(a) The mass m of the rod is m = (k L²sin²(30°)) / (2 g (I/L + L/2)) (b) The angular velocity is 1.89 rad/s of the rod when the angular displacement is 15° below the horizontal.
To solve this problem, we can use the principle of conservation of energy and the principle of conservation of angular momentum.
(a) Let's start by finding the mass of the rod. When the rod is released from rest, the spring will start to pull on the rod, causing it to rotate downwards. At the maximum angular displacement of 30° below the horizontal, the spring is fully compressed and all the potential energy stored in the spring has been converted into kinetic energy of the rod.
The potential energy stored in the spring when it is fully compressed is given by:
U = (1/2) k x²
where k is the spring constant and x is the displacement of the spring from its unstretched position. Since the spring is unstretched when the rod is released, x is equal to the length of the cord AC.
The kinetic energy of the rod when it reaches its maximum angular displacement is given by:
K = (1/2) I w²
where I is the moment of inertia of the rod about the pivot point O and w is the angular velocity of the rod at that point.
Since the rod is rotating about a fixed axis, the principle of conservation of angular momentum tells us that the angular momentum of the rod is conserved throughout the motion. The angular momentum of the rod is given by:
L = I w
where L is the angular momentum, I is the moment of inertia, and w is the angular velocity.
At the maximum angular displacement, the velocity of the rod is perpendicular to the cord AC, and hence the tension in the cord provides the necessary centripetal force for circular motion. Therefore, we have:
mg sin(30°) = T
where m is the mass of the rod, g is the acceleration due to gravity, and T is the tension in the cord.
Substituting T = kx into the above equation, we get:
mg sin(30°) = kx
Substituting the expressions for potential energy and kinetic energy into the principle of conservation of energy, we get:
(1/2) k x² = (1/2) I w²+ mgh
where h is the vertical displacement of the center of mass of the rod from its initial position.
Substituting the values of x and h in terms of the length and geometry of the rod, we can solve for the mass m:
m = (k L²sin²(30°)) / (2 g (I/L + L/2))
where L is the length of the rod.
(b) To find the angular velocity of the rod when the angular displacement is 15° below the horizontal, we can use the principle of conservation of angular momentum. At this point, the angular momentum of the rod is:
L = I w
where I is the moment of inertia of the rod about the pivot point O and w is the angular velocity of the rod.
Since the angular momentum is conserved, we have:
L = I w = constant
Therefore, we can find the angular velocity w when the angular displacement is 15° below the horizontal by using the initial conditions at rest:
I w0 = I w = (1/2) m L²w²
where w0 is the initial angular velocity (zero) and m is the mass of the rod. Solving for w, we get:
w = √t(2 g (cos(15°) - cos(30°))) / L
Substituting the values of g, L, and the previously calculated value of m, we get:
w = 1.89 rad/s
To know more about rod
https://brainly.com/question/31727490
#SPJ4
Two spheres are moving towards each other. Which of the following is the
best evidence that the spheres have transferred energy from one to the other?
A.The friction of the surface decreases
B.Gravity is always acting on the spheres
C.The motion of the sphere changes
Or
D.Both of the spheres have the same mass
Answer:
D
Explanation:
If they are both moving at the same speed then its D.
A plane has a take off speed of 1 point
300 km/h. What is the
acceleration in m/s2 of the
plane if the plane started from
rest and took 45 seconds to
take off? *
Answer:
Acceleration = 1.85m/s²
Explanation:
Given the following data;
Final velocity = 300km/h to m/s = 300*1000/3600 = 83.33m/s
Time = 45 seconds
Since the plane started from rest, initial velocity is equal to 0m/s.
To find the acceleration;
In physics, acceleration can be defined as the rate of change of the velocity of an object with respect to time.
This simply means that, acceleration is given by the subtraction of initial velocity from the final velocity all over time.
Mathematically, acceleration is given by the equation;
[tex]Acceleration (a) = \frac{final \; velocity - initial \; velocity}{time}[/tex]
Where,
a is acceleration measured in [tex]ms^{-2}[/tex]
v and u is final and initial velocity respectively, measured in [tex]ms^{-1}[/tex]
t is time measured in seconds.
Substituting into the equation, we have;
Acceleration = (83.33 - 0)/45
Acceleration = 83.33/45
Acceleration = 1.85m/s²
Therefore, the acceleration of the plane is 1.85m/s².
Select the correct answer.
Which pair of atoms has the highest electronegativity difference?
OA.
H-S
B.
H-Cl
o c.
N-H
OD.
О – Н
O E.
C-H
Answer:O – H
Explanation:
Which of the following have the most GPE. 1.) a car at the top of a hill 2.) a car at the bottom of the hill 3.) a car half way down the hill 4.) on the straight part of the track. (I don't know how to give Brainly)
Answer: car at the top of a hill
Explanation:
What is the direction of the current in the loop as the north pole of the magnet is pulled away (to the right) from the loop of wire. Answer as you face the loop from the magnet.
Answer:
Explanation:
Applying Fleming's right hand rule, the induced current would flow in a clockwise direction in the loop. Explanation: Current, magnetic field and motion are mutually dependent and perpendicular to one another.Aug 27, 2019
A rock with a mass of 80grams dropped into a graduated cylinder with 30 ml of water in it the readingof water became 70 ml what is the density of the rock
Explanation:
[tex]b = m \div v \\ 80 \div 30 \times 10 { -}^{2} [/tex]
Complete the sentence. Friction always ____________
a. helps the motion
b. opposes the motion
c. both of these
d. none of these
Answer:
B- Opposes the motion
Explanation:
When two object touches each other. friction acts in a opposite direction to the motion of the object
A force of 10 N acts to the left and a force of 5 N acts to the right on an object of mass 1 kg. If its initial speed is zero , what is its velocity after 1 second ?
Answer: -5 m/s
Explanation:
First find the net force by summing up the forces:
-10N + 5N = -5N
Use Newton's Second Law of motion to solve for the acceleration:
F = ma
-5N = 1kg(a)
a = -5 m/s^2
Use the first kinematic equation to solve for the final velocity:
Vf = Vi + at
Vf = 0 + (-5)(1)
Vf = -5 m/s
A tractor pulls a 1,000 kg wagon with a force of 4,000N. What is the wagon’s acceleration in m/s2? *
Answer:
4m/s^2
Explanation:
acceleration=force/mass
therefore a=4000/1000
=4m/s^2
What is the kinetic energy of a 5kg ball that is rolling 3m/s?
Answer:
22.5
Explanation:
As the mass is 5 kg,velocity is 3m/s so the derivation use for kinetic energy is 1÷2 mv*2 . By this derivation we will find out the kinetic energy
How are the sun and Earth's moon different?(2 points)
The sun is a ball of gases that revolves around Earth, while the moon is the center of the solar system,
The sun is a ball of rock and gas, while the moon is a ball of rock that revolves around the sun.
The sun is the center of the solar system, while the moon is a ball of rock that revolves around Earth
The moon is the center of the solar system, while the sun is the center of the Milky Way.
Answer: The Sun measures 1.4 million km across, while the Moon is a mere 3,474 km across. In other words, the Sun is roughly 400 times larger than the Moon. But the Sun also happens to be 400 times further away than the Moon, and this has created an amazing coincidence.
Explanation:
the force required to lift a load of 800 Newton by using a Lever having a mechanical advantage of 1.6 is
Answer:force required to lift the load = 500N
Explanation:
Mechanical advantage for a lever is given by the formulae
= force output/force input
or
Mechanical Advantage = Load / Effort
where
Force output / Load= 800 N
mechanical advantage = 1.6
Force input / Effort =??
Force input= Force output /Mechanical advantage
= 800N / 1.6
=500N
OR
Effort = Load/ Mechanical Advantage = 800/ 1.6 = 500N
plzz helpppp meee!!!!
A farmer cannot get his cow to move without help. The cow has a mass of 425 kg. He returns with some neighbors, and they are able to exert a net force of 900 N on the cow. What is its acceleration?
Answer:
hhh
Explanation:
can you suggest improvement that can be made towards the design of siphon so that the transfer of liquid is much higher.
Answer:
A siphon is a tube that makes use of the potential energy of fluid at an elevated level to transfer the fluid to a lower level, due to pressure differences between the inlet and the outlet points of the tube, such that the pressure at the outlet is higher than the pressure at the inlet
The pressure energy is converted into velocity (kinetic) energy, and therefore, in other to increase the flow rate through the tube of a siphon, with constant diameter, the level of the fluid in the container at the inlet (supply) of the siphon is raised higher than the level at the outlet receiving) container or the outlet point of the siphon tube
The larger the difference between the inlet and outlet levels, the faster the transfer of fluid by the siphon
Explanation:
Importance of Forest
Answer:
to help keep fresh air
Explanation:
please please help!!!!!
give three example what are the aims of each team in playing basketball?
Answer:
The main objective of basketball is to make a goal and score points.Each team should not only try to make a goal and prevent the opposite team from taking control of the ball, but should also try to protect the basket in their court and prevent the opponent from making a goal.
hope that helps..
the organelles are giving their job description to you can you identify which organelle are they? write your answers in your answer sheet.
1. Hi! My responsibility is to add stability and protection to plant cells. What am I?
2. Hi! produce proteins inside the cell. What am I ?
3. Hello! I have a green pigment called the clorophyll. I also absorb solar energy to do the process of photosynthesis. What am I?
4. Good morning po! my work is to store food materials and excretes waste materials. I take a large space on plants. I make the leaves of plants fresh. what am i?
5. Hi! All organelles are embedded in me. I am a "jelly- like" substance. What am I?
Please real answer
1. cell wall?
2. ribosomes?
3. chloroplast
4. vacuoles
5. cytoplasm
which is not a cinstellation?
Answer:
The Big Dipper
Explanation:
A rocket at rest with a mass of 942 kg is acted on by an average net force of 6,731 N upwards for 21 s. What is the final velocity of the rocket?
Answer:
Final velocity, V = 150.15 m/s
Explanation:
Given the following data;
Mass = 942kg
Net force = 6,731N
Time = 21secs
To find the final velocity of the rocket;
First of all, we would determine the acceleration of the rocket with respect to time.
Force = mass * acceleration
Substituting into the equation, we have;
6,731 = 942*acceleration
Acceleration = 6731/942
Acceleration = 7.15m/s²
Now, to find the final velocity we would use the first equation of motion.
V = U + at
Since the rocket started from rest, its initial velocity (U) is zero.
V = 0 + 7.15*21
Final velocity, V = 150.15 m/s
Help please if u don’t know one don’t answer it but do the most that u can
(2) 120 * 0.4 = 48 W
(3) 500 / 2 = 250 V
(4) 1000 / 300 = 3.3 A
(5) 700/3 = 233.3 V
(6) 1600 / 240 = 6.7 A
(7) 160 / 2 = 80 V
(8) 120 * 6 = 720 W
(9) 1000 / 240 = 4.17 A
Power (watts) = electric potential difference(volts) * intensity(amps)
Pls , give me Brainliest pls pls pls pls
Answer:
1. 1689 v 259 v p＝v 1* + 8.3 answer 2090
solve: A car travels 2 km North , 10 km East, then 3 km West. pythagorean theorem
________b_____ 7 km east
|
| 2km north.
|a
|
°
pythagorean theorem : ✓a² + b² = c²
c² = a² + b² = 4 + 49 = 53
c = ✓53 km
displacement = c = ✓53 km
distance = 10 + 3 + 2 = 15 km
percent of Earth's surface is made up of Oxygen.
a) 30
b) 46
c) 62
Answer: it's made up about 21% so if you do not have this option I say go with 30
Explanation:
what is the wavelength of the wave
Explanation:
it is equal to the speed (v) of a wave train in a medium divided by its frequency (f): λ = v/f. Waves of different wavelengths.
Answer:
It is measured in the direction of the wave. Description: Wavelength is the distance from one crest to another, or from one trough to another, of a wave (which may be an electromagnetic wave, a sound wave, or any other wave).
Electrical energy in motion is what type of energy ?
Answer:
kinetic energy
Explanation:
Electrical energy is a type of kinetic energy caused by moving electric charges. The amount of energy depends on the speed of the charges – the faster they move, the more electrical energy they carry.
This tasty snack starts as a kernel and is “popped” then
covered in salt, butter, caramel, peanuts, you name it.
Through thermal energy we've learned to heat things, you
could use conduction, convection and/or radiation. Describe
1 cooking option in detail including whether it is convection,
conduction or radiation. Must be at least 2 sentences.
how do I write an essay on how I feel about online school
Answer:
Some students appreciated the social aspect of Zoom classrooms, while others felt online education worked best for them when they were working on their own. ... Students said they appreciated having a well-planned work week and didn't appreciate “surprise” assignments online any more than they appreciate them in class
Explanation:
What's I know I said
What do you u write it
someone please helppp
okay, so what i have learned from my experiences with doing school on e.d.g.e.n.u.i.t.y (they won't let me say the website name on here lol) is that after you write an extended response, they show you a sample response as well as these checkboxes which show things they wanted you to have included in your answer. ideally they want you to select all of them, meaning that all of those elements were included in your answer. it's not a matter or right or wrong; none of those checkboxes contain a wrong answer. you just select the ones that apply to your answer, and you won't get penalized if you don't select all of the checkboxes. you don't even have to select any of them. there's been times where my answer has been not at all what it should've been and i just click done without checking any of those boxes because i did not include any of those elements in my response. as long as the box that you wrote your answer in is outlined in green (which yours is, and that means that the computer likes your answer), you will be fine.
i hope this makes sense! it's sort of hard to explain. if you have any questions, just comment and i'll try my best to explain better lol. have a great rest of your day! <3
How many total molecules are present in the formula below
2H2O
I'm guessing 6.
the coefficient of two turns our hydrogen into 4 and our oxygen into 2 which makes a total of 6 molecules.
what are common in the pictures?
Answer:
the flowers the left have them on there heads the middle on there chest and the right one has them on there shoulders