A ball of mass m is attached to a string of length r and negligible mass. The ball moves clockwise in a vertical circle, as shown above. When the ball is at point p, the string is horizontal. Point q is at the bottom of the circle and point z is at the top of the circle. Air resistance is negligible. Express all algebraic answers in terms of the given quantities and fundamental constants.
Answers
the minimum speed of the ball at point Z is given by v = √(g(r/g - 1)/(1 - r/g)).
we have T = mv²/r... (1)
where v is the speed of the ball at point P.
We can rewrite this equation as v = √(Tr/m)... (2)
At point Q, the ball has its maximum speed and minimum tension.
Thus, we can write T - mg = mv²/r... (3)
where v is the speed of the ball at point Q.
From equation (3), we can write v² = (T/m)(r + g)... (4)
Substituting the value of v² from equation (4) into equation (3), we get
T - mg = (T/m)(r + g)T - mg = Tr/m + Tg/mT/m = g/(1 - r/g)T = mg/(1 - r/g)... (5)
Substituting the value of T from equation (5) into equation (4), we getv² = g(r/g + 1)/(1 - r/g)v²
= g(2 - r/g)v = √(g(2 - r/g))... (6)
At point Z, the ball has its minimum speed and maximum tension.
Thus, we can write T + mg = mv²/r... (7)
where v is the minimum speed of the ball at point Z. From equation (7), we can write
v² = (T/m)(r - g)... (8)
Substituting the value of T from equation (5) into equation (8), we get
v² = g(r/g - 1)/(1 - r/g)v
= √(g(r/g - 1)/(1 - r/g))... (9)
Hence, the tension at point P is given by
T = mv²/r or T = mg/(1 - r/g),
the speed of the ball at point Q is given by
v = √(g(2 - r/g)), and the minimum speed of the ball at point Z is given by
v = √(g(r/g - 1)/(1 - r/g)).
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Related Questions
10. A ball is attached to a string of length 4 m to make a pendulum. The pendulum is placed at a location that is away from the Earth’s surface by twice the radius of the Earth. What is the acceleration due to gravity at that height and what is the period of the oscillations?
Please show all of your work.
Answers
Let's see
Radius of earth=6371mTwice of it=6371(2)=12742m\(\\ \rm\rightarrowtail T=2\pi\sqrt{\dfrac{l}{g}}\)
\(\\ \rm\rightarrowtail T=2\pi \sqrt{\dfrac{4}{g}}\)
\(\\ \rm\rightarrowtail T=2\pi\dfrac{2}{\sqrt{g}}\)
\(\\ \rm\rightarrowtail T=\dfrac{4\pi}{\sqrt{g}}\)
So
\(\\ \rm\rightarrowtail g=\dfrac{16\pi ^2}{T^2}\)
Answer:
g' = 1.09 m/s²
T = 12 s
Explanation:
Gravity due to acceleration
Distance from center of Earth = r + 2r = 3rgravity due to acceleration on surface, g = GM/r²Substitute 3r in the denominatorg' = GM/(3r)² = GM/9r²⇒ g' = g/9 = 9.8/9 = 1.09 m/s²
Time period
T = 2π√L/g'T = 2π√4/1.09T ≅ 12 sLiquid ammonia flows through a pipe at a mass flow rate of 100
kg/s .
If the cross-sectional area of the pipe is 0.01
m^2, determine the flow rate of momentum through the
pipe.
Answers
The momentum flow rate through the pipe carrying liquid ammonia is 1 × \(10^6\) kg·m/s.
The flow rate of momentum (Ṁ) through the pipe can be calculated by multiplying the mass flow rate (ṁ) by the velocity (v). The speed can be determined using the equation v = ṁ / (ρA), where ρ is the density of the liquid ammonia and A is the pipe's cross-sectional area.
Given:
ṁ = 100 kg/s
A = 0.01 m²
Assuming the density (ρ) of liquid ammonia is 700 kg/m³, we can calculate the velocity (v):
v = ṁ / (ρA)
v = 100 kg/s / (700 kg/m³ × 0.01 m²)
v = 10000 m/s
Now, we can calculate the flow rate of momentum (Ṁ):
Ṁ = ṁv
Ṁ = 100 kg/s × 10000 m/s
Ṁ = 1 × \(10^6\) kg·m/s
Therefore, the momentum flow rate through the pipe is 1 × \(10^6\) kg·m/s.
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A common activity like cooking a meal can use many natural _________.
Answers
A common activity like cooking a meal can use many natural Ingredients
Ingredients
Ingredients are substances combined to make a particular mixture such as a meal. most of the ingredients used for the preparation of a meal are sourced naturally.
In cooking different recipes of a meal the use of specific ingredients for each recipe differentiates the recipes.
Therefore we can conclude that cooking a meal requires the use of natural ingredients.
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much like a battery these generate electricity from chemical events
Answers
The term you are looking for is "chemical battery". Chemical batteries work by converting chemical energy into electrical energy through a series of chemical reactions. These reactions take place within the battery's cells, which are composed of two electrodes and an electrolyte.
When the battery is connected to a circuit, the chemical reactions produce an electrical current that can be used to power devices. Chemical batteries are widely used in many applications, including consumer electronics, electric vehicles, and renewable energy systems. They are a crucial component of our modern technological society, and ongoing research is focused on developing more efficient and sustainable battery technologies to meet growing energy demands.
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23) When an earthquake occurs,________ is the amour of energy released
A.) intensity
B.) magnitude
C.) seismogram
D.) force
Answers
Answer:
b. magnitude is the correct option
Answer:
B.) magnitude
Explanation:
The magnitude of an earthquake is a measure of the amount of energy released by the earthquake. The magnitude is typically expressed on the Richter scale, which is a logarithmic scale that quantifies the size of an earthquake based on the amplitude of the seismic waves it generates. The magnitude of an earthquake is a measure of the earthquake's size and power, and is not the same as its intensity, which is a measure of the earthquake's effects on a specific location. A seismogram is a record of the ground motion during an earthquake, as recorded by a seismograph. Force is not directly related to an earthquake.
The body is lowered to slide from the top of a smooth steep plane inclined at 45°. How long will it take the body to go down the plane of length 2.82m?
Answers
Answer:
12tfr
Explanation:
as per as calculations
an airplane has a mass of 1.10 104 kg, and each wing has an area of 39.0 m2. during level flight, the pressure on the lower wing surface is 6.00 104 pa. (a) suppose the lift on the airplane were due to a pressure difference alone. determine the pressure on the upper wing surface.
Answers
The pressure on the upper wing surface is 4.10 x 10^3 Pa.
The lift force on an airplane wing is due to the pressure difference between the upper and lower surfaces of the wing. According to Bernoulli's principle, the pressure of a fluid decreases as its speed increases. Therefore, the air moving over the curved upper surface of the wing must have a lower pressure than the air moving over the flat lower surface of the wing.
The lift force can be calculated using the formula:
L = Cl * ρ * A * v^2 / 2
where L is the lift force, Cl is the lift coefficient, ρ is the density of the air, A is the area of the wing, and v is the speed of the air.
Since the airplane is in level flight, the lift force is equal to the weight of the airplane:
L = mg
where m is the mass of the airplane and g is the acceleration due to gravity.
We can use these two equations to find the speed of the air over the wing:
mg = Cl * ρ * A * v^2 / 2
v^2 = 2mg / (Cl * ρ * A)
v = sqrt(2mg / (Cl * ρ * A))
Let's assume that the lift coefficient is the same for both the upper and lower surfaces of the wing. Then, the lift force on each wing is:
L/2 = Cl * ρ * A * v^2 / 4
The pressure difference between the upper and lower surfaces of the wing can be found using the formula:
ΔP = 2 * (L/2) / A
Substituting the expressions for L/2 and v^2, we get:
ΔP = Cl * ρ * v^2
ΔP = Cl * ρ * (2mg / (Cl * ρ * A))
ΔP = 2mg / A
Substituting the given values, we get:
ΔP = 2 * (1.10 x 10^4 kg) * 9.81 m/s^2 / (39.0 m^2)
ΔP = 5.59 x 10^4 Pa
Since the pressure on the lower wing surface is given as 6.00 x 10^4 Pa, the pressure on the upper wing surface is:
Pupper = Plower - ΔP
Pupper = (6.00 x 10^4 Pa) - (5.59 x 10^4 Pa)
Pupper = 4.10 x 10^3 Pa
Therefore, the pressure on the upper wing surface is 4.10 x 10^3 Pa.
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which is a harmful role of bacteria of bacteria?
Answers
Answer:
Harmful bacteria are called pathogenic
Explanation:
Harmful bacteria are called pathogenic bacteria because they cause disease and illnesses like strep throat, staph infections, cholera, tuberculosis, and food poisoning.
Please help, asap!
Will mark as brainliest!
Answers
Answer:
a1)gravity
not sure on others
Explanation:
cause the gravity force pulls u down
Answer:
a) i) Gravitational force
ii) Air resistance
b) (I cannot understand what is the question saying but the unit of acceleration is m/\(s^{2}\) or \(ms^{-2}\))
ii) Because when the parachutist is falling, the gravitational force is pulling him down. But the air resistance is pushing him upwards acting against the gravitational force resulting in a decreasing acceleration.
iii) This is because soon the air resistance catches up with that of the gravitational force and it cancels the gravitational force so he is falling in a constant velocity. This is called terminal velocity when the gravitational force gets cancelled resulting in a free fall where his weight brings him down.
3 points
1. Using the digram below, determine which two atoms have the same
atomic number. *
8P
8N
9P
8N
8P
9N
10P
9N
2 and 3
o
2 and 4
1 and 3
ОО
3 and 4
3 points
2. The diagram below is a modern drawing of an atom. Why are no
electrone orbits drawn? *
Answers
Answer:
1 and 2 because atomic number is equal to the numbers of protons in the nucleus
Answer:
yes answer in 1 and 2 these is answer
Select the correct answer. Which electric component provides energy to the circuit of a flashlight? A. Battery B. Motor C. Resistor D. Switch.
Answers
Answer:
A battery
Explanation:
A battery puts energy through wire to power flashlight
Answer:
Your answer would be (A) Battery
Explanation:
A battery is found in most flashlights, and the flashlight is too small for a plugin.
A motor would be unreasonable, and you would have to put in the battery anyway. The resistor just slows down the speed of electron currents, and all the switch does is start and stop the flow of electron currents.
Conclusion:
I hope this helped! Please give Brainliest if I gave the best answer :)
Tell me if I had the wrong answer, and I'll fix it.
A periodic wave has a wavelength of 1.6 m and a speed of 16 m/s. What is the wave frequency?
Answers
ANSWER
10 Hz
EXPLANATION
Given:
• The wavelength of a periodic wave, λ = 1.6 m
,• Its speed, v = 16 m/s
Find:
• The wave frequency, f
The frequency of a wave is given by the quotient between the wave's speed and its wavelength,
\(f=\frac{v}{\lambda}\)Replace the known values and solve,
\(f=\frac{16m\/s}{1.6m}=10\text{ }\frac{1}{s}=10\text{ }Hz\)Hence, the frequency of the wave is 10 Hz.
a body is placed at a height of 500m calculate the velocity with which it will move when released
Answers
The velocity with which will move the body when released from height of 500m is 100m/s
How to calculate velocity?The vertical acceleration is known to be a constant g.
d^2y/dt^2=−g
After integrating, we'll refer to our constant as v0.
dy/dt=v0−gt
That's our time-dependent vertical velocity. In our situation, the starting velocity v0=0, implying that we began at rest at time t=0.
dy/dt=−gt
Let us integrate once more, with the integration constant. y0.\s
y=y0−1/2gt^2
We have
y0=500 and want t when y=0.
2=1000
t=√1000g
We frequently employ the assumption g=10m/s2, which yields t=10
At t=10t=10, how fast is it moving?
dy/dt=−gt=−(10)(10)=−100
DOWN, 100 meters per second.
Gravity's acceleration is always constant and downward, although the amplitude and direction of velocity change. The ball has zero velocity at its greatest point in its trajectory, and the magnitude of velocity increases as the ball descends back toward the earth.
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A target lies flat on the ground 7 m from the
side of a building that is 10 m tall, as shown
below.
The acceleration of gravity is 10 m/s
Air resistance is negligible.
A student rolls a 7 kg ball off the horizontal
roof of the building in the direction of the
target.
Answers
Can you give me any more information?
What’s the maximum height of the second hill? Use your answer from part E and the formula PE=m•g•h to determine the answer. Assume that g = 9.8m/sec2.
Answers
Answer:
111.4 m
Explanation:
PE = m x g x h
349,300 = 320 x 9.8 x h
h = 349300 : 3136
h = 111,384 m
An arrow is shot horizontally with a speed of 20 m/s from the top of a tower 60 m high. The time to reach the ground will be -----------------.
Answers
Answer:
3
Explanation:
You will do 60÷20=30
This is the answer and please follow me
Suppose a creature from another planet has eyes that are sensitive to infrared radiation. Describe what the alien would see if it looked around your library. In particular, what would appear bright and what would appear dim
Answers
The incandescent lamp will glow quite brightly in the eyes of the creature because emits less visible light and more infrared light.
What is infrared light?The infrared light is a part of the electromagnetic spectrum that is emitted by a hot object.
As such, the incandescent lamp will glow quite brightly in the eyes of the creature because emits less visible light and more infrared light. The florescent light which does not produce inferred rays will not be visible at all.
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The vitreous humor, a transparent, gelatinous fluid that fills most of the eyeball, has an index of refraction of 1.34. Visible light ranges in wavelength from 400 nm (violet) to 700 nm (red), as measured in air. This light travels through the vitreous humor and strikes the rods and cones at the surface of the retina.
What are the ranges of the wavelength of the light just as it approaches the retina within the vitreous humor?
Answers
The ranges of the wavelength of the light just as it approaches the retina within the vitreous humor is 298.5 nm to 522.3 nm.
The refractive index of the fluid in the eyeball, n = 1.34
Initial wavelength in the wavelength range, λ₁ = 400 nm
Final wavelength in the wavelength range, λ₂ = 700 nm
When light enters a substance with a higher refractive index, the angle of refraction will be lower than the angle of incidence, and the light will be refracted in the direction of the surface normal.
The refractive index determines how near to the typical direction of travel light will be.
Refractive index can be defined as the ratio of the wavelength of light in the air and the wavelength of light in the medium.
So, the expression for the new wavelength in the medium is given by,
λ' = λ/n
So, for the initial wavelength,
λ' = λ₁/n
λ' = 400/1.34
λ' = 298.5 nm
Similarly, for the final wavelength,
λ' = λ₂/n
λ' = 700/1.34
λ' = 522.3 nm
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Calculate the mass (in kg) of 54.3 m³ of granite. The density of granite is 2700 kg/m³. (Remember: density = mass / volume)
Answers
To determine the mass of granite, we must first understand the definition of density. Density is defined as the amount of matter present in a substance per unit volume.
We use the formula: density = mass/volume to calculate the mass of a substance given its density and volume. To calculate the mass of 54.3 m³ of granite, we use the following steps:
Given Density of granite = 2700 kg/m³Given volume of granite = 54.3 m³Let us substitute the values in the formula of density:density = mass/volume Solving for mass, we get:mass = density × volume Substitute the given values of density and volume into the formula:mass = 2700 kg/m³ × 54.3 m³
The m³ unit in the volume cancels out, leaving us with kg as the unit for mass.
We then solve the equation to get the mass:mass = 146,610 kg
Therefore, the mass of 54.3 m³ of granite is 146,610 kg.
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If you increase the pressure on a sprinkler nozzle from 46 psi to 66 psi, what will the new flow rate be
Answers
if you increase the pressure on a sprinkler nozzle from 46 psi to 66 psi, the new flow rate will be approximately 32.496 gallons per minute, assuming a flow rate coefficient (K) of 4.0.
Q = K * √(P)
where sqrt(P) is the square root of the pressure in psi.
Using this formula, we can calculate the new flow rate as follows:
New flow rate = 4.0 * √(66) = 4.0 * 8.124 = 32.496 gallons per minute (approx.)
Pressure is a physical quantity that describes the force exerted per unit area. It can be defined as the amount of force applied to a given area or surface. Pressure is typically measured in units of Pascals (Pa), which is equivalent to one Newton per square meter (N/m²).
Pressure can be exerted by any type of matter, including gases, liquids, and solids. For example, the pressure of the air around us is the result of the weight of the atmosphere pushing down on the surface of the Earth. In general, pressure increases with increasing depth in a fluid or with increasing force applied to a surface. It also varies with temperature and can be affected by the properties of the material being measured.
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The weight of passengers on a roller coaster increases by 50%as the car goes through a dip with a 30 m radius of curvature.What is the car’s speed at the bottom of the dip?
Answers
Answer:
12.12 m/s
Explanation:
The net force of the car at the bottom of the dip is equal to
\(\begin{gathered} F__{net}=F_{seat}-mg=ma_c \\ F_n-mg=m\frac{v^2}{r} \end{gathered}\)Where Fn is the normal force that acts upwards, m is the mass of the car, g is the gravity, v is the car's speed at the bottom of the dip and r is the radius.
We know that the weight of the passenger increase by 50%, so
Fn = 1.5mg
Replacing this on the first equation and solving for the car speed v, we get
\(\begin{gathered} 1.5mg-mg=\frac{mv^2}{r} \\ 0.5mg=\frac{mv^2}{r} \\ 0.5g=\frac{v^2}{r} \\ 0.5gr=v^2 \\ v=\sqrt{0.5gr} \end{gathered}\)Finally, replacing g = 9.8 m/s² and r = 30 m, we get:
\(v=\sqrt{0.5(9.8)(30)}=12.12\text{ m/s}\)So, the car’s speed at the bottom of the dip is 12.12 m/s
Can anyone please help
Answers
a) The motion of the object between 15 s to 30 s is increasing velocity, to a constant velocity and finally a decreasing velocity.
(b) The average velocity of the object between 0 and 15 seconds is 0.167 m/s.
(c) The position of the object at 5.0 seconds is 0.5 m.
(d) Between 30 and 40 seconds, the velocity of the object is decreasing and the object is decelerating.
What is the motion of the object?(a) The motion of the object between 15 s to 30 s can be described as increasing velocity, to a constant velocity and finally a decreasing velocity.
(b) The average velocity of the object between 0 and 15 seconds is calculated as;
average velocity = total displacement / total time
average velocity = (2.5 m - 0 m ) / ( 15 s - 0 s ) = 0.167 m/s
(c) The position of the object at 5.0 seconds is calculated as follows;
at 5.0 seconds, the position of the object is traced from the graph as 0.5 m.
(d) The motion of the object between 30 and 40 seconds is calculated as;
velocity = ( 0 m - 4 m ) / ( 40 s - 30 s ) = - 0.4 m/s
Between 30 and 40 seconds, the velocity of the object is decreasing and the object is decelerating.
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The angle of reflection is equal to angle of incidence
Answers
Answer:
yes it is true
Explanation:
I’m NC the wind is blowing from the north. If the wind changes direction and begins to blow from the south, what will most likely result.
Answers
NC means North Carolina.
Answer:
The temperatures will increase.
Explanation:
What will happen is that the temperature will increase. This is because, in wind direction and weather forecasting, a wind that shifts from the south means that warmer air/temperatures are approaching whereas a wind shift from the north implies that cooler air/temperatures are approaching.
sanjay, a stockbroker, runs two miles every day after work because it reduces his level of stress. sanjay's running habit is maintained by a____reinforcer.
negative
Answers
Sanjay's running habit is maintained by a Negative reinforcer.
What are the effects of stress?When a situation demands more of a person than they can mobilize, that situation is said to be stressful. Different types of stress can cause negative behaviour in people.An individual needs stress to survive, yet too much stress can harm our bodies. An individual in a distressed state is more susceptible to a number of health issues, including headaches, chest pain, difficulty sleeping, mental disturbances, and high blood pressure. Emotional stress has been linked to immune system deterioration and heart muscle exhaustion. Epinephrine is released in cases of stress-related conditions. Our hearts are harmed by excessive stress.To learn more about effects of stress refer to:
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Please help!!A camera lens 13.3 cm from a
flower makes an image at a
distance of 2.25 cm from the lens,
on the film. What is the focal
length of the lens?
(Unit = cm)
Answers
Answer:
f=1.92 cm
If ans is correct reply for explanation.
The typical focal length formula looks as follows: 1/Focal length = 1/Image distance + 1/Object distance , where: Image distance and Object distance are given in mm.
1/f = 1/u + 1/v
1/f = 1/133 + 1/22.5
= 0.007 + 0.044
= 0.0514 mm
What is focal length ?"The focal length of an optical system is a measure of how strongly the system converges or diverges light; it is the inverse of the system's optical power. A positive focal length indicates that a system converges light, while a negative focal length indicates that the system diverges light."
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Is it possible for an object at rest to have forces acting upon it? Explain.
Answers
When an object is at rest, it is often misinterpreted that it cannot be moved from its initial state; however, that is untrue. When an object is at rest, any unbalanced force can cause it to exit its stationary state. An example of this would be if a ball was not moving. Somebody could blow it and it would move. In this process, the ball goes from balanced to unbalanced force, meaning its state of rest was interrupted.
However, there is another perspective of this. When an object is at rest (meaning nothing is bothering it), there is no force acting upon it. It is in a balanced position, and nothing is altering its state.
Newer aircraft jet catapult systems use magnets instead of steam. The launch still takes 1.19 seconds, but the acceleration is a about 47.41 m/s2. Determine the length of the runway on the carrier, assume the aircraft starts from REST
Answers
Answer:
33.6 m
Explanation:
Given:
v₀ = 0 m/s
a = 47.41 m/s²
t = 1.19 s
Find: Δx
Δx = v₀ t + ½ at²
Δx = (0 m/s) (1.19 s) + ½ (47.41 m/s²) (1.19 s)²
Δx = 33.6 m
wassup people of this wor;d
Answers
A cube of iron, 0.0800 m on a side,
has a density of 7874 kg/m^3.
what is its mass?
Answers
If a cube of iron, 0.0800 m on a side, has a density of 7874 kg/m³, the mass of the iron cube is 4.03 kg.
To find the mass of the iron cube, we need to use the formula:
density = mass / volume
Rearranging the formula to solve for mass, we get:
mass = density x volume
The volume of the cube can be calculated as:
volume = side³
Substituting the given values, we get:
volume = (0.0800 m)³ = 5.12 x 10^-4 m³
Now we can calculate the mass of the cube:
mass = density x volume
mass = 7874 kg/m³ x 5.12 x 10^-4 m³
mass = 4.03 kg
Therefore, the mass of the iron cube is 4.03 kg.
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