On a horizontal frictionless surface a mass M is attached to two light elastic strings both having length l and both made of the same material. The mass is displaced by a small displacement Δy such that equal tensions T exist in the two strings, as shown in the figure. The mass is released and begins to oscillate back and forth. Assume that the displacement is small enough so that the tensions do not change appreciably. (a) Show that the restoring force on the mass can be given by F = -(2T∆y)/l (for small angles) (b) Derive an expression for the frequency of oscillation.
Answers
Answer:
(a) By small angle approximation, we have;
F = -2×T×Δy/l
(b) [tex]The \ frequency \ of \ oscillation, \ f = \dfrac{1}{2\cdot \pi }\cdot\sqrt{\dfrac{2 \cdot T}{l \cdot M} }[/tex]
Explanation:
(a) The diagram shows the mass, M, being restored by two equal tension, T acting on the elastic strings l, such the restoring force, F acts along the path of motion of the mass, with distance Δy
Therefore, the component of the tension T that form part of the restoring force is given as follows;
Let the angle between the line representing the extension of the elastic strings T and the initial position of the string = ∅
Then we have;
String force, [tex]F_{string}[/tex] = T×sin∅ + T×cos∅ + T×sin∅ - T×cos∅ = 2×T×sin∅
Whereby the angle is small, we have;
sin∅ ≈ tan∅ = Δy/l
Which gives;
[tex]F_{string}[/tex] = 2×T×sin∅ = 2×T×Δy/l (for small angles)
Restoring force F = [tex]-F_{string}[/tex] = -2×T×Δy/l
F = -2×T×Δy/l
(b) Given that the the tensions do not change appreciably as the mass, M, oscillates from Δy we have;
By Hooke's law, F = -k×x
Whereby Δy corresponds to the maximum displacement of the mass, M from the rest position, which gives;
Which gives;
F = M×a = -k×Δy
a = -k×Δy/M
d²(Δy)/dt² = -k×Δy/M
When we put angular frequency as follows;
ω² = k/M
We get;
d²(Δy)/dt² = -ω²×Δy
Which gives;
Δy(t) = A×cos(ωt + Ф)
The angular frequency is thus, ω = √(k/M)
Period of oscillation = 2·π/ω = 2·π/√(k/M)
The frequency of oscillation, f = 1/T = √(k/M)/(2·π)
Where:
k = 2·T/l, we have;
f = √(k/M)/(2·π) = √(2·T/l)/m)/(2·π)
The frequency of oscillation is given as follows;
[tex]f = \dfrac{1}{2\cdot \pi }\cdot\sqrt{\dfrac{2 \cdot T}{l \cdot M} }[/tex]
Related Questions
4. Going back to the dog whistle in question 1, what is the minimum riding speed needed to be able to hear the whistle? Remember, you can assume the following things: The whistle you use to call your hunting dog has a frequency of 21.0 kHz, but your dog is ignoring it. You suspect the whistle may not be working, but you can't hear sounds above 20.0 kHz. The speed of sound is 330 m/s at the current air temperature.
Answers
Answer:
The minimum riding speed relative to the whistle (stationary) to be able to hear the sound at 21.0 kHz frequency is 15.7 m/s
Explanation:
The Doppler shift equation is given as follows;
[tex]f' = \dfrac{v - v_o}{v + v_s} \times f[/tex]
Where:
f' = Required observed frequency = 20.0 kHz
f = Real frequency = 21.0 kHz
v = Sound wave velocity = 330 m/s
[tex]v_o[/tex] = Observer velocity = X m/s
[tex]v_s[/tex] = Source velocity = 0 m/s (Assuming the source is stationary)
Which gives;
[tex]20 = \dfrac{330- v_o}{330+0} \times 21[/tex]
330 - [tex]v_o[/tex] = (20/21)*330
[tex]v_o[/tex] = 330 - (20/21)*330 = 15.7 m/s
The minimum riding speed relative to the whistle (stationary) to be able to hear the sound at 21.0 kHz frequency = 15.7 m/s.
Are films just a means of entertainment? Do you think films are instructional in nature? What are the functions of films? what is the role of films in a society?
Answers
Answer:
Explanation:
Films are widely popular and their audio visual nature provides them a pervasive power for social influence. Therefore, they have the potential to play an important role as a medium of entertainment, information and education and as a catalyst for social change. Films are popular because they entertain.
Movies are about sitting in a theatre, watching something- watching a story unfold with people you don't know- watching that happen and emoting an emotion knowing that for those two hours or so, when one walks into that theatre, he/she don't have to worry about what is going on outside.
A refrigerator recieves 240 V of electricity. If it use 32 A of current, what is the resistance of the refrigerator?
Answers
Answer:
7.5 Ω
Explanation:
Voltage = Current x Resistance
(V = IR)
240 = 32 R
R = 240 / 32
= 7.5 Ω
Which of the following best represents a double replacement reaction?
A. AB → A + B
B. A + B → AB
C. A + BC → AC + B
D. AC + BD → AD + BC
Answers
Answer:
D. AC+BD -> AD +BC
Explanation:
I got it right
A double displacement reaction is also called the double replacement reaction or double decomposition reaction. Here AC + BD → AD + BC is a double displacement reaction. The correct option is D.
What is double displacement reaction?A double displacement reaction is defined as a chemical reaction in which the positive and negative ions of two ionic compounds exchange their places to form two new compounds. The general form of a double displacement reaction is given as:
AC + BD → AD + BC
Here 'A' and 'B' are positively charged cations, whereas 'C' and 'D' are negatively charged anions. The double displacement reactions generally occur between the substances in an aqueous solution. In order for a reaction to occur, one of the products is usually a solid precipitate, a gas or a molecular compound like water.
Thus the correct option is D.
To know more about double replacement reaction, visit;
https://brainly.com/question/13870042
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Write the equation for simple harmonic motion (x-t),(v-t), and find v at t=2s and t=3s if the object is initially at the right extreme of origin and moving in the negative x-direction. (A=2cm, T=8s)
Answers
Answer:
Explanation:
T = 8 s
angular frequency ω = 2π / T
= 2 π / 8
= π / 4
x ( t ) = A ( sinωt + π / 2 ) because initial phase difference is π / 2
= A cos ωt
= A cos π t / 4
v = Aω sinωt
= 2 x π / 4 sinωt
= .5 π sinπt / 4
when t = 2
v = .5 π sinπ x 2 / 4
= .5 π x 1
= 1.57 cm /s
At t = 3 s
v = .5 π sin π x 3 / 4
= .5 π sin 135°
= .5 π / √ 2
= 1.11 cm /s
A railroad car having a mass of 15 Mg is coasting at 1.5 m/s on a horizontal track. At the same time another car having a mass of 12 Mg is coasting at 0.75 m/s in the opposite direction. If the cars meet and couple together, determine the speed of both cars just after the coupling. Find the difference between the total kinetic energy before and after coupling has occurred. Explain qualitatively what happened to this energy.
Answers
Answer:
Explanation:
We shall apply law of conservation of momentum to know velocity after collision . Let it be v .
total momentum before collision = total momentum after collision
15 x 1.5 - 12 x .75 = ( 15 + 12 ) v
v = .5 m /s
kinetic energy before collision
1/2 x 15 x 1.5² + 1/2 x 12 x .75²
= 16.875 + 3.375
= 20.25 J
kinetic energy after collision
= 1/2 x ( 15 + 12 ) x .5²
= 3.375 J
Loss of energy = 16.875 J
This energy appear as heat and sound energy that is produced during collision .
1. A uniform magnetic field is directed vertically upwards. In which direction in this field should an alpha particle be projected so that it is deflected south ward? Name and state the rule you have used to find the direction in this case.
Answers
Answer:
1. Fleming's left hand rule
2. It must be projected towards the east
Explanation:
Fleming's left-hand rule states that; When a current-carrying conductor is placed in an external magnetic field, the conductor experiences a force perpendicular to both the field and to the direction of the current flow. This rule was first put forward by John Ambrose Fleming in the later part of the nineteenth century.
Hence if the thumb, fore finger and middle finger of the lefthand are held mutually at right angles to each other; the thumb shows the direction of motion, the fore finger shows the direction of the field while the middle finger shows the direction of the current.
Hence, if the alpha particle is projected eastwards(at right angles) to the uniform magnetic field, it will be deflected southwards in the magnetic field.
1. Analogies exist between rotational and translational physical quantities. Identify the rotational term analogous to each of the following: acceleration, force, mass, work, translational kinetic energy, linear momentum, impulse.
2. Explain why centripetal acceleration changes the direction of velocity in circular motion but not its magnitude.
Answers
Answer:
1) a α, m I, W=F.d W =τ . θ,
2) a = v²/r
Explanation:
1) The amounts of rotational and translational motion are related
acceleration is
a = d²x / dt²
linear displacement is equivalent to angular rotation, therefore angular acceleration is
α = d²θ / dt²
force in linear motion is equivalent to moment in endowment motion
F = m a
τ = I α
the mass is the inertia of the translation, in rotational motion the moment of inertia is the rotational inertia
I = m r²
Work is defined by W = F. d
in rotation it is defined by W = τ . θ
The linear momentum is p = mv
the angular momentum L = I w
momentum the linear motion is I = F dt
in the rotation it is I = τ dt
2) The velocity is a vector therefore it has modulus and direction, linear acceleration changes the modulus of velocity, whereas circular motion changes the direction (the other element of the vector).
[tex]a_{c}[/tex]Ac = v²/r
(b) Calculate the momentum when a mass of 40kg is moving with a velocity of 20m/s in the forward
direction.
Answers
Explanation:
momentum = mass x velocity
momentum = 40 x 20 = 800kgm/s
Answer:
800kgm/s
Explanation:
momentum= mass×velocity
= 40×20
= 800kgm/s
help me its emergency I need a correct answer please if you don't know then please dont guess
Answers
Answer:
True.
Explanation:
Total internal reflection is bound to occur when light travels from dense medium to less dense.
From the table given in the question above, we obtained:
Refractive Index of Crown glass = 1.52
Refractive Index of Asphalt = 1.635
From the above, Crown glass has a lower refractive index when compared to Asphalt. This means that Crown glass is less dense than Asphalt.
Therefore, total internal reflection will not occur when light travels from Crown glass to Asphalt because Crown glass is less dense than Asphalt.
A small pollutant particle falls to the ground through the air at rest with a speed limit of 0.3 mm / s. The particle has a mass of 10 ^ -10 g and the drag force is of the form bv. What is the value of b?
Answers
Answer:
3.3×10⁻⁹ kg/s
Explanation:
There are two forces on the particle: weight force pulling down and drag force pushing up. At terminal velocity, the speed is constant, so the acceleration is zero.
∑F = ma
bv − mg = 0
b = mg / v
b = (10⁻¹³ kg) (9.8 m/s²) / (3×10⁻⁴ m/s)
b = 3.3×10⁻⁹ kg/s
What is an electron?
A. A negative particle inside the nucleus
B. A negative particle outside the nucleus
C. A positive particle inside the nucleus
D. A particle inside the nucleus that has no charge
Answers
Answer:
B. A negative particle outside the nucleus
Explanation:
Electrons are very small particles orbiting outside of the nucleus of an atom. They carry negative charges.
The nucleus only contains protons and neutrons. Protons are positive, and neutrons have no charge (i.e. neutral)
Pink
Green
Red
Black
Blue
Yellow
Orange
"Milk colour"
what planet colour is that ??
thankyou for helping
Answers
Answer:
Pink - Pluto
Green - Mercury
Red - Mars
Black - Saturn
Blue - Neptune
Yellow - Jupiter
Orange - Jupiter
Milk Color - Venus
Explanation:
The galaxy is full of colors. There are various planets in the galaxy which are different colored. Their color is usually determined by the gases present there. The pink gases present near the Pluto makes Pluto appears to be of magenta or pink colored. The mercury is green colored because it reflects green rays. Mars is called the Red planet because of presence of Martin Rocks there.
7.Why are we able to drink cold drink with straw from a bottle?
Answers
Answer:
BETTER EXPLANATION
Explanation:
When you drink from a straw, you create a little space of low pressure inside your mouth and in the top of the straw. Then the air outside the straw pushes down on the surface of the drink and forces the liquid up through the straw and into your mouth.
(b) 360 days into seconds.
Sec
(c)
(d) A body has weight 60
0 N on the surface of the mars then what is its mass on the
[Ans: 157.89 kg)
What is weight of a body of mass 100 kg on the surface of the moon? [Ans: 166N]
Answers
Explanation:
(b) We know that,
1 day = 24 hours
1 hour = 3600 s
So, we found that, 1 day = 86400 s
We need to find the 360 days into seconds. So,
1 day = 86400 s
360 days = 86400×360
360 days = 31104000 seconds
(d) Weight of a body, W = 600 N
Acceleration due to gravity on mars is 3.7 m/s²
Weight, W = mg
m is mass of body
[tex]m=\dfrac{W}{g}\\\\m=\dfrac{600}{3.7}\\\\m=162.16\ kg[/tex]
(e) Mass of body, m = 100 kg
Acceleration due to gravity on the moon, 1.6 m/s²
Weight, W = 100 × 1.6
W = 160 N
A stone is dropped from a height of 49m and simultaneously another ball is thrown upward from the ground with a speed of 40m/s. when and where do the two stone meet
Answers
Answer:
S1 = 1/2 g t^2 distance stone falls in time t
S2 = Vy t - 1/2 g t^2 distance thrown stone rises in time t
H = 49 = S1 + S2 = Vy t
t = 49 / 40 sec time when stones meet
Check:
Stone 1 falls: 1/2 g t^2 = 1/2 * 9.8 * (49 / 40)^2 = 7.35 m
Stone 2 rises : 40 * (49 / 40) - 1/2 * 9.8 (49 / 40)^2 = 41.65 m
A carpenter measured the lengeth of a small piece of timber as 24.6cm .Calculate the relative error in the measurement if the true length is 24.5cm
Answers
ANSWER:
0.4081%
Explanation:
Difference=24.6-24.5=0.1
Relative error = 0.1/24.5*100=0.4081%
Relative error is equal to the = difference between both the values/The true value *100
Power is _________________the force required to push something the work done by a system the speed of an object the rate that the energy of a system is transformed the energy of a system
Answers
Answer:
[defined as]
Explanation:
it is the missing word
= 21000
19
20
= 19,950
TRY THESE
Amachinery worth 10.500 depreciated by 5% Find its value after one year
Find the population of a city after 2 years, which is at present 12 lakh, if the rate
of increase is 49
6
M
EXERCISE 8.3
Calculate the amount and compound interest on
원
(a) * 10,800 for 3 years at 12% per annum compounded annually.
125%
18,000 for 2 years at 10% per annum compounded annually.
(c) 62,500 for 12 years at 8% per annum compounded half yearly.
(d) *8,000 for 1 year at
at 9% per annum compounded half yearly.
(You could use the year by year calculation using SI formula to verify).
(e) $10,000 for 1 year 48% per annum compounded half yearly.
from Bant to buy a conter at a rate of 15% pa
Answers
One solution to minimize resonance with buildings is to ______ the width to span ratio.
Answers
Answer:
Increase
Explanation:
Resonance is a phenomenon which occurs when a body A in motion set another body B into motion of it own natural frequency. So for resonance to be minimize in a body is to increase the width to span ratio. So as to reduce the overall vibration which affects directly building resonance, the stiffness or trusses and girders should be increase. The increase in this aspect helps to reinforce building structure and support.
A polonium isotope with an atomic mass of 211.988868 u undergoes alpha decay, resulting in a daughter isotope with an atomic mass of 207.976652 u. Ignoring any recoil of the daughter, find the kinetic energy of the emitted alpha particle in megaelectronvolts (MeV).
Answers
Answer:
K = 9.53 MeV
Explanation:
The kinetic energy that the alpha particle has emitted, is the energy in excess after removing the resting energy of the atoms and the helium nucleus that forms the alpha particle
Since energy and masses are related and cannot be
m₀ c² = [tex]m_{f}[/tex] c² + m_He c²+ K
K = c² (m₀ - m_{f} - m_He)
the mass of the Helium atom is 4 u
K = (3 10⁸)² (211,988868 -207.976652 - 4,002) 1,661 10⁻²⁷
K = 14,949 10⁻¹¹ (0.0102)
K = 1,527 10⁻¹² J
let's reduce 1 J = 6,242 10¹² MeV
K = 9.53 MeV
Which property describes the amount of energy that flows past a given area
per unit of time?
A. Wavelength
B. Speed
c. Intensity
D. Pitch
Answers
Answer:
c. Intensity
Explanation:
Wavelength is a distance (meters).
Speed is distance per time (meters / second).
Intensity is power per area (Watts / square meter).
Pitch is frequency (cycles / second).
What are the signs of the velocity, force, and acceleration (components) afterthe cart is released and is moving qway from the motion sensor? (The positive xdirection is toward the motion sensor, to the right.
Answers
Answer:
car is moving away its direction is negative.
the speed must also be negative.
speed this distance decreases the acceleration is negative and if the speed is increasing the acceleration is positive.
Explanation:
In the exercise they indicate that the direction to the motion sensor is positive, as they indicate that the car is moving away its direction is negative.
The speed of the car is
v = (x₂-x₁) / t
As the positions are negative, and the car moves away the speed must also be negative.
The analysis for acceleration must be very careful if the speed this distance decreases the acceleration is negative and if the speed is increasing the acceleration is positive.
During a collision with another car, the occupants of a minivan initially travelling at 4.0 m/s come to a complete stop in 0.5 s. What was the acceleration of the occupants of the minivan?
a) 8.0 m/s2
b) –8.0 m/s2
c) 2.0 m/s2
d) –2.0 m/s2
Answers
Answer: b) - 8.0 [tex]m/s^{2}[/tex]
Explanation: Acceleration is a vector indicating a rate an object's velocity changes over time:
a = [tex]\frac{v}{t}[/tex]
and its SI unit is [tex]m/s^{2}[/tex]
For the minivan to stop, it takes a period of 0.5s:
a = [tex]\frac{4.0}{0.5}[/tex]
a = 8.0 [tex]m/s^{2}[/tex]
As a vector, acceleration has magnitude (8[tex]m/s^{2}[/tex]) and direction. Since it is stopping, the minivan has a direction opposite to the other car, which means acceleration is negative. So: a = [tex]- 8.0 m/s^{2}[/tex].
A wall in a house contains a single window. The window consists of a single pane of glass whose area is 0.15 m2 and whose thickness is 7 mm. Treat the wall as a slab of the insulating material Styrofoam whose area and thickness are 17 m2 and 0.20 m, respectively. Heat is lost via conduction through the wall and the window. The temperature difference between the inside and outside is the same for the wall and the window. Of the total heat lost by the wall and the window, what is the percentage lost by the window
Answers
Answer:
88 %
Explanation:
The rate of heat loss by a conducting material of thermal conductivity K, cross-sectional area,A and thickness d with a temperature gradient ΔT is given by
P = KAΔT/d
The total heat lost by the styrofoam wall is P₁ = K₁A₁ΔT₁/d₁ where K₁ =thermal conductivity of styrofoam wall 0.033 W/m-K, A₁ = area of styrofoam wall = 17 m², ΔT₁ = temperature gradient between inside and outside of the wall and d₁ = thickness of styrofoam wall = 0.20 m
The total heat lost by the glass window is P₂ = K₂A₂ΔT₂/d₂ where K₂ =thermal conductivity of glass window pane wall 0.96 W/m-K, A₂ = area of glass window pane = 0.15 m², ΔT₂ = temperature gradient between inside and outside of the window and d₂ = thickness of glass window pane = 7 mm = 0.007 m
The total heat lost is P = P₁ + P₂ = K₁A₁ΔT₁/d₁ + K₂A₂ΔT₂/d₂
Now, since the temperatures of both inside and outside of both window and wall are the same, ΔT₁ = ΔT₂ = ΔT
So, P = K₁A₁ΔT/d₁ + K₂A₂ΔT/d₂
Since P₂ = K₂A₂ΔT₂/d₂ = K₂A₂ΔT/d₂is the heat lost by the window, the fraction of the heat lost by the window from the total heat lost is
P₂/P = K₂A₂ΔT/d₂ ÷ (K₁A₁ΔT/d₁ + K₂A₂ΔT/d₂)
= 1/(K₁A₁ΔT/d₁÷K₂A₂ΔT/d₂ + 1)
= 1/(K₁A₁d₂÷K₂A₂d₁ + 1)
= 1/[(0.033 W/m-K × 17 m² × 0.007 m ÷ 0.96 W/m-K × 0.15 m² × 0.20 m) + 1]
= 1/(0.003927/0.0288 + 1)
= 1/(0.1364 + 1)
= 1/1.1364
= 0.88.
The percentage is thus P₂/P × 100 % = 0.88 × 100 % = 88 %
The percentage of heat lost by window of the total heat is 88 %
advantages of cutting crops with sickle ? please friends give this answer in easy way....
Answers
Answer: The only advantage cutting crops with a sickle is that its very effective for cutting lodged crops.
what is a primary source?
Answers
Answer:
A primary source is an original document such as diaries, speeches, manuscripts, letters, interviews, records, eyewitness accounts, autobiographies. Empirical scholarly works such as research articles, clinical reports, case studies, dissertation
Explanation:
Answer:
Scientific paper
Explanation:
A p e x
The gas in a balloon has T=280K and V=0.0279m^3. If the temperature increases to 320K at constant pressure, what is the new volume of the balloon? (Hint: n and P are constant) (Unit= m^3)
Answers
Answer:
[tex]\boxed{ V_{2}= 0.03189 m^3}[/tex]
Explanation:
According to Charles Law
=> [tex]\frac{V_{1}}{T_{1}} = \frac{V_{2}}{T_{2}}[/tex]
Where [tex]V_{1}[/tex] = 0.0279 m³, [tex]T_{1}[/tex] = 280 K and [tex]T_{2}[/tex] = 320 K
=> [tex]\frac{0.0279}{280} = \frac{V_{2}}{320}[/tex]
=> [tex]V_{2}[/tex] = 0.03189 m³
A very thin film of soap, of thickness 170 nm, in between air seems dark. On the other hand, when placed on top of glass some visible light is seen to shine from the film. How can this happen and what is the smallest visible light that creates constructive interference when we place the film on top of glass
Answers
Answer:
λ₀ = 2 d n
Explanation:
A soap film is a layer where the lus is reflected on the surface and on the inside of the film, these two reflected rays can interfere with each other either constructively or destructively.
Let's analyze the general conditions of this interference,
* When the ray of light reaches the surface of the film it is reflected, as the index of refraction of the air is less than the index of the film, the reflected ray has a phase change of 180º
* When the ray penetrates the film, its wavelength changes due to the refractive index of the film.
λ = λ₀ / n
where lick is the wavelength in the vacuum or air and n index of refraction of the film, in general this interference is observed perpendicular to the film, so the sine veils 1. the expression for constructive interference taking in what previous remains
2d = (m + ½) λ
the expression for destructive interference remains
2d = m λ
2d = m λ₀ / n
When the film is placed on a glass plate whose index of refraction is greater than the index of refraction of the film, in the reflection in the lower part of the film another phase difference of 180º is created, for which we have a difference of total phase of 180 +180 = 360º, which is equivalent to no phase difference, therefore the two previous equations are interchanged.
Therefore where we had destructive interference now a cosntructive interference happens we can see the reflected light.
Find us the wavelength that this constructive interference creates
2d n = m λ₀
λ₀ = 2 d n / m
To find the minimum wavelength, suppose we observe the first interference pattern m = 1
λ₀ = 2 d n
where d is the thickness of the film and n the index of refraction of the same
What does addition of two vectors give you?
Answers
Answer:
Explanation:
To add or subtract two vectors, add or subtract the corresponding components. Let →u=⟨u1,u2⟩ and →v=⟨v1,v2⟩ be two vectors. The sum of two or more vectors is called the resultant. The resultant of two vectors can be found using either the parallelogram method or the triangle method .