radius of curvature of 34.0 cm. Where will the image be located, and how tall will it be? Please show all work. Please help
Answer:
1.Theimage will be located at -0.13m or -13 cm
2.The height of the image will be 0.052m or 5.2cm
Explanation:
Given that;
Height of object, h=20 cm = 0.2m
Object distance in front of convex mirror, o,= 50 cm =0.5m
Radius of curvature, r, =34 cm =0.34m
Let;
Image distance, i,=?
Image height, h'=?
You know that focal length,f, is half the radius of curvature,hence
f=r/2 = 0.34/2 = 0.17m ( this length is inside the mirror, in a virtual side, thus its is negative)
f= -0.17m
Apply the relationship that involves the focal length;
[tex]=\frac{1}{o} +\frac{1}{i} =\frac{1}{f}[/tex]
[tex]=\frac{1}{0.5} +\frac{1}{i} =-\frac{1}{0.17}[/tex]
Re-arrange to get i
[tex]\frac{1}{i} =-2-5.88\\\\\\\frac{1}{i} =-7.88\\\\i=-0.13m[/tex]
This is a virtual image formed at a negative distance produced through extension of drawing rays behind the mirror if you use rays to locate the image behind the mirror
Apply the magnification formula
magnification, m=height of image÷height of object
[tex]m=\frac{h'}{h} =-\frac{i}{o}[/tex]
substitute the values to get the height of image h'
[tex]\frac{h'}{0.20} =-\frac{-0.13}{0.5} \\\\\\h'=\frac{0.13*0.20}{0.5} \\\\\\h'=\frac{0.025}{0.5} =0.052m\\\\\\h'=5.2cm[/tex]
The particles of a medium will settle the rest position after a mechanical wave passes
A. at
B. behind
C. In front of
After the mechanical waves passes by, the particles of the medium will settle right back at their rest position (A).
It doesn't matter whether the wave was a longitudinal or a transverse one.
Use the formula below to solve the given problem. In the formula, d
represents the distance an object falls, in feet, and I represents the time that
an object falls, in seconds. Do not include units in your answer.
A penny is dropped from the top of a building and takes 5 seconds to fall to
the ground. What is the height of the building?
Answer here
[tex]a = \frac{v - u}{t} [/tex]
^^acceleration formula
[tex]s = \frac{1}{2} (u + v) \: t[/tex]
^^displacement formula
since the acceleration due to gravity is 9.8m/s^2 or 10m/s^2
9.8 = v-0/5
v = 49m/s
s= 1/2 (49m/s +0 m/s) 5
s= 122.5m
A natural resource that is in limited supply is known as a _________________.
Answer:
Limited Resources
Answer:I’m sure it lime red resources
Explanation:
Going up and down each isle in the grocery story to find milk is an example of what problem solving strategy?
Answer:
Blind search
Explanation:
The blind search is a problem solving strategy which can be used to solve the problems of relatively simpler nature, and can only distinguish non-goal and goal state with no idea that which state is more promising.
In this example, blind search was used to reach the goal (Going up and down each isle).
Hope it helps!
what is the kinetic energy of a 60 kg person jogging at 2 m/s
Ek = 1/2 m v^2
Ek = 1/2 × 60 × 2^2
Ek = 1/2 × 60 × 4
Ek = 120 J
the kinectic energy is 120 J
What factor reduces the accuracy of radiocarbon dating? Atmospheric carbon-14 levels change over time. Bones and objects absorb carbon dioxide. Bones and fossilized plants absorb carbon over time.
Explanation:
Carbon-14 is a radioactive isotope of carbon and has a half-life of 5730 years. Due to its presence in all organic materials, this radioisotope is used in the dating of organic specimens.
However, this test is only useful for samples of thousands of years, for samples with ages of millions of years is not useful because the half-life of carbon-14 is lower.
In addition, there is a factor that negatively influences the accuracy of the test, the fact that the concentration of carbon-14 in the terrestrial atmosphere has not remained constant over time. This is due to changes in the flow of cosmic radiation and solar activity, changes in the intensity of the earth's magnetic field and the artificial production of this radiosotope between the 1950s and 1960s with the nuclear tests carried out.
Answer:
the answer is a
Explanation:
A piston in a gas supply pump has an
area of 500 cm2 and it moves a distance
of 30 cm during one stroke. The pump
moves the gas against a fixed pressure
of 4000 Pa. The work done by the piston
during on strikes is
A. 60 joule
B. 70 joule
C. 55 joul
D. None
Answer:
A. 60 Joule
Explanation:
First find the force given the pressure and area.
F = AP
F = 500 cm² × (1 m / 100 cm)² × 4000 N/m²
F = 200 N
Now find the work:
W = Fd
W = 200 N × 30 cm × (1 m / 100 cm)
W = 60 J
Explanation:
Pressure is the ratio of normal force to the area.
[tex]\texttt{Pressure = }\frac{\texttt{Normal force}}{\texttt{Area}}[/tex]
Force = Pressure x Area
Area = 500 cm² = 0.05 m²
Pressure = 4000 Pa
Force = 0.05 x 4000 = 200 N
We know that
Work done = Force x Displacement
W = F x d
Displacement, d = 30 cm = 0.3 m
W = 200 x 0.3 = 60 Joules.
Option A is the correct answer.
The flywheel of a steam engine runs with a constant angular velocity of 150 rev/min. When steam is shut off, the friction of the bearings and of the air stops the wheel in 2.2 h. (a) What is the constant angular acceleration, in revolutions per minute-squared, of the wheel during the slowdown? (b) How many revolutions does the wheel make before stopping? (c) At the instant the flywheel is turning at 75 rev/min, what is the tangential component of the linear acceleration of a flywheel particle that is 50 cm from the axis of rotation? (d)What is the magnitude of the net linear acceleration of the particle in (c)?
Answer:
a) -1.14 rev/min²
b) 9900 rev
c) -9.92×10⁻⁴ m/s²
d) 30.8 m/s²
Explanation:
First, convert hours to minutes:
2.2 h × 60 min/h = 132 min
a) Angular acceleration is change in angular velocity over change in time.
α = (ω − ω₀) / t
α = (0 rev/min − 150 rev/min) / 132 min
α = -1.14 rev/min²
b) θ = θ₀ + ω₀ t + ½ αt²
θ = 0 rev + (150 rev/min) (132 min) + ½ (-1.14 rev/min²) (132 min)²
θ = 9900 rev
c) The tangential component of linear acceleration is:
a_t = αr
First, convert α from rev/min² to rad/s²:
-1.14 rev/min² × (2π rad/rev) × (1 min / 60 s)² = -1.98×10⁻³ rad/s²
Therefore:
a_t = (-1.98×10⁻³ rad/s²) (0.50 m)
a_t = -9.92×10⁻⁴ m/s²
d) The magnitude of the net linear acceleration can be found from the tangential component and the radial component:
a² = (a_t)² + (a_r)²
The radial component is the centripetal acceleration:
a_r = v² / r
a_r = ω² r
First, convert 75 rev/min to rad/s:
75 rev/min × (2π rad/rev) × (1 min / 60 s) = 7.85 rad/s
Find the radial component:
a_r = (7.85 rad/s)² (0.50 m)
a_r = 30.8 m/s²
Now find the net linear acceleration:
a² = (-9.92×10⁻⁴ m/s²² + (30.8 m/s²)²
a = 30.8 m/s²
The angular acceleration of the flywheel is -1.14 rev/min². It makes 9,900 revolutions before stopping. The tangential component of the linear acceleration at 75 rev/min is 3.927 m/s² and the net linear acceleration is 31.08 m/s².
Explanation:The following are the solutions to those physics problems (assuming no slip, only the deceleration is involved) :
Angular acceleration can be calculated by the formula = final angular speed - initial angular speed/time. Here, the final angular speed is 0 (since it stops) and the initial speed is 150 rev/min. The time here should be converted to minutes, which is 2.2 x 60 = 132 min. So, Angular acceleration = (0 - 150) / 132 = -1.14 rev/min².The total number of revolutions the flywheel makes before stopping can be calculated by the equation = initial speed x time + 0.5 x angular acceleration x time² = 150 x 132 + 0.5 x -1.14 x (132)² = 9,900 revolutions.The tangential component of the linear acceleration when the flywheel is turning at 75 rev/min can be calculated by angular speed (in rad/sec) x radius. Angular speed should be converted to rad/sec from rev/min. So, Angular Speed = 75 x 2π / 60 = 7.854 rad/sec. Therefore, Tangential acceleration = angular speed x radius = 7.854 x 0.5 = 3.927 m/s².The net linear acceleration is the vector sum of the tangential acceleration and radial (centripetal) acceleration. Centripetal acceleration can be calculated by (angular velocity)² x radius (for this, angular velocity should be in rad/sec). Hence, Centripetal acceleration = (7.854)² x 0.5 = 30.796 m/s². Therefore, Net linear acceleration = sqrt(tangential acceleration² + centripetal acceleration²) = sqrt((3.927)² + (30.796)²) = 31.08 m/s².Learn more about Physics here:https://brainly.com/question/32123193
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give two mathematical examples of Newton's first law and the solutions
Explanation:
those are the examples
For heavy elements, what is the ratio of neutrons to protons that predicts a stable nucleus?
A.
1:1
B.
1.5:1
C.
2:1
D.
10:5
Answer:
B. 1.5:1
Explanation:
Let's take mercury(Hg) for an example.
Mercury have proton number of 80 and neutron number of 121.
To know the ration, you need to divide the neutron number with the proton number.
121/80
=1.5/1
Then, change the answer to ratio form=1.5:1
A charge of 24 µC is at a location where the electric potential is 8.0 V.
What is the electric potential energy of the charge?
A. 3.0 × 10^-6 J
B. 1.9 × 10^-4 J
C. 3.0 × 10^0 J
D. 1.9 × 10^2 J
B. The electric potential energy of charge is [tex]1.9 \times 10^{-4} \ \mathrm{J}[/tex] if charge of [tex]24 \ \mu \mathrm{C}[/tex] is at a location where electric potential is 8.0 V.
Explanation:The capacity required charge to move from a place to another is termed as electric potential energy.
The potential energy is given by the formula:
[tex]P E=q \Delta V[/tex]
Where,
PE is electric potential energy
q is charge
[tex]\Delta V[/tex] is electric potential
Given:
[tex]q=24 \ \mu \mathrm{C}=24 \times 10^{-6} \ \mathrm{C}[/tex]
[tex]\Delta V=8.0 \ \mathrm{V}[/tex]
Now,
[tex]\Rightarrow P E=24 \times 10^{-6} \times 8.0[/tex]
[tex]\therefore P E=1.92 \times 10^{-4} \ J[/tex]
Hence, we can say that [tex]1.92 \times 10^{-4} \ J[/tex] is electric potential energy for the given conditions.