Answer:
A. 1.4 m/s to the left
Explanation:
To solve this problem we must use the principle of conservation of momentum. Let's define the velocity signs according to the direction, if the velocity is to the right, a positive sign will be introduced into the equation, if the velocity is to the left, a negative sign will be introduced into the equation. Two moments will be analyzed in this equation. The moment before the collision and the moment after the collision. The moment before the collision is taken to the left of the equation and the moment after the collision to the right, so we have:
[tex]M_{before} = M_{after}[/tex]
where:
M = momentum [kg*m/s]
M = m*v
where:
m = mass [kg]
v = velocity [m/s]
[tex](m_{1} *v_{1} )-(m_{2} *v_{2})=(m_{1} *v_{3} )+(m_{2} *v_{4})[/tex]
where:
m1 = mass of the basketball = 0.5 [kg]
v1 = velocity of the basketball before the collision = 5 [m/s]
m2 = mass of the tennis ball = 0.05 [kg]
v2 = velocity of the tennis ball before the collision = - 30 [m/s]
v3 = velocity of the basketball after the collision [m/s]
v4 = velocity of the tennis ball after the collision = 34 [m/s]
Now replacing and solving:
(0.5*5) - (0.05*30) = (0.5*v3) + (0.05*34)
1 - (0.05*34) = 0.5*v3
- 0.7 = 0.5*v
v = - 1.4 [m/s]
The negative sign means that the movement is towards left
Answer:
A. 1.4 m/s to the left
Explanation:
1. Which of these is not a natural fibre?
a. leather
b. jute
C.Wool
d. cotton
Answer:
leather
Explanation:
plz mark as brainliest......hope it helps
Answer:
a. leather
Explanation:
Hello friend!!!!
a. leather is the correct option because jute, wool and cotton are all natural fibres whereas leather is a synthetic fibre.
Hope this helps
plz mark as brainliest!!!!!!
The consequence that an element of society produces for the maintenance of its social system.
Answer:
Function
Explanation:
This question defines a function. It is any consequence that is made up of positive structures which has a way of affecting the society in a positive way. And it also has a way of impacting structural continuity in the society. The functionalism idea has the postulation that all cultural or social phenomena is of positive function and cannot be ignored
Answer:
function
Explanation:
answer EDGE2020
Hypothesis
If an object rolls over plywood board (type of material). (describe the prediction of distance, it
will travel).
Answer:
it depend what you are.rolling down and how far would be the lighter the object the farther like a marble
A 6 gram coin is which is initially at rest is dropped from the observation deck of a skyscraper 300 meters above the street below.
Required:
a. What is the work done by gravity on the coin as it falls?
b. Because there is air resistance the coin was slowed and hit the ground with a final velocity of 60 m/s. What is the kinetic energy of the coin at this speed? Joules
c. How much work was lost to air resistance as the coin fell? Joules
d. What is the average force exerted on the coin due to the air resistance as it fell?
Answer:
a) The work done by gravity on the coin as it falls is 17.653 joules.
b) The kinetic energy of the coin at a speed of 60 meters per second is 10.8 joules.
c) The work lost due to air resistance is 6.853 joules.
d) The average force exerted on the coin due to air resistance as it fell is 0.023 newtons.
Explanation:
a) We must remind that situation with Earth-coin system must be represented by Principle of Energy Conservation and Work Energy Theorem. According to this latter, work done by gravity equals to the change in gravitational potential energy:
[tex]\Delta U_{g} = m\cdot g \cdot \Delta z[/tex] (Eq. 1)
Where:
[tex]\Delta U_{g}[/tex] - Change in gravitational potential energy, measured in joules.
[tex]m[/tex] - Mass, measured in kilograms.
[tex]g[/tex] - Gravitational accelerations, measured in meters per square second.
[tex]\Delta z[/tex] - Height of the skyscraper, measured in meters.
If we know that [tex]m = 0.006\,kg[/tex], [tex]g = 9.807\,\frac{m}{s^{2}}[/tex] and [tex]\Delta z = 300\,m[/tex], the work done gravity on the coin is:
[tex]\Delta U_{g} = (0.006\,kg)\cdot \left(9.807\,\frac{m}{s^{2}} \right)\cdot (300\,m)[/tex]
[tex]\Delta U_{g} = 17.653\,J[/tex]
The work done by gravity on the coin as it falls is 17.653 joules.
b) By definition of translation kinetic energy, we get the following model:
[tex]K = \frac{1}{2}\cdot m\cdot v^{2}[/tex]
Where:
[tex]K[/tex] - Kinetic energy of the coin right before hitting the street, measured in joules.
[tex]v[/tex] - Speed of the coin, measured in meters per second.
If we get that [tex]m = 0.006\,kg[/tex] and [tex]v = 60\,\frac{m}{s}[/tex], the kinetic energy at this speed is:
[tex]K = \frac{1}{2}\cdot (0.006\,kg)\cdot \left(60\,\frac{m}{s} \right)^{2}[/tex]
[tex]K = 10.8\,J[/tex]
The kinetic energy of the coin at a speed of 60 meters per second is 10.8 joules.
c) The work lost due to air resistance is obtained derived from Principle of Energy Conservation and Work-Energy Theorem:
[tex]W_{lost} = \Delta U_{g}-K[/tex] (Eq. 2)
Where [tex]W_{lost}[/tex] is the work lost due to air resistance, measured in joules.
If we know that [tex]\Delta U_{g} = 17.653\,J[/tex] and [tex]K = 10.8\,J[/tex], the work lost due to air resistance is:
[tex]W_{lost} = 17.653\,J-10.8\,J[/tex]
[tex]W_{lost} = 6.853\,J[/tex]
The work lost due to air resistance is 6.853 joules.
d) The average force exerted on the coin due to air resistance can be determined by applying definition of work, as air resistance force was antiparallel to the displacement of the coin. That is:
[tex]W_{lost} = F\cdot \Delta z[/tex]
[tex]F = \frac{W_{lost}}{\Delta z}[/tex] (Eq. 3)
Where [tex]F[/tex] is the average force exerted on the coin due to air resistance, measured in newtons.
If we know that [tex]W_{lost} = 6.853\,J[/tex] and [tex]\Delta z = 300\,m[/tex], then the average force exerted on the coin is:
[tex]F = \frac{6.853\,J}{300\,m}[/tex]
[tex]F = 0.023\,N[/tex]
The average force exerted on the coin due to air resistance as it fell is 0.023 newtons.
PLEASE SOLVE FAST!!! If the average American watches hours of TV every day , how many minutes will be spent in front of the TV by a person's 65th birthday? Solve using Dimensional Analysis.
Answer:
5694000 min
Explanation:
Let's suppose the average American watches 4 hours of TV every day. First, we will calculate how many minutes they watch per day. We will use the conversion factor 1 h = 60 min.
(4 h/day) × (60 min/1 h) = 240 min/day
They watch 240 minutes of TV per day. Now, let's calculate how many minutes they watch per year. We will use the conversion factor 1 year = 365 day.
240 min/day × (365 day/year) = 87600 min/year
They watch 87600 min/year. Finally, let's calculate how many minutes they spend watching TV in 65 years.
87600 min/year × 65 year = 5694000 min
Velocity which stone gains when falling from height of 80 m is approximately equal to *
A. 0
B. 1 m/s
C. 8 m/s
D. 40 m/s
E. 300 m/s
Answer:
40
Explanation:
On top of a cliff of height h, a spring is compressed 5m and launches a projectile perfectly horizontally with a speed of 75 m s . It hits the ground with speed 90 m s . How high above the ground was the cliff? (Hint: use energy conservation to make the problem easier!)
Answer:
The height of the cliff is 121.276 m
Explanation:
Given;
initial velocity of the projectile, v₁ = 75 m/s
final velocity of the projectile, v₂ = 90 m/s
spring compression = 5 m
Apply the law of conservation of energy;
mgh₀ + ¹/₂mv₁² = mgh₂ + ¹/₂mv₂²
gh₀ + ¹/₂v₁² = gh₂ + ¹/₂v²
gh₁ - gh₂ = ¹/₂v₂² - ¹/₂v₁²
g(h₀ - h₂) = ¹/₂ (v₂² - v₁²)
h₀ - h₂ = ¹/₂g (v₂² - v₁²)
h₀ = h(cliff) + 5m
when the projectile hits the ground, Final height, h₂ = 0
[tex]h_o - 0 = \frac{1}{2g}(v_2^2-v_1^2)\\\\h_{cliff} + 5= \frac{1}{2g}(v_2^2-v_1^2)\\\\h_{cliff} = \frac{1}{2g}(v_2^2-v_1^2) - 5\\\\h_{cliff} = \frac{1}{2*9.8}(90^2-75^2) - 5\\\\h_{cliff} = 121.276 \ m[/tex]
Therefore, the height of the cliff is 121.276 m
It took 500 newtons of force to push a car 4 meters. How much work was done?
Answer:
The answer is 2000 JExplanation:
The work done by an object can be found by using the formula
workdone = force × distanceFrom the question
force = 500 N
distance = 4 m
We have
workdone = 500 × 4
We have the final answer as
2000 JHope this helps you
a car is moving at 12 m/s and has a mass of 600 kg what is the. kinetic energy of the car?
Answer:
43200 J
Explanation:
(1/2(mass)) (speed)^2
the diagram shows a contour map. letter a through k are reference points on the map. which points are located at the same elevation above sea level?
Answer:
K and I
Explanation:
Contour maps use lines that represent spaces in a map that have the same elevation, this means that all the lines should be continuous and closed, in this case, we are not able to see the full extent of most of the lines, but since the points are located in different lines we can assume that they are at different heights, so since only point K and point I are on the same line, we know that these two points are at the same height.
A student rides a bicycle 2400 meters in four minutes to get to school. What is the student's speed?
Answer:
10 mls2
Explanation:
speed =distance /time
A baseball is thrown through the air. It's initial velocity, described as a vector, is → v ( t = 0 ) = 17.1 ˆ i + 14.7 ˆ j m / s The ball accelerates only due to gravity. You can take the magnitude of this acceleration to be 9.8 m / s 2 . What is the acceleration of the ball, described as a vector?
Answer:
a = - 9.8 j ^ m/s²
Explanation:
This is a projectile launch problem, they give us the initial velocity in the two components
v₀ₓ = 17.1 m / s
[tex]v_{oy}[/tex] = 14.7 m / s
They indicate that the only acceleration that exists is the acceleration of gravity, which acts in the direction towards the center of the Earth, in general in a coordinate system it coincides with the direction of the y axis.
a = - g j ^
a = - 9.8 j ^ m /s²
A region around the nucleus of an atom where electrons are likely to be found
Answer:
The region where an electron is most likely to be is called an orbital. Each orbital can have at most two electrons. Some orbitals, called S orbitals, are shaped like spheres, with the nucleus in the center.
Explanation:Hope this helps :)
By definition, a region around the nucleus of an atom where electrons are likely to be found is called an orbital.
First of all, an atom is the smallest constituent unit of ordinary matter that has the properties of a chemical element.
All atoms are made up of subatomic particles: protons and neutrons, which are part of their nucleus, and electrons, which revolve around them. Protons are positively charged, neutrons are neutrally charged, and electrons are negatively charged.
In other words, every atom consists of a nucleus in which neutrons and protons meet and energy levels where electrons are located.
This is, the atomic nucleus is the central part of the atom that is made up of protons and neutrons, while the orbitals or peripheral region is an area where electrons are found.
In summary, a region around the nucleus of an atom where electrons are likely to be found is called an orbital.
Learn more:
https://brainly.com/question/10866484?referrer=searchResultshttps://brainly.com/question/1275002?referrer=searchResultsbrainly.com/question/1814899?referrer=searchResults brainly.com/question/2449569?referrer=searchResultsA single living thing.
Answer:
What do you mean ma´am/sir?
Explanation:
which statement is correct about the strength of forces?
-Electrostatic forces are exactly 10 times stronger than gravitational forces.
-Electrostatic forces are exactly 10 times weaker than gravitational forces.
-Electrostatic forces are trillions of times stronger than gravitational forces.
-Electrostatic forces are trillions of times weaker than gravitational forces.
Answer:
Thanks!!!!! adding this so it doesn’t get deleted.
Explanation:
1. Electrostatic forces are trillions of times stronger than gravitational forces. 2. normal force and friction 3. contact forces 4. The electrostatic forces from the contact of the hands with the paper causes the paper molecules to separate. 5. The electrostatic forces between the molecules of the board prevent the force of gravity from breaking the board apart.
The correct statement over here is that electrostatic forces are trillions of times stronger than gravitational forces. Hence, option C is correct.
What is an Electrostatic Force?One of the basic forces in the cosmos is electrostatic force. In the universe, there are four basic forces. These include gravitational force, electromagnetic force, weak nuclear force, and strong nuclear force. Under the umbrella of electromagnetic force is electrostatic force. Two charges placed apart are subject to the electrostatic force. The size of each charged and the separation between them determines how much electrostatic force there will be.
When two charges of the same type are brought together, whether positive or negative, they repel one another. It is known as the electrostatic force of repelling when it operates among two charges that are similar.
Therefore, the electrostatic forces are trillions of times stronger than the gravitational forces.
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HELP ASAP. will mark brainiest
Answer:
4.8min
Explanation:
The police car is traveling at 100/km and is 1.6km away from red car that is traveling at 80/km
A 12 kg bowling ball would require what force to accelerate it down an alley at a rate of 2.5 m/s ^ 2
Answer:
hi
Explanation:
hiijjjjjjjjjjjjjjj
Rhea kicks a soccer ball at 13km/h to Sean after kicking the ball the speed of the soccer ball from Rhea reference frame is 13km/h the speed of the soccer ball from Sean rrefrence frame is 13km the speed of the soccer ball from Sean's reference frame 22km/h.
Answer:
Sean is standing still, and Rhea is running toward Sean while kicking the ball.
Note: The question is in complete. The complete question is given below:
Rhea kicks a soccer ball at 13 km/h to Sean. After kicking the ball, the speed of the soccer ball from Rhea's reference frame is 13 km/h. The speed of the soccer ball from Sean's reference frame is 22 km/h. Which conclusion is best supported by the information?
Sean is standing still, and Rhea is running toward Sean while kicking the ball.
Rhea is standing still after kicking the ball, and Sean is running away from Rhea.
Both soccer players are standing still after the ball is kicked.
Both soccer players are running while the ball is in motion.
Explanation:
A reference frame is a position from which something is observed.
Since from the reference frame of Rhea, the ball is moving at a speed of 13 km/h after he kicks the ball at a speed of 13km/h whereas from the frame of reference of Sean, the ball is moving at a speed of 22km/h, there is a difference in the speed of the ball as seen from Rhea's and Sean's frame of reference of about 9 km/h. This difference can only be due to relative motion between the ball and Rhea.
Therefore, the best conclusion supported by the given information is that Sean is standing still, and Rhea is running toward Sean while kicking the ball.
Answer:
Sean is standing still, and Rhea is running toward Sean while kicking the ball.
Note: The question is in complete. The complete question is given below:
Rhea kicks a soccer ball at 13 km/h to Sean. After kicking the ball, the speed of the soccer ball from Rhea's reference frame is 13 km/h. The speed of the soccer ball from Sean's reference frame is 22 km/h. Which conclusion is best supported by the information?
Sean is standing still, and Rhea is running toward Sean while kicking the ball.
Rhea is standing still after kicking the ball, and Sean is running away from Rhea.
Both soccer players are standing still after the ball is kicked.
Both soccer players are running while the ball is in motion.
Explanation:
A reference frame is a position from which something is observed.
Since from the reference frame of Rhea, the ball is moving at a speed of 13 km/h after he kicks the ball at a speed of 13km/h whereas from the frame of reference of Sean, the ball is moving at a speed of 22km/h, there is a difference in the speed of the ball as seen from Rhea's and Sean's frame of reference of about 9 km/h. This difference can only be due to relative motion between the ball and Rhea.
Therefore, the best conclusion supported by the given information is that Sean is standing still, and Rhea is running toward Sean while kicking the ball.
Based on the information in the table, which elements are most likely in the same periods of the periodic table?
Answer:
Just to help, periods on the periodic table are those running horizontally from left to right
Answer:
The answer is A.Boron and carbon are likely together in one period because they have very close atomic numbers, while gallium and germanium are likely together in another period because they have very close atomic numbers.
Explanation:
just took test
Under the assumption that the beam is a rectangular cantilever beam that is free to vibrate, the theoretical first natural frequency of the beam in terms of the length, L, width, b, thickness, h, density, p, and Young's Modulus, E, in Hertz is given by:
fn= h/2πL^2 √E/rho
The density of steel used in the beam is 7800 kg/m^3, and its Young's Modulus is 210 GPa. You measure the dimensions of the clamped steel beam with a set of calipers and gather the following data:
L = 233.5 mm, b = 24.9 mm, h = 3.3 mm
The calipers used to measure the dimensions of beam have a resolution of 0.01 mm and therefore have an uncertainty of +0.005 mm.
Required:
a. What is the uncertainty of the natural frequency (in Hz) due to the uncertainty of the length measurement?
b. What is the uncertainty of the natural frequency (in Hz) due to the uncertainty of the width measurement?
c. What is the uncertainty of the natural frequency (in Hz) due to the uncertainty of the thickness measurement?
d. What is the total uncertainty of the natural frequency due to the beam measurements (in Hz)?
e. What is the theoretical first natural frequency of the beam including the measurement uncertainty?
Answer:
a) Δf = 0.7 n , e) f = (15.1 ± 0.7) 10³ Hz
Explanation:
This is an error about the uncertainty or error in the calculated quantities.
Let's work all the magnitudes is the SI system
The frequency of oscillation is
f = n / 2π L² √( E /ρ)
where n is an integer
Let's calculate the magnitude of the oscillation
f = n / 2π (0.2335)² √ (210 10⁹/7800)
f = n /0.34257 √ (26.923 10⁶)
f = n /0.34257 5.1887 10³
f = 15.1464 10³ n
a) We are asked for the uncertainty of the frequency (Df)
Δf = | df / dL | ΔL + df /dE ΔE + df /dρ Δρ
in this case no error is indicated in Young's modulus and density, so we will consider them exact
ΔE = Δρ = 0
Δf = df /dL ΔL
df = n / 2π √E /ρ | -2 / L³ | ΔL
df = n / 2π 5.1887 10³ | 2 / 0.2335³) 0.005 10⁻³
df = n 0.649
Absolute deviations must be given with a single significant figure
Δf = 0.7 n
b, c) The uncertainty with the width and thickness of the canteliver is associated with the density
In your expression there is no specific dependency so the uncertainty should be zero
The exact equation for the natural nodes is
f = n / 2π L² √ (E e /ρA)
where A is the area of the cantilever and its thickness,
In this case, they must perform the derivatives, calculate and approximate a significant figure
Δf = | df / dL | ΔL + df /de Δe + df /dA ΔA
Δf = 0.7 n + n 2π L² √(E/ρ A) | ½ 1/√e | Δe
+ n / 2π L² √(Ee /ρ) | 3/2 1√A23 |
the area is
A = b h
A = 24.9 3.3 10⁻⁶
A = 82.17 10⁻⁶ m²
DA = dA /db ΔB + dA /dh Δh
dA = h Δb + b Δh
dA = 3.3 10⁻³ 0.005 10⁻³ + 24.9 10⁻³ 0.005 10⁻³
dA = (3.3 + 24.9) 0.005 10⁻⁶
dA = 1.4 10⁻⁷ m²
let's calculate each term
A ’= n / 2π L² √a (E/ρ A) | ½ 1 /√ e | Δe
A ’= n/ 2π L² √ (E /ρ) | ½ 1 / (√e/√ A) |Δe
A ’= 15.1464 10³ n ½ 1 / [√ (24.9 10⁻³)/ √ (81.17 10⁻⁶)] 0.005 10⁻³
A '= 0.0266 n
A ’= 2.66 10⁻² n
A ’’ = n / 2π L² √ (E e /ρ) | 3/2 1 /√A³ |
A ’’ = n / 2π L² √(E /ρ) √ e | 3/2 1 /√ A³ | ΔA
A ’’ = n 15.1464 10³ 3/2 √ (24.9 10⁻³) /√ (82.17 10⁻⁶) 3 1.4 10⁻⁷
A ’’ = n 15.1464 1.5 1.5779 / 744.85 1.4 10⁴
A ’’ = 6,738 10²
we write the equation of uncertainty
Δf = n (0.649 + 2.66 10⁻² + 6.738 10²)
The uncertainty due to thickness is
Δf = 3 10⁻² n
The uncertainty regarding the area, note that this magnitude should be measured with much greater precision, specifically the height since the errors of the width are very small
Δf = 7 10² n
d) Δf = 7 10² n
e) the natural frequency n = 1
f = (15.1 ± 0.7) 10³ Hz
What is the probability that a junior non-Physics major and then a freshman non-Physics major are chosen at random?
Answer:
Probability = 0.0244
Explanation:
Probability that Junior Non Physics Major & then a Freshman Non Physics Major are chosen:
Prob (Jr No-Ph Mjr) = Jr No-Ph Mjr / Total
= 18 / 82 = 0.2195
Prob (Fr No-Ph Mjr) = Fr No-Ph Mjr / Total (remaining)
= 9 / 81 = 0.1111
Prob [ Jr No-Ph Mjr & Fr No-Ph Mjr ] = 0.2195 x 0.1111 = 0.02439
≈ 0.0244
in a controlled experiment do none of the variables change?
Answer:
Yes
Explanation:
The variables change in and experiment.
Answer:
If you are carefully enough to control everything, then everything that could change the result of your experiment won't happen.
Explanation:
Children ages 6-15 normal heart rate is __________ beats per minute ??
Answer:
70-100 BPM
Explanation:
To pull a nail out of a wood board a carpenter does 1000 J of work. The hammer he uses does 835 J of work. What is the efficiency of the hammer?
Answer:
83.5%
Explanation:
A student studies the effect of an object's speed on its amount of kinetic energy. This graph summarizes the data from the study Kinetic energy Speed Which statement best describes what the graph shows?
A. As speed increases, kinetic energy increases exponentially
B. As speed increases, kinetic energy stays the same
C. As speed decreases, kinetic energy doubles each time.
D. As kinetic energy increases, speed decreases exponentially
The answer is A I Hope this answer helps you (i got the question right)
Answer:
A. As speed increases, kinetic energy increases exponentially.
Explanation:
The amount of kinetic energy an object has depends on the speed. Kinetic energy is also known as "motion energy." This being said, if speed is increasing, decreasing, or staying constant, the kinetic energy of the object will too.
What are the three different types of muscle tissue?
Answer:
skeletal,cardiac,and smooth.
Explanation:
Answer:
Skeletal, smooth, and cardiac.
Explanation:
Skeletal Muscles:
Skeletal muscles are the most familiar type of muscles; they make up most of the muscle mass in the body. Flexible bands of connective tissue called tendons attach these muscles to the bones in the body. Skeletal muscles control voluntary movement in the body.
Smooth Muscles:
Smooth muscles are involuntary muscles that we don’t consciously control. They are found within the walls of many organs and control the movement of these organs. For example, they enable the movement of food through the digestive system.
Cardiac Muscles:
Cardiac muscles are a special type of involuntary muscle. Located in the heart, these muscles control the contractions of the heart.
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What is it called when scientists in the same or similar field of study judge the quality of a fellow scientist’s scientific claim?
academic claim
academic review
peer claim
peer review
Answer:
When scientists in the same or similar field of study judges the quality of a fellow scientist’s scientific claim, it is known as peer review.
When scientists in the same or similar field of study judge the quality of a fellow scientist’s scientific claim it is called Peer review.
what is the scientific claim?Scientific claims are statements made in science based on an experiment.
These Scientific claims are backed by the experimental data and their true results obtained from scientific investigation and experimentation.
Peer review is done when scientists in the same or similar field of study judge the quality of a fellow scientist’s scientific claims.
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During a testing process, a worker in a factory mounts a bicycle wheel on a stationary stand and applies a tangential resistive force of 115 N to the tire's rim. The mass of the wheel is 1.80 kg and, for the purpose of this problem, assume that all of this mass is concentrated on the outside radius of the wheel. The diameter of the wheel is 50.0 cm. A chain passes over a sprocket that has a diameter of 8.50 cm. In order for the wheel to have an angular acceleration of 4.30 rad/s2, what force, in Newtons, must be applied to the chain
Answer:
The force is [tex] F_c = 789.03 \ N [/tex]
Explanation:
From the question we are told that
The tangential resistive force is [tex]F_t = 115 \ N[/tex]
The mass of the wheel is m = 1.80 kg
The diameter of the wheel is [tex]d = 50.0 cm = 0.5 \ m[/tex]
The diameter of the sprocket is [tex]d_c = 8.50 \ cm =0.085 \ m[/tex]
The angular acceleration considered is [tex]\alpha = 4.30\ rad/s^2[/tex]
Generally the radius of the wheel is
[tex]r = \frac{d}{2}[/tex]
=> [tex]r = \frac{0.5}{2}[/tex]
=> [tex]r = 0.25 \ m [/tex]
Generally the radius of the sprocket is
[tex]r_c = \frac{d_c}{2}[/tex]
=> [tex]r_c = \frac{0.085}{2}[/tex]
=> [tex]r_c = 0.0425 \ m [/tex]
Generally the moment of inertia of the wheel is mathematically represented as
[tex]I = m * r^2[/tex]
=> [tex]I = 1.80 * 0.25^2[/tex]
=> [tex]I = 1.1125 \ kg \cdot m^2[/tex]
Generally the torque experienced by the wheel due to the forces acting on it is mathematically represented as
[tex]\tau = F_c * r_c - F_t * r [/tex]
Here [tex]F_c[/tex] is the force acting on the sprocket
So
[tex]\tau = F_c * 0.0425 - 115 * 0.25 [/tex]
[tex]\tau = 0.0425F_c - 28.75 [/tex]
Generally the torques that will cause the wheel to move with [tex]\alpha = 4.30\ rad/s^2[/tex] is mathematically represented as
[tex]\tau = I * \alpha[/tex]
So
[tex] 0.0425F_c - 28.75 = I * \alpha [/tex]
[tex] 0.0425F_c - 28.75 = 1.1125 *4.30 [/tex]
[tex] 0.0425F_c - 28.75 = 1.1125 *4.30 [/tex]
[tex] F_c = 789.03 \ N [/tex]
A soccer player kicking a ball; the ball soaring through the air and landing on the ground
A 31.0 cm long spring is hung vertically from a ceiling and stretches to 36.9 cm when an 8.00 kg mass is hung from its free end.
(a) Find the spring constant (in N/m).
(b) Find the length of the spring (in cm) if the 8.00 kg weight is replaced with a 185 N weight.
Answer:
The length of the spring is 44.92 cm
Explanation:
Hooke's Law
Suppose a spring of constant k and natural length x0. If a force F is applied to the spring and it stretches to a distance x1. Hooke's Law states that:
[tex]F=k.x[/tex]
Where x is the elongation of the spring:
[tex]x=x1-x0[/tex]
We are given the characteristics of a spring of x0=31 cm. When a mass of m=8 Kg is hung from the spring, it stretches to x1=36.9 cm. We need to calculate the force of the mass of 8 Kg. It can be done by calculating the weight:
[tex]F = m.g=8\ Kg\cdot 9.8\ m/s^2[/tex]
[tex]F=78.4\ N[/tex]
The elongation of the spring is
[tex]x=36.9\ cm - 31\ cm = 5.9\ cm[/tex]
Converting to meters:
[tex]x=5.9/100=0.059\ m[/tex]
(a)
From Hooke's Law, we solve for k:
[tex]\displaystyle k=\frac{F}{x}=\frac{78.4}{0.059}[/tex]
[tex]k=1,329\ N/m[/tex]
(b) With the value of k, the equation for the spring is:
[tex]F=1,329.x[/tex]
Now if a weight of F=185 N is hung from the spring, the elongation is:
[tex]\displaystyle x=\frac{F}{1,329}=\frac{185}{1,329}[/tex]
[tex]x=0.1392\ m=13.92\ cm[/tex]
Thus, the length of the spring is:
[tex]x1=xo+x=31\ cm+13.92\ cm=44.92\ cm[/tex]
The length of the spring is 44.92 cm
(a)The spring constant will be 1,329 N/m.
(b)The length of the spring will be 44.92 cm.
What is the spring constant?Spring constant is defined as the ratio of force per unit displaced length. The spring force is balanced by the weight;
The given data in the problem is;
L₁ is the long spring is hung vertically from a ceiling= 31.0 cm
L₂ = 36.9 cm
m is the mass= 8.00 kg
The net elongation of the spring is
x= 36.9-31 =5.9 cm = 0.059 m
The force acted on the spring due to which the elongation is done;
F=mg
F= 8 × 9.81
F=78.4 n
From the Hooke's law the spring constant is found as;
[tex]\rm K = \frac{F}{x} \\\\ \rm K = \frac{78.4}{0.059} \\\\ \rm K = 1,329 \ N/m[/tex]
Hence the spring constant will be 1,329 (in N/m).
(b) The length of the spring will be 44.92 cm.
For the weight of F=185 N is hung from the spring, the elongation is:
[tex]\rm x= \frac{185}{1,329} \\\\ \rm x=0.10392 m = 13.92 \ cm[/tex]
The length of spring is;
[tex]\rm x_1 = x_0+x \\\\ \rm x_1 = 31+13.92 \\\\ \rm x_1=44.92\ cm[/tex]
Hence the length of the spring will be 44.92 cm.
To learn more about the spring constant reference to the link;
https://brainly.com/question/4291098
