A horizontal disc of radius 45 cm rotates about a vertical axis through its centre. The disc makes one full
revolution in 1.40 s. A particle of mass 0.054 kg is placed at a distance of 22 cm from the centre of the disc.
The particle does not move relative to the disc.
a On a copy of the diagram draw arrows to represent the velocity and acceleration of the particle. [2]
b Calculate the angular speed and the linear speed of the particle. [2]
c The coe cient of static friction between the disc and the particle is 0.82. Determine the largest distance
from the centre of the disc where the particle can be placed and still not move relative to the disc. [3]
d The particle is to remain at its original distance of 22cm from the centre of the disc.
i Determine the maximum angular speed of the disc so that the particle does not move relative to
the disc. [2]
ii The disc now begins to rotate at an angular speed that is greater than the answer in d i. Describe
qualitatively what happens to the particle. [2]
Answers
Answer:
a. Please find attached the diagram of the disc, having arrows that represent the velocity and the acceleration of the particle placed on it
b. The angular speed is approximately 4.488 rad/s
The linear speed is approximately 0.987 m/s
c. The largest distance from the center of the disc where the particle can be placed and still not move is approximately 0.399 m from the center of the disc
d. i The maximum angular speed of the disk so that the particle does not move relative to the disk is approximately 6.044 rad/sec
ii When the angular speed with which the disc rotates is more than the the answer of question d i above, the particle slips on the disc, and the disc begins to rotate faster than the particle, while the particle is swung in an outward radial direction off the disc due to the centrifugal forces
Explanation:
The given parameters are;
The radius of the horizontal disc, r = 45 cm = 0.45 m
The time the disc makes one full revolution, T = 1.40 s
The mass of the particle placed on the disc = 0.054 kg
The location on the disc the particle is placed = 22 cm from the disc's center
a. Please find attached the diagram of the disc created with Microsoft Visio, with arrows representing the velocity and the acceleration of the particle placed on the disk
b. The angular speed, ω = 2·π/T = 2 × π/1.4 ≈ 4.488 rad/s
The linear speed, v = ω × r = 4.488 rad/s × 0.22 m ≈ 0.987 m/s
The linear speed, v ≈ 0.987 m/s
c. The given coefficient of static friction = 0.82
Therefore;
The frictional force that prevents motion = Weight of the particle × The coefficient of static friction
The frictional force that prevents motion is [tex]F_f[/tex] = 0.054 × 9.8 × 0.82 ≈ 0.434 N
[tex]F_f[/tex] ≈ 0.434 N
Therefore, for the largest distance from the center of the disc where the particle can be placed and still not move, r, is given by the formula for the centripetal force, [tex]F_c[/tex], acting on the particle as follows;
For static equilibrium, no movement of the particle relative to the disc, we have;
[tex]F_f[/tex] = [tex]F_c[/tex]
Where;
[tex]F_c = \dfrac{m \times v^2}{r} = m \times \omega ^2 \times r[/tex]
Which gives;
[tex]F_c = {0.054 \ kg \times (4.488 \ rad/s)^2} \times r = F_f = 0.434 \ N[/tex]
r = 0.434 N/(0.054 kg × (4.488 rad/s)²) ≈ 0.399 m
The largest distance from the center of the disc where the particle can be placed and still not move, r = 0.399 m from the center of the disc
d. i From the static equilibrium equation where r = 0.22 m, we have;
[tex]F_c = {0.054 \ kg \times \omega ^2} \times 0.22 \ m = F_f = 0.434 \ N[/tex]
ω = √(0.434 N/(0.054 kg × (0.22 m))) ≈ 6.044 rad/sec
The maximum angular speed of the disk so that the particle does not move relative to the disk, ω ≈ 6.044 rad/sec
ii When the angular speed with which the disc rotates is more than the the answer of question d i above, we have
The particle begins to slip on the disc such that the disc rotates faster than the particle and the particle tends to rotate slower than the speed pf the disc and is swung off the disc by centripetal force acting on the particle due to the rotational motion of the disc.
Related Questions
What current in a solenoid 15-cm long wound with 100 turns would produce a magnetic field equal to that of the Earth, 5 cross times 10 to the power of negative 5 end exponentT ?
Answers
Answer:
The value is [tex]I= 0.0597\ A[/tex]
Explanation:
From the question we are told that
The length of the solenoid is [tex]l = 15 \ cm = 0.15 \ m[/tex]
The number of turns is [tex]N = 100[/tex]
The magnetic field of the earth is [tex]B = 5* 10^{-5} \ T[/tex]
Gnerally magnetic field is mathematically represented as
[tex]B = \frac{\mu_o * N * I }{ l }[/tex]
=> [tex]I= \frac{Bl}{ \mu_o *N }[/tex]
=> [tex]I= \frac{ 5 *10^{-5} * 0.15}{4\pi *10^{-7} *100 }[/tex]
=> [tex]I= 0.0597\ A[/tex]
A ray of light incident in water strikes the surface separating water from air making an angle of 10 ° with the normal to the surface. (refractive index of water = 1.3) a) What is the angle of refraction? b) What should be the angle of incidence if we want an angle of refraction not greater than 45 ° ? c) What is the critical angle?
Answers
Answer:
a
[tex]\theta _2 = 13^o[/tex]
b
[tex]\theta _1 =32.94^o[/tex]
c
[tex]\theta_c = 53.05^o[/tex]
Explanation:
From the question we are told that
The angle of incidence is [tex]\theta_1 = 10^o[/tex]
The refractive index of water is [tex]n_1 = 1.3[/tex]
Generally Snell's law is mathematically represented as
[tex]n_1 sin(\theta_1) = n_2 sin(\theta_ 2)[/tex]
Here [tex]n_2[/tex] is the refractive index of air with value [tex]n_2 = 1[/tex]
[tex]\theta_2[/tex] is the angle of refraction
So
[tex]\theta _2 = sin^{-1}[\frac{n_1 * sin(\theta _1)}{n_2} ][/tex]
=> [tex]\theta _2 = sin^{-1}[\frac{1.3 * sin(10)}{1} ][/tex]
=> [tex]\theta _2 = 13^o[/tex]
Given that the angle should not be greater than [tex]\theta _2 =45^o[/tex] then the angle of incidence will be
[tex]\theta _1 = sin^{-1}[\frac{n_2 * sin(\theta _2)}{n_1} ][/tex]
=> [tex]\theta _1 = sin^{-1}[\frac{1 * sin(45)}{1.3} ][/tex]
=> [tex]\theta _1 =32.94^o[/tex]
Generally for critical angle is mathematically represented as
[tex]\theta_c = sin^{-1}[\frac{n_2}{n_1} ][/tex]
=> [tex]\theta_c = sin^{-1}[\frac{1}{1.3} ][/tex]
=> [tex]\theta_c = 53.05^o[/tex]
What is 3,278,000 as scientific notation?
Answers
The diagrams show the four primary steps in the production of work in a four-stroke heat engine.
An illustration of a internal combustion engine cylinder at four different stages. The first illustration is labeled W with red ejected out of the left valve, the second is labeled X with purple in the cylinder trapped by the piston and valves, the third is labeled Y with the piston going down and the fluid red, the last is labeled Z with purple coming into the cylinder from the right valve.
What is the correct order in which these steps occur?
Answers
Answer:
D) Z,X,Y,W
Explanation:
TOOK THE QUIZ MATE, TOOK THE MF QUIZ
Answer:
D
Explanation:
edge 21
What is the displacement of the particle in the time interval 7 seconds to 8 seconds? A. 0 meters B. 1.5 meters C. 3 meters D. 7 meters
Answers
Answer:
It's 1.5 meters
Explanation:
plato
PLS HELP ASAP
I NEED HELP
HAPPY HOLIDAYS
Answers
Answer:
Displacement is calculated using the following formula: [tex]d = v \times t[/tex]Where v in meters per second is the velocity and t in seconds representing time Hence d = 14,542.32Jonas and his family are moving to another part of the city. As Jonas, his brother, and his Dad were driving one of the trucks filled with furniture to their new home, Jonas noticed that the truck seemed to take longer to stop now that it was heavier with the furniture. Which Newton's Law explains why this happens?
Answers
Answer:newtons second law
Explanation:
To get something to accelerate you have to apply a pull force . if the mass increase a grater pull is required
The law that explains the fact that a heavier truck takes a longer time to stop is Newton's law of inertia.
According to Newtons first law of motion also called the law of inertia, a body will continue in a state of rest or uniform motion unless it is acted upon by an external, unbalanced force.
This law explains the reluctance of heavier objects to move or stop. The law that explains the fact that a heavier truck takes a longer time to stop is Newton's law of inertia.
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Falling Faster
Imagine that you are standing on the observation deck of the Empire
State Building. You drop a hammer and a feather at the same time
over the edge of the building.
1. Will the hammer or the feather reach the ground first? Explain.
per anstre here
2. Why do the hammer and the feather fall to the ground?
Answers
Gravity
Which one produces the brightest light out put on a miniature bulb,the solar panels connected in series or parallel???
Answers
If you have a liquid with a mass of 6g and a density of 25g/ml, what volume of liquid do you have?
Answers
Hello!!
For calculate the volume of the liquid, lets applicate the formula:
[tex]\boxed{V=m/ p }[/tex]
[tex]\textbf{Being:}[/tex]
[tex]\sqrt{}[/tex] V = Volume = ?
[tex]\sqrt{}[/tex] m = Mass = 6 g
[tex]\sqrt{}[/tex] p = Density = 25 g/ml
[tex]\text{Let's \textbf{replace} and resolve: }[/tex]
[tex]V = 6 \ g / 25 \ g / m l[/tex]
[tex]V = 0,24 \ m l[/tex]
[tex]\textbf{Result:}[/tex]
The volume of the liquid is 0,24 ml.
A golf player hits a 0.045 kg golf ball that is initially at rest, changing its momentum by 4.2 kg times m/., What is the final speed of the golf ball?
Answers
Answer:
v₂ = 93.33 [m/s]
Explanation:
In order to solve this problem, we must apply the definition of momentum and amount of movement, which can be calculated by means of the following expression.
[tex]P=m*v[/tex]
where:
P = momentum [kg*m/s]
m = mass [kg]
v = velocity [m/s]
The amount of movement before and after the impact should be analyzed.
[tex](m_{1}*v_{1})+Imp_{1-2}=(m_{1}*v_{2})[/tex]
where:
m₁ = mass of the ball = 0.045 [kg]
v₁ = velocity of the ball before the hit = 0
Imp₁₋₂ = Impulse [kg*m/s]
v₂ = velocity after the hit [m/s]
[tex](0.045*0)+4.2=(0.045*v_{2})\\4.2 = 0.045*v_{2}\\v_{2}= 93.33 [m/s][/tex]
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Why is the value of a substance’s specific gravity always the same numerically as its density?
Because it is always the substance’s density divided by the density of water which is 1 g/cm 3
Because it is always the substance’s density multiplied by the density of water which is 1 g/cm 3
Because specific gravity is the inverse of density
Because these represent the same measurement
Answers
Answer:
Because it is always the substance’s density divided by the density of water which is 1 g/cm 3
Explanation:
The density of water is 1g/cm³;
Specific gravity = [tex]\frac{density of substance}{density of water}[/tex]
Since specific gravity is a relative comparison of a substance density with that of water, the values always the same.
Density of water is 1 and it will have no effect on the density of the substance.
The only difference is in the units. The density of a substance will have a unit but that of the specific gravity will have no unit.
Numerically, dividing by 1 has no implication.
Answer: the answer is C
Explanation:Specific gravity is the density of a substance divided by the density of water. Since (at standard temperature and pressure) water has a density of 1 gram/cm3, and since all of the units cancel, specific gravity is usually very close to the same value as density
the work of warren washington would be most likely to explain which of the following phenomena
Answers
Answer:
t
Explanation:
A gradual shift of the North Magnetic Pole's position on Earth a steady rise in the planet's average temperature, a reduction in the Moon's light reflection.
What is the work of warren Washington?Dr. Washington and his team were able to recreate the impacts of physics on several components of weather, such as “how heat energy, water vapor, and chemicals travel between Earth's seas and the atmosphere,”
Through the use of climate models. 3 After that, computers projected atmospheric changes using the information from the climate models.
The 2007 Intergovernmental Panel on Climate Change (IPCC) report, which found that human behavior has a direct impact on the environment, used these models to support its findings.
As a result, Dr. Washington and his team were awarded the 2007 Nobel Peace Prize3.
Therefore, a slow change in the location of Earth’s North Magnetic Pole A gradual increase in Earth’s average temperature A decrease in the light reflection of the Moon
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Which ball has larger Inertia before touching the ground when it falls freely from a
certain height (air friction is zero)
a. mass 50 kg b. mass 25 kg
c. mass 10 kg d. All of these
Answers
Answer:
[tex]Mass = 50kg[/tex]
Explanation:
Required
Which has the larger inertia
Inertia (I) is calculated as follows:
[tex]I = mr^2[/tex]
Where m represents the mass of the object and r represents the distance from the axis.
Take for instance m = 10 and r = 4
The inertia would be:
[tex]I = 10 * 4^2[/tex]
[tex]I = 160[/tex]
Assume r is constant and m is increased to 25
The inertia becomes:
[tex]I = 25 * 4^2[/tex]
[tex]I = 25 * 16[/tex]
[tex]I = 400[/tex]
Notice that there is an increment in inertia, when the mass increased.
Hence, mass of 50kg will have the larger inertia.
Which celestial body would have the strongest gravitational pull on a satellite orbiting 100 km above its surface? Explain your answer.
Answers
Answer:
Jupiter
Explanation:
Since the mass of Jupiter is the greatest from the given choices, it will exert the most force on any object orbiting 100km above its surface.
This is compliance with the Newton's law of universal gravitation which states that "the force of attraction between two bodies is directly proportional to the magnitude of their masses and inversely proportional to the distances between them".
Therefore, the more the masses of two bodies, the higher the gravitational attractionSince the distance is the same, the planet with the greater mass will exert the most force on the satellite.Answer:
Sample Response: Jupiter would have the strongest gravitational pull on a satellite orbiting above its surface because gravity is directly proportional to mass and Jupiter is the most massive planet.
Explanation:
edge 2021
why can't birds fly in space
Answers
Answer:
wouldn't they be dead and there's no oxygen in space....right???
Answer:
no gravity and no oxygen
Explanation:
the bird would die of lack of oxygen before they're even able to fly, but they can't fly anyway because there's no gravity so they'd just float
A stunt-rider on a motorcycle rides down a ramp and into a vertical loop-the-loop. If the diameter of the loop is 7.50 m, then the slowest speed the motorcycle can have at the top of the loop if it is to remain in contact with the loop is _________ km/h.
Answers
Answer:
v = 6.06 m/s
Explanation:
In order for the rider to pass the top of the loop without falling, his weight must be equal to the centripetal force:
[tex]Centripetal Force = Weight \\\frac{mv^2}{r} = mg\\\\\frac{v^2}{r} = g\\\\v = \sqrt{gr}[/tex]
where,
v = minimum speed of motorcycle at top of the loop = ?
g = acceleration due to gravity = 9.8 m/s²
r = radius of the loop = diameter/2 = 7.5 m/2 = 3.75 m
Therefore, using these values in equation, we get:
[tex]v = \sqrt{(9.8\ m/s^2)(3.75\ m)}[/tex]
v = 6.06 m/s
How far does a car travel in 30.0 s while its velocity is changing from 50.0 km/h to 80.0 km/h at a uniform rate of acceleration?
Answers
Answer:
The car will travel 541.67 m
Explanation:
Constant Acceleration Motion
It's a type of motion in which the velocity of an object changes by an equal amount in every equal period of time.
The relation between the initial and final speeds is:
[tex]v_f=v_o+a.t[/tex]
Where:
vf = Final speed
vo = Initial speed
a = Acceleration
t = Elapsed time
The acceleration can be calculated by solving for a:
[tex]\displaystyle a=\frac{v_f-v_o}{t}[/tex]
And the distance traveled is:
[tex]\displaystyle x=v_o.t+\frac{a.t^2}{2}[/tex]
The car travels during t=30 s, and its speed changes from vo=50 Km/h to vf=80 Km/h.
Let's convert the speeds to m/s. Recall 1 Km=1000 m and 1 h= 3600 s:
vo=50 Km/h * 1000/3600 = 13.89 m/s
vf=80 Km/h * 1000/3600 = 22.22 m/s
Calculating the acceleration:
[tex]\displaystyle a=\frac{22.22-13.89}{30}[/tex]
[tex]a = 0.28\ m/s^2[/tex]
Now for the distance:
[tex]\displaystyle x=13.89*30+\frac{0.28.30^2}{2}[/tex]
[tex]x=416.67\ m+125\ m[/tex]
[tex]\boxed{x = 541.67\ m}[/tex]
The car will travel 541.67 m
According to the question,
Final speed, [tex]v_f = 80 \ km/h \ ,or \ 22.22 \ m/s[/tex]Initial speed, [tex]v_o = 50 \ km/h, or \ 13.89 \ m/s[/tex]Elapsed time, [tex]t = 30 \ s[/tex]We know the relation,
→ [tex]v_f = v_o +at[/tex]
or,
→ [tex]a = \frac{v_f-v_o}{t}[/tex]
Now,
The acceleration,
→ [tex]x = v_o.t+ \frac{a.t^2}{2}[/tex]
By substituting the values,
[tex]= \frac{22.22-12}{30}[/tex]
[tex]= 0.28 \ m/s^2[/tex]
hence,
The distance traveled be:
→ [tex]x = 13.89\times 30+\frac{0.28.30^2}{2}[/tex]
[tex]= 416.67+125[/tex]
[tex]= 541.67 \ m[/tex]
Thus the above answer is right.
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A car of weight 11000 N moves with constant velocity along a horizontal road.A driving force of 5000 N acts on the car what is the force opposing the motion of the car
Answers
Answer:
5000 N
Explanation:
Since F - f = ma, where F = driving force = 5000 N, f = opposing force, m = mass of car and a = acceleration of car.
Since the car is moving with constant velocity, a = 0.
So, F - f = ma
F - f = m(0)
F - f = 0
F = f.
Since F = 5000 N and F = f, f = 5000 N.
So, the opposing force is 5000 N
The opposing force car, weight 11000 N that is moving at constant velocity is 5000 N.
The opposing force can be calculated by the formula,
F - f = ma
Where,
F = driving force = 5000 N,
f = opposing force = ?
m = mass of car = 11000 N
a = acceleration of car
Since, the car is at constant velocity, a = 0.
So,
F - f = m(0)
F - f = 0
F = f.
Therefore, the opposing force car, weight 11000 N that is moving at constant velocity is 5000 N.
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Explain how organelles and other structures interact to secrete substances from the cell.
Answers
Answer:
Vacculoes, vesicles
Explanation:
Organelles and other structures within the cells have vesicles collectively referred to as the endo-membrane system. The Lysosomes pack up the substances, and the vesicles go through the porsous membrame and secrete the substances.
Which law represents a balanced chemical equashion
Answers
Answer:
law of conservation of mass
Explanation:
hope that helped :)
a student determines the circumference of a golf ball. a man pulls a sledge of mass 25 kg across level ground with a horizontal force of 60 N. a constant force of friction of 20 N acts on sledge. what is the acceleration of the sledge?
Answers
Explanation:
Fnet = Ft - Ff = 60N - 20N = 40N
a = Fnet / m = 40N / 25kg = 1.6m/s².
Calculate resultant force:
R = ma
Descomposing:
F - Fr = ma
Replacing we have:
60 N - 20 N = 25 kg * a
Resolving:
40 N = 25 kg * a
40 N / 25 kg = a
1,6 m/s^2 = a
The aceleration is 1,6 meters per second squared.
Two equal forces act at the same time on the same motionless object, but in opposite directions. Which statement best describes the object’s resulting motion?
A. The object will accelerate.
B. The object will move at a constant speed.
C. The object will remain motionless.
D. The object will change direction.
Answers
We work in less time.
3.
Differentiate between:
a)
Work and energy
b)
Work and power
c) Kinetic energy
Kinetic energy and potential energy
Work from burning fuel and work from moving objects
d)
110
Answers
Answer:
1 work is scalar quantity
2 it si unit of work is joule
3The equation of caculate is work= Force× Displacement
1 power is scalar quantity
2 it si unit of power is watt
3 the equation of calculateis power= work \time
A tourist stands at the top of the Grand Canyon, holding a rock, overlooking the valley below. Find the final velocity and displacement of the rock after 4.0 seconds give the three initial conditions listed below:
a. the rock is dropped vertically from rest
b. the rock is tossed vertically upward with 8.0m/s of speed
c. The rock is tossed vertically downward with 8.0 m/s speed
Answers
Answer:
a. -39.2 m/s; -78.4 m
b. -31.2 m/s; -46.4 m
c. -47.2 m/s; -110.4 m
Explanation:
Part (a)We are given/can infer these variables:
t = 4.0 sa = -9.8 m/s² v_0 = 0 m/sWe want to find the displacement and the final velocity of the rock.
Δx = ?v = ?We can use this equation to find the final velocity:
v = v_0 + atPlug in the known variables into this equation.
v = 0 + (-9.8)(4.0) v = -9.8 * 4.0 v = -39.2 m/sThe final velocity of the rock is -39.2 m/s.
Now we can use this equation to find the displacement of the rock:
Δx = v_0 t + 1/2at²Plug in the known variables into this equation.
Δx = 0 * 4.0 + 1/2(-9.8)(4.0)² Δx = 1/2(-9.8)(4.0)² Δx = -4.9 * 16 Δx = -78.4 mThe displacement of the rock is -78.4 m.
Part (b)We are given/can infer these variables:
v_0 = 8.0 m/sa = -9.8 m/s²t = 4.0 sWe can use this equation to find the final velocity:
v = v_0 + atPlug in the known variables into this equation.
v = 8.0 + (-9.8)(4.0) v = 8.0 + -39.2 v = -31.2 m/sThe final velocity of the rock is -31.2 m/s.
We can use this equation to find the displacement:
Δx = v_0 t + 1/2at²Plug in known variables:
Δx = 8.0(4.0) + 1/2(-9.8)(4.0)² Δx = 32 - 4.9(16)Δx = -46.4 mThe displacement of the rock is -46.4 m.
Part (c)We are given/can infer these variables:
v_0 = -8.0 m/sa = -9.8 m/s²t = 4.0 sWe can use this equation to find the final velocity:
v = v_0 + atPlug in the known variables into this equation.
v = -8.0 + (-9.8)(4.0) v = -8.0 - 39.2 v = -47.2 m/sThe final velocity of the rock is -47.2 m/s.
We can use this equation to find the displacement:
Δx = v_0 t + 1/2at²Plug in known variables:
Δx = -8.0(4.0) + 1/2(-9.8)(4.0)²Δx = -32 - 4.9(16)Δx = -110.4 mThe displacement of the rock is -110.4 m.
Which option is an element?
A. Carbon dioxide
B. Carbon
C. Air
D. Water
Answers
Hope this helped! :))
Un bloque de 25 n se encuentra suspendido por un hilo al techo vitamina la tensión que aparece en el hilo
Answers
Answer:
T = 25 N
Explanation:
The question says that "A 25 n block is suspended by a wire from the ceiling vitamin the tension that appears in the wire ?"
Weight of the block, W = 25 N
Weight of a body acts in downward direction and tension acts in upward direction. It would mean that,
Tension = weight of the block
T = mg
T = 25 N
Hence, the tension in the wire is 25 N.
What do the most abundant elements in Earth’s atmosphere have in common?
Answers
Answer: Since the oceans are mostly water, the elements hydrogen and oxygen are the most common. Sodium and chlorine are found in the salt in ocean water. Earth's atmosphere is made up of a combination of gases, including nitrogen, oxygen, and carbon dioxide. Nitrogen and oxygen are the most common elements in the atmosphere..
an object on a planet has a mass of 243 Kg. what is the acceleration of the object, if the radius of the planet is 2.32 x 10^7m and the mass of the planet is 6.35 x 10^30 Kg estimate g as 6.67 x 10^-11 N (m/kg)
Answers
Answer:
7.87x10^5m/s^2
Explanation:
PLEASE ANSWER - WILL MARK BRAINLIEST - THANKS
List three scientific ideas, discoveries, concepts, or issues that interest you.
Answers
Answer:
Evolution, Big Bang Theory and Cell theory.
Explanation:
These theories interest me because they talk about life and how life started.