Answer:
y = 5 cos 2πt
Explanation:
We will use the formula for simple harmonic motion curve where;
y = a cos ωt
Where;
a is amplitude
t is period
ω is angular frequency with the formula; ω = 2π/t
We are told that when the spring is compressed, the mass is located 5 cm above its rest position.
Thus;
a = 5 cm
it's highest point is 5 cm, but we are told that after 1/2 second of being released, it reaches its lowest point.
Since highest point is 5, then lowest point will be -5.
The difference in time between the highest and lowest point is ½ s. Which is half of the period.
Thus;
t/2 = ½
Thus, t = 1 s
Now, we know that;
t = 1/f = 2π/ω
Since t = 1, then 1 = 1/f
f = 1
Thus;
2π/ω = 1
Thus, ω = 2π
Thus, the equation is;
y = 5 cos 2πt
The equation that describes the motion of the mass is y = 5 cos 2πt.
The given parameters;
maximum displacement of the spring, A = 5 cmtime taken for the mass to reach the lowest point (half period), t = 0.5 sThe general equation of the wave is given as;
[tex]y = A\ cos\ \omega t[/tex]
where;
A is the amplitude of the vibrationω is the angular speed of massThe angular speed of the mass is calculated as;
[tex]\omega = 2\pi f\\\\[/tex]
The period of the oscillation is calculated as;
[tex]T = 2t \\\\T = 2(0.5 s) = 1 \ s[/tex]
The frequency of the wave is calculated as;
[tex]f = \frac{1}{T} \\\\f = \frac{1}{1} \\\\f = 1\ Hz[/tex]
The equation that describes the motion of the mass is calculated as;
[tex]y = A\ cos \ \omega t\\\\y = A\ cos \ 2\pi ft\\\\y = 5\ cos \ 2\pi (1) t\\\\y = 5 \ cos \ 2\pi t[/tex]
Thus, the equation that describes the motion of the mass is y = 5 cos 2πt.
Learn more here:https://brainly.com/question/14017869
(1) Define uniform acceleration
Answer:
Explanation:
When an object's speed increases at a constant rate, we say it has constant/uniform acceleration.
Three children are riding on the edge of a merry-go-round that is 182 kg, has a 1.60 m radius, and is spinning at 15.3 rpm. The children have masses of 17.4, 28.5, and 32.8 kg. If the child who has a mass of 28.5 kg moves to the center of the merry-go-round, what is the new angular velocity in rpm
Answer:
The new angular velocity of the merry-go-round is 18.388 revolutions per minute.
Explanation:
The merry-go-round can be represented by a solid disk, whereas the three children can be considered as particles. Since there is no external force acting on the system, we can apply the principle of angular momentum conservation:
[tex]\left(\frac{1}{2}\cdot M + m_{1}+m_{2} + m_{3} \right)\cdot R^{2}\cdot \dot n_{o} = \left(\frac{1}{2}\cdot M + m_{1} + m_{3})\cdot R^{2}\cdot \dot n_{f}[/tex] (1)
Where:
[tex]M[/tex] - Mass of the merry-go-round, in kilograms.
[tex]m_{1}[/tex], [tex]m_{2}[/tex], [tex]m_{3}[/tex] - Masses of the three children, in kilograms.
[tex]R[/tex] - Radius of the merry-go-round/Distance of the children with respect to the center of the merry-go-round, in meters.
[tex]\dot n_{o}[/tex], [tex]\dot n_{f}[/tex] - Initial and final angular speed, in revolutions per minute.
If we know that [tex]M = 182\,kg[/tex], [tex]m_{1} = 17.4\,kg[/tex], [tex]m_{2} = 28.5\,kg[/tex], [tex]m_{3} = 32.8\,kg[/tex], [tex]R = 1.60\,m[/tex] and [tex]\dot n_{o} = 15.3\,\frac{rev}{min}[/tex], then the final angular speed of the system is:
[tex]\dot n_{f} = \dot n_{o}\cdot \left(\frac{\frac{1}{2}\cdot M + m_{1} + m_{2} + m_{3} }{\frac{1}{2}\cdot M + m_{1} + m_{3} } \right)[/tex]
[tex]\dot n_{f} = \left(15.3\,\frac{rev}{min} \right)\cdot \left[\frac{\frac{1}{2}\cdot (182\,kg) + 17.4\,kg +28.5\,kg + 32.8\,kg }{\frac{1}{2}\cdot (182\,kg) + 17.4\,kg + 32.8\,kg } \right][/tex]
[tex]\dot n_{f} = 18.388\,\frac{rev}{min}[/tex]
The new angular velocity of the merry-go-round is 18.388 revolutions per minute.
Object A is 8 kg and at rest and Object B is 16 kg and moving at 10 m/s to the Right. If Object B hits Object A and Object B is at rest after the collision, what is the velocity of Object A after the collision? Why?
Answer:
Initially...
Object A is at rest(v=0)
With Mass =8kg
Object B moving at 10ms- and Mass of 16kg.
Now After collision(Elastic)... B Came to rest...Meaning its final vel =0
But its mass remains the same
What velocity would A be moving with?
From Conversation of Momentum
M'U' + M"U"= M'V' + M"V"
8(0) + (16)(10) = 8V' + 16(0)
0 + 160 = 8V' + 0
8V'= 160
V'= 160/8
V'=20ms-¹.
A would be Moving at 20ms-¹ after collision.
why the walls of tyres becomes warm as the car moves
Answer:
the particles vibrate inside the tyre
Explanation:
as the car moves kinetic energy is transfered in the tyres which causes the particles to vibrate inside the tyre so the kinetic store is. transferred into thermal
If 1.02 ✕ 1020 electrons move through a pocket calculator during a full day's operation, how many coulombs of charge moved through it?
Answer:
Explanation:
one electron has [tex]1.60217662*10^{-19}~coulombs~then\\\\1.02*10^{20}~electrons------->1.02*10^{20}*1.60217662*10^{-19}~coulombs= 16.3422~coulombs[/tex]
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Answer:
ok
Explanation:
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There are two substances, 1 and 2, that diffuse through a medium. The substances have diffusion constants D1 and D2, and D1 > D2. Which substance will spread out farther over a 10 s time interval?
Answer:
D1
Explanation:
Higher diffusion constants mean that the substance diffuses more in a given time. Because D1>D2, D1 should diffuse more.
Some scientists hypothesize that icy debris arrived on other terrestrial planets in a similar manner to how it arrived on Earth. On Earth, the ice eventually turned to water and water vapor, forming extensive oceans and a life-sustaining atmosphere. But the same is not exactly true for the other terrestrial planets. What are two reasons why?
Temperatures on Earth are ideal for water to exist in solid, liquid, and gaseous forms.
Magnetic forces generated in Earth’s mantle are directly responsible for Earth’s oceans.
Earth’s gravity holds the water vapor in Earth’s atmosphere close to its surface.
Earth’s solid outer core is sufficiently rigid to keep water above its surface.
Answer:
Temperatures on Earth are ideal for water to exist in solid, liquid, and gaseous forms.
Earth's gravity holds the water vapor in Earth's atmosphere close to its surface.
Answer: a and c
Explanation:
from plato
N 4. Which of the following can cause a short circuit?
Answer:
pretty sure its A
Explanation:
please give brainliest if i'm correct
Answer:
A.
Explanation:
I have done this and that was correct
hope this helps
please someone help I have to hand this in asap
I will give u 5 stars all that - give steps if u can
Explanation:
the answer is in the above image
What is Magnetic field
The area around a magnet in which it's magnetic force can ne experienced.
➛ Magnetic field has both magnitude and direction.
➛ Magnetic field can be described with help of a magnetic compass.
➛ It's SI unit is Tesla( T ) .
Explanation:
An area around a magnet or materials that behave like a magnet, where there is a force that will attract some metals towards it.
[tex] \: [/tex]
A ship is flying away from Earth at 0.9c (where c is the speed of light). A missile is fired that moves toward the Earth at a speed of 0.5c relative to the ship. How fast does the missile move relative to the Earth
Answer:
the required speed with which the missile move relative to the Earth is -0.727c
Explanation:
Given the data in the question;
relative velocity relation;
u' = u-v / 1 - [tex]\frac{uv}{c^2}[/tex]
so let V[tex]_B[/tex] represent the velocity as seen by an external reference frame; u=V[tex]_B[/tex]
and let V[tex]_A[/tex] represent the speed of the secondary reference frame; v=V[tex]_A[/tex]
hence, u' is the speed of B as seen by A
so
u' = V[tex]_B[/tex]-V[tex]_A[/tex] / 1 - [tex]\frac{V_BV_A}{c^2}[/tex]
now, given that; V[tex]_A[/tex] = 0.9c and V[tex]_B[/tex] = 0.5c
we substitute
u' = ( 0.5c - 0.9c ) / 1 - [tex]\frac{(0.5c)(0.9c)}{c^2}[/tex]
u' = ( 0.5c - 0.9c ) / 1 - [tex]\frac{c^2(0.5)(0.9)}{c^2}[/tex]
u' = ( 0.5c - 0.9c ) / 1 - (0.5 × 0.9)
u' = ( -0.4c ) / 1 - 0.45
u' = -0.4c / 0.55
u' = -0.727c
Therefore, the required speed with which the missile move relative to the Earth is -0.727c
A car moves at a constant speed of 90km/h from a starting point. Another car moves at 70km/h after 2hours from the same starting point. if both cars moves in the same direction, after how many hours will the distance between the first car and the second car to be 40 km.
Answer:
400
Explanation:
how many grams are in 5 kilos
1 kilo = 1000 gms
Therefore, 5 kilo = 5000 gms
The tendon from the flexor hallucis longus muscle in the hindlimb of a turkey (Meleagris gallopavo) has a resilience of 0.93. If 9.00 J of work are done on the tendon to stretch it out, how many Joules of work does the tendon do as it is relaxing?
Answer:
8.37 Joules
Explanation:
The amount of energy that a substance, such as animal tissue or rubber can take and yet return to its original condition is known as resilience. When we stress such a substance and then let it restore to its previous state, we are referring to the substance to maintain its elastic area of the stress-strain curve.
From the given information:
the resilence is 0.93
The amount of work done during stretching of the tendon = 9.00 J
Thus,
the work done when relaxing = 0.93 × 9.00 J
= 8.37 Joules
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MAnswer:
Explanation:
The efficiency of a machine can be increased by
Explanation:
the efficiency of a machine can be increased by reducing the friction
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In young Goodman’s Brown hawthornes reveals his feelings about his Puritan ancestors when
Answer:
In "Young Goodman Brown," Hawthorne reveals his feelings about his Puritan ancestors when the dark man reveals that he helped Brown's forebears persecute others.
Explanation:
hey mate i know it is right so don't worry this is the correct
Answer:
In "Young Goodman Brown," Hawthorne reveals his feelings about his Puritan ancestors when the dark man reveals that he helped Brown's forebears persecute others. so that means the answer is D.
Explanation:
A. brown strives to resist his dark mission
B. faith expresses her anxieties about young brown's departure
C. brown discovers his catechism teacher is on speaking terms with the devil
D. the dark man reveals that he helped brown's forebears persecute others(correct answer)
Calculate the period of a spring if it has a mass of 5 kg and a spring constant of 6 N/m
Answer: The period of a spring if it has a mass of 5 kg and a spring constant of 6 N/m is 5.73 sec.
Explanation:
Given: Mass = 5 kg
Spring constant = 6 N/m
Formula used to calculate period is as follows.
[tex]T = 2 \pi \sqrt\frac{m}{k}[/tex]
where,
T = period
m = mass
k = spring constant
Substitute the values into above formula as follows.
[tex]T = 2 \pi \sqrt\frac{m}{k}\\= 2 \times 3.14 \times \sqrt\frac{5}{6}\\= 5.73 s[/tex]
Thus, we can conclude that the period of a spring if it has a mass of 5 kg and a spring constant of 6 N/m is 5.73 sec.
what is kinematics ???
explain !!!
copied answer = 20 answers reported xD
Explanation:
2 one is kinametics
please check attachment
Kinematics is the branch of classical mechanics that describes the motion of points, objects and systems of groups of objects, without reference to the causes of motion (i.e., forces ). The study of kinematics is often referred to as the “geometry of motion.”
Un recipiente contiene 224 dm3 de Ozono de masa 4.561 Kg a 51.09 grados celsius. Calcula la presión del Ozono
Answer:
Por lo tanto, la presión del ozono es:
[tex]P=0.011\: atm[/tex]
Explanation:
Podemos usar la ecuacion de los gases ideales;
[tex]PV=nRT[/tex] (1)
Tenemos:
El volumen V = 224 dm³ = 224 L
La temperatura T = 51.09 C = 324.09 K
La masa es m = 4.561 kg
Lo necesitamos ahora es calvular n que es el numero de moles;
recordemos que el peso molecular del ozono M = 48 g/mol.
[tex]n=\frac{m}{M}=\frac{4.561}{48}=0.095\: mol[/tex]
Finalmente, usando la ecuacion 1 despejamos la presion P
[tex]P=\frac{nRT}{V}[/tex]
[tex]P=\frac{0.095*0.082*324.09}{224}[/tex]
Por lo tanto, la presion del ozono es:
[tex]P=0.011\: atm[/tex]
Espero te haya ayudado!
Three people are trying to move a box. Which set of forces will result in a net
force on the box of 20 N to the left?
Answer:
yes the answer is D as the two people if we calculate
Answer:
A
Explanation:
correct on A P E X
why are cows is important?
Answer:
cause they give u milk
Explanation:
Answer:
Cows are important as they provide humans many things for survival. They provide milk, meat, and leather, all of these are important resources.
Calculate the height that the ball bounces.
Sketch the position-time graph for the motion of the ball during the 2,89 s.
(Use the ground as zero position)
Show the following on the graph:
The position of the ball at 0 s.
The position of the ball at 0,5 s.
The position of the ball at time ty. how the graph will be?
Answer:
im bouta get 50 points
Explanation:
The latent heat of vaporization of water is roughly 10 times the latent heat of fusion of water. The amount of heat required to boil away 1 kg of water is __________ the amount of heat required to melt 1 kg of ice.
Answer:
The amount of heat required to boil away 1 kg of water is 10 times the amount of heat required to melt 1 kg of ice
Explanation:
let the latent heat of fusion of ice = L
then, the latent heat of vaporization of water = 10L
The heat of fusion of 1 kg of ice = 1 x L = L
The heat of vaporization 1 kg of water = 1 x 10L = 10L
Therefore, the amount of heat required to boil away 1 kg of water is 10 times the amount of heat required to melt 1 kg of ice
the unit of area is called a derived unit.why?
Explanation:
the unit of area is called a derived unit because it is made of two fundamental unit metre and metre.
A digital signal differs from an analog signal because it a.consists of a current that changes smoothly. b. consists of a current that changes in pulses. c.carries information. d. is used in electronic devices.
Answer:
d.it is used in electronic devices
What is 3*10^-6 divided by 2.5*10^6 expressed in standard notation?
Answer:
1.2 x 10^-12
Explanation:
3/2.5 x 10^-6/10^6
1.2 x 10^-6 x 10^-6
1.2 x 10^-12
Một electron di chuyển theo đường tròn vuông góc từ trường đều 2 mT. Nếu tốc độ của electron là 1,5×〖10〗^7 ∕〖 〗, hãy xác định
bán kính của đường tròn và
khoảng thời gian cần thiết để electron di chuyển hết vòng tròn.
Answer:
can u translate in English?
Explanation:
if u mind please it would help alot
As shown in Fig. 4, an ideal gas of monatomic molecules expands from its initial state A to a state B through an isobaric process and then further expands to a volume C. Find the work done by the gas, increase in internal energy, and the energy transferred by heat to the gas over the whole process
