Answer:
Gravitational potential energy is greater for the rock [tex]20\; {\rm m}[/tex] above the river.
Explanation:
The gravitational field near the surface of the earth is approximately uniform. Let [tex]g[/tex] denote the strength of the gravitational field near the surface of the earth.
Let [tex]m[/tex] denote the mass of each rock. Assume that the gravitational potential energy of the two rocks is [tex]0[/tex] when the rocks are at the surface of the river.
When the rock is at a height of [tex]h[/tex] above the river, the gravitational potential energy ([tex]\text{GPE}[/tex]) of that rock would be [tex]\text{GPE} = m\, g\, h[/tex]. In other words, the [tex]\text{GPE}\![/tex] of the rock is proportional to its height relative to the ground.
Hence, among the two rocks, [tex]\text{GPE}[/tex] would be greater for the rock that is higher above the ground ([tex]20\; {\rm m}[/tex]) than the rock [tex]10\; {\rm m}[/tex] above the ground.
when 82.5 calories of heat are given to a metallic rod of mass 150g its temperature raises from 20 degree celcius to 25 degree Celsius. what is the specific heat of the metal.
A 150-g metallic rod with a specific heat of 0.11 cal/g.°C absorbs 82.5 calories of heat and its temperature increases from 20 °C to 25 °C.
What is specific heat?It is the heat required to raise the temperature of the unit mass of a given substance by a given amount (usually one degree).
A metallic rod of mass 150 g (m) absorbs 82.5 cal of heat (Q) and its temperature raises from 20 °C to 25 °C. We can calculate the specific heat (c) of the metal using the following expression.
Q = c × m × ΔT
c = Q / m × ΔT
c = 82.5 cal / 150 g × (25 °C - 20 °C) = 0.11 cal/g.°C
A 150-g metallic rod with a specific heat of 0.11 cal/g.°C absorbs 82.5 calories of heat and its temperature increases from 20 °C to 25 °C.
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A space probe sent to Mars has a weight of 10,000 N on Earth (g = 10). What is its mass?
Answer:
[tex]1,\!000\; {\rm kg}[/tex].
Explanation:
The "[tex]g[/tex]" given in the question likely refers to the strength of the gravitational field. The standard unit of [tex]g[/tex] is [tex]{\rm m \cdot s^{-2}}[/tex], same as the standard unit of acceleration. However, since [tex]1\; {\rm N} = 1\; {\rm kg \cdot m \cdot s^{-2}[/tex], the standard unit of [tex]g[/tex] is equivalent to [tex]{\rm N \cdot kg^{-1}}[/tex].
For instance, the gravitational strength on the surface of the earth is approximately [tex]g = 10\; {\rm N \cdot kg^{-1}}[/tex]. However, the question did not specify the unit of this value.
If the mass of an object is [tex]m[/tex], the weight of that object would be [tex](\text{weight}) = m\, g[/tex] when the gravitational field strength around that object is [tex]g[/tex]. It is given that for the object in this question, [tex]m\, g = (\text{weight}) = 10,\!000\; {\rm N}[/tex] when [tex]g = 10\; {\rm N \cdot kg^{-1}}[/tex]. Therefore, the mass [tex]m\![/tex] of this object would be:
[tex]\begin{aligned}m &= \frac{(\text{weight})}{g} \\ &= \frac{10,\!000\; {\rm N}}{10\; {\rm N \cdot kg^{-1}}} \\ &= 1,\! 000\; {\rm kg}\end{aligned}[/tex].
A cup of tea at room temperature of 24°C is heated until it has twice the internal energy. Calculate the final temperature of the tea.
The final temperature of the tea cup is 100°C.
What is internal energy?The Internal energy is the energy of a substance due to to the constant random motion of its particles.
The symbol for internal energy of a substance is U and it is measured in Joules.
ΔU = q + W
q is the heat, q = mcΔTW is the mechanical work.In conclusion, the final temperature of the tea cup at room temperature of 24 °C which is heated until it has twice the internal energy is 100°C.
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What is the mass of mars
the mass of mars is
6.39 × 10^23 kg
Hi! Whoever can answer this question the best I will give the brainliest answer!!
Describe the structure of a battery and how it works.
Thank you!! ✨
In an attempt to escape his island, Gilligan builds a raft and sets to sea. The wind shifts a great deal during the day, and he is blown along the following straight lines:
2.5 km 45° north of west; then
4.70 km 60° south of east; then
5.1 km straight east; then
7.2 km 55° south of west; and finally
2.8 km 5° north of east.
What is his final position relative to the island?
km
° south of east
The final position of Gilligan in kilometers and degrees south of east relative to the island is 9.07 km, 61.4° south of east.
What is a vector simple ?A vector is a quantity or phenomenon that has two independent properties: magnitude and direction.
The term also denotes the mathematical or geometrical representation of such a quantity.
According to the question,
Suppose, the direction east as i, direction west as -i, direction north as j and direction south as j.
Therefore,
1. : 2.5 km 45° north of west
[tex]= 2.5 cos45 (-i) + 2.5 cos45 (j)\\ = -1.77(i) + 1.77(j)[/tex]
2. : 4.7 km 60° south of east
[tex]= 4.7 cos60 (i) + 4.7 sin60 (-j) \\= 2.35(i) - 4.07(j)[/tex]
3. : 5.1 km straight east
[tex]=5.1(i)[/tex]
4 : 7.2 km 55° south of west
[tex]= 7.2 cos55 (-i) + 7.2 sin55 (-j)\\ = -4.13(i) - 5.9(j)[/tex]
5: 2.8 km 5° north of east
[tex]= 2.8 cos5 (i) + 2.8 sin5 (j)\\= 2.79(i) + 0.24(j)[/tex]
The sum of all the above yields,
[tex]R = 4.34(i) + 7.96(-j)[/tex]
The magnitude of the resultant is:
[tex]|R| =\sqrt{4.34^{2} + (-7.96)^{2} }= 9.07[/tex]
The angle that the resultant makes is as follows.
θ= [tex]tan^-^1(\frac{7.96}{4.34} )\\[/tex]
θ = 61.4°
Hence,
Final position relative to the island is 9.07 km, 61.4° south of east.
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PLS HELP:
Find the magnitude of an electric field located 7.00 cm from a source charge of - 11 nC. (1nC = 1 x 10-9 C). Will the field lines point toward or away from the source charge? Show your work and include an electric field diagram assuming the source is a point charge
Answer:
E=kQ/r*2
=(9. 10*9)(11.10*-9)/(0,07)*2
=20204 N. C*-1
The field lines will point towards the source charge because it is negatively charged.
If the current in a wire increases from 5A to 10A, what happens to its magnetic field?
If the current in a wire increases from 5A to 10A, the magnetic field generated will also be doubled.
IntroductionHi ! I will help you to discuss about "magnetic field around a conducting wire". A conducting wire that carried electric current can generate amount of magnetic fields. In a standard winding condition, the increase number of electric current will be proportional to the increase number of the generated magnetic field. In other condition, the increase in distance (between center of field with a point) will be inversly proportional to the increase in the generated magnetic field. So, the magnetic field that generated around a current-carrying wire can be expressed in the following equation.
[tex] \boxed{\sf{\bold{B = \frac{\mu_0 \cdot I}{2\pi \cdot d}}}}[/tex]
With the following condition:
B = perceived magnetic field at a point (Wb/m² or T)[tex]\sf{\mu_0}[/tex] = vacuum permeability = [tex]\sf{4\pi \times 10^{-7} \: Wb/A.m}[/tex] I = electric current (A)d = distance of a point from the wire (m)Problem SolvingWe can assume that:
Only the increase in current affects the change in the value of the magnetic field.Other provisions such as the distance of the point from the conducting wire is considered the same.We know that :
[tex]\sf{I_1 : I_2}[/tex] = 5 : 10 = 1 : 2 >> the ratio between the current flowing in first and second sample.[tex]\sf{d_1 : d_2}[/tex] = 1 : 1What was asked ?
B = perceived magnetic field at a point = ... : ...Step by step :
[tex] \sf{B_1 : B_2} [/tex]
[tex] \sf{\frac{\cancel{\mu_0} \cdot I_1}{\cancel{2\pi} \cdot d_1} : \frac{\cancel{\mu_0} \cdot I_2}{\cancel{2\pi} \cdot d_2}} [/tex]
[tex] \sf{\frac{I_1}{d_1} : \frac{I_2}{d_2}} [/tex]
[tex] \sf{\frac{I_1}{\cancel d} : \frac{I_2}{\cancel d}} [/tex]
[tex] \sf{I_1 : I_2} [/tex]
[tex] \boxed{\sf{\bold{1 : 2}}} [/tex]
ConclusionFrom the above comparison, we can see that the ratio of the magnetic field at a point will be the same as the ratio of the current flowing through the conducting wire is 1 : 2. So, The magnetic field generated will also be doubled.
A ball is rolling across the floor at a constant velocity. What is the value of the change in its kinetic energy, ΔEk?
Positive
Zero
Negative
B. When the ball is rolling across the floor at a constant velocity, the change in its kinetic energy is zero.
What is change in kinetic energy?
The change in kinetic energy of an object is the dereference between the final kinetic energy and the initial kinetic energy.
ΔK.E = K.Ef - K.Ei
ΔK.E = 0.5m(vf² - vi²)
where;
K.Ef is the final kinetic energyK.Ei is the initial kinetic energyvf is final velocityvi is initial velocityAt constant velocity, the initial velocity and final velocity are equal.
ΔK.E = 0.5m(0) = 0
Thus, when the ball is rolling across the floor at a constant velocity, the change in its kinetic energy is zero.
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What is standard one kilogram ?
Answer:
As of the 2019 redefinition of the SI base units, the kilogram is defined in terms of the second and the metre, both based on fundamental physical constants.
It is defined as the mass of a particular international prototype made of platinum-iridium and kept at the International Bureau of Weights and Measures. It was originally defined as the mass of one liter (10-3 cubic meter) of pure water. At the Earth's surface, a mass of 1 kg weighs approximately 2.20 pounds ( lb ).
Explanation:
A frog leaps from flat ground at 6.32 m/s
at a 36.3 angle. What maximum height
does it reach?
(Unit = m)
Answer:
.714 m
Explanation:
The VERTICAL component is all we are interested in for this Q
Vertical velocity = 6.32 m/s sin 36.3° = 3.742 m/s
Vertical displacement = vo t - 1/2 at^2
= -1/2 at^2 + vo t
max occurs at - b/2a = -3.742/ (2(-1/2(9.81)) = .3814 sec
then vot-1/2 at^2 =
3.742 (.3814) - 1/2 ( 9.81)(.3814^2) = .714 m
Answer:
.714
Explanation:
For the circuit shown in the figure, the switch S is initially open and the capacitor is uncharged. The switch is then closed at time t = 0. How many seconds after closing the switch will the energy stored in the capacitor be equal to 50.2 mJ?
Hi there!
To start, we can use the equation for the charge of a capacitor versus time.
[tex]q(t) = C\epsilon (1 - e^{-\frac{t}{\tau}})[/tex]
[tex]q(t)[/tex] = Charge on capacitor vs. time
[tex]\epsilon[/tex] = EMF of battery (40 V)
**Note: 'Cε' is equal to the MAXIMUM CHARGE on a capacitor.
Where the time constant is given as:
[tex]\tau = RC[/tex]
[tex]\tau[/tex] = Time Constant (s)
[tex]R[/tex] = Resistance (0.5 MΩ)
[tex]C[/tex] = Capacitance (90 μF)
Let's first convert the given units to the necessary 'J', 'Ω' and 'F' to make things easier:
[tex]J = 50.2 mJ[/tex]
[tex]50.2 mJ * \frac{0.001J}{1mJ} = 0.0502 J[/tex]
[tex]R = 0.5 M\Omega\\\\0.5M\Ohm * \frac{1000000\Omega}{1M\Ohm} = 500000\Omega[/tex]
[tex]F = 90 \mu F[/tex]
[tex]90 \mu F * \frac{0.000001 F}{1\mu F} = 0.00009 F[/tex]
Now, let's calculate the time constant.
[tex]\tau = RC = (500000)(0.00009) = 45 s[/tex]
Time to use the equation for energy stored in a capacitor:
[tex]E_C = \frac{1}{2}\frac{Q^2}{C}[/tex]
Our 'Q' varies with time, so:
[tex]E(t)= \frac{1}{2}\frac{( C\epsilon (1 - e^{-\frac{t}{\tau}}))^2}{C}\\\\E(t) = \frac{1}{2}\frac{( C^2\epsilon^2 (1 - e^{-\frac{t}{\tau}})^2)}{C}\\\\E(t) = \frac{1}{2}( C\epsilon^2 (1 - e^{-\frac{t}{\tau}})^2)[/tex]
Let's now plug values into our equation.
[tex]0.0502 = \frac{1}{2}(0.00009)(40^2) (1 - e^{-\frac{t}{45}})^2[/tex]
Simplifying:
[tex]0.697 = (1 - e^{-\frac{t}{45}})^2[/tex]
Take the square root of both sides.
[tex]0.835 = 1 - e^{-\frac{t}{45}}\\\\ e^{-\frac{t}{45}} = 0.165[/tex]
Take the natural log of both sides.
[tex]-\frac{t}{45} = ln(0.165) \\\\\frac{t}{45} = 1.802\\\\t = \boxed{81.08 s}[/tex]
a man carries a hand bag by hanging on his hand and moves horizontally where the bag does not move up or down. What is the work done on the bag? The man gets tired after sometime of the movement. Why?
The work done by the man is the product of his applied force and the displacement of the bag and the man gets tired because his internal energy has be converted to work.
What is work done by the man?The work done by the man is the product of his applied force and the displacement of the bag.
Why the man gets tiredThe man gets tired because his internal energy has be used to do work on the bag.
Thus, the work done by the man is the product of his applied force and the displacement of the bag and the man gets tired because his internal energy has be converted to work.
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A thin flexible gold chain of uniform linear density has a mass of 17.1 g. It hangs between two 30.0 cm long vertical sticks (vertical axes) which are a distance of 30.0 cm apart horizontally (x-axis), as shown in the figure below which is drawn to scale.
Evaluate the magnitude of the force on the left hand pole.
The magnitude of the force on the left-hand pole is mathematically given as
f'=0.167N
Q=45 degrees
What is the magnitude of the force on the left-hand pole.?Generally, the equation for Force is mathematically given as
[tex]\frac{mg}{sin \theta}[/tex]
Therefore
[tex]F=\frac{17.1*10^{-3}*9.8}{sin45}[/tex]
F=0.237N
Considering horizontal axis or plane
f'-fcos=0
Therefore
f'=0.237*cos45
f'=0.167N
In conclusion, the slope
[tex]tan\theta= 30/30\\\\tan\theta=1\\\\\theta=45[/tex]
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Mithun wants to test if a convex lens produces an inverted image of an object placed at a distance away from the lens. Which of the following should he use directly as an object for the test?
a. A
b. B
c. C
d. D
Answer:
(D) any of these objects can be used as long as all points on the object lie farther away from the lens than the focal length of the lens.
Points lying between the focal point and the lens will be erect and will not form an object visible on a screen.
D
Question 2
What are the coefficients needed to balance this chemical equation?
___O₂ → CO₂ +___ H₂O
C₂H5OH +_
O 6, 2, 6, 4
O 6, 6, 2,4
O 1, 3, 2, 3
1, 2, 2, 1
2 pts
Hello and Good Morning/Afternoon:
Original Question: C₂H₅OH + __O₂ → __CO₂ + __ H₂O
To balance this equation:
⇒ must ensure that there is an equal number of elements on both sides of the equation at all times
Let's start balancing:
On the left side of the equation, there are 2 carbon molecule⇒ but only so far one on the right side
C₂H₅OH + __O₂ → 2CO₂ + __ H₂O
On the left side of the equation, there are 6 hydrogen molecules⇒ but only so far two on the right side
C₂H₅OH + __O₂ → 2CO₂ + 3H₂O
On the right side of the equation, there are 7 oxygen molecules⇒ but only so far three on the left side
C₂H₅OH + 3O₂ → 2CO₂ + 3H₂O
Let's check and make sure we got the answer:
C₂H₅OH + 3O₂ → 2CO₂ + 3H₂O
2 Carbon ⇔ 2 Carbon
6 Hydrogen ⇔ 6 Hydrogen
7 Oxygen ⇔ 7 oxygen
Thefore the coefficients in order are:
⇒ 1, 3, 2, 3
Answer: 1,3,2,3
Hope that helps!
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A cart is being pulled forward by a hanging mass. What is the value of the change in its kinetic energy, ΔEk?
Positive
Zero
Negative
The value of change in kinetic energy, ΔEk when a cart is being pulled forward by a hanging mass is Positive
In order words, ΔEk in the above question is positive
What is kinetic energy?Kinetic energy can be defined as the energy a body possess when the body is in motion or due its motion
In conclusion, the value of change in kinetic energy, ΔEk when a cart is being pulled forward by a hanging mass is Positive
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Vanessa made a list comparing the differences between the outer coverings in plants and animals, but she made a mistake. Read the table and then choose the statement that explains why the list is incorrect. Structure Description of Function Spines Protects the plant from predators and helps increase water loss Skin Protects the animal from changes in weather and its environment The skin is a reproductive organ. The skin offers little protection against the weather. The spines attract predators. The spines help decrease water loss.
The skin is NOT a reproductive organ and the spines attract predators are the incorrect statements.
Why the list is incorrect?The list is incorrect because skin is not a reproductive organ and the spines do not attract predators towards each other. Skin protects the body from the outer environment whereas the spines repel the predators from the plant body.
So we can conclude that the skin is NOT a reproductive organ and the spines attract predators are the incorrect statements.
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The bars in the drawing above are magnets. According to chapter 21 which of the following picture(a) is true? Explain. Then explain why the other 2 pictures are incorrect. Make sure to explain all 3 sets.
Magnets are materials which are able to attract others to themselves by producing a magnetic field.
Based on the properties of magnetic lines of forces;
Picture 1 is correct because the magnetic lines of forces originate from the North pole and are directed towards the south pole.Picture 2 is incorrect because unlike poles attractPicture 3 is incorrect because like poles repel.In conclusion, the law of magnetism states that like poles repel whereas unlike poles attract.
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A car moves at a speed of 45 km/h, when traveling 1500 meters, how long did it take to go that distance?
A proton has a positive electric charge of q = 1.6 × 10–19 coulombs. what is the electric potential at a point 5.3 × 10–11 m from the proton? 4.4 × 10–18 volts 2.7 × 101 volts 3.0 × 10–9 volts 5.1 × 101 volts
B. The electric potential at the given point from the proton is 2.7 x 10¹ volts
Electric potential of the proton
The electric potential of the proton is calculated as follows;
V = kq/r
where;
k is Coulomb's constantq is charger is distanceV = (9 x 10⁹ x 1.6 x 10⁻¹⁹)/(5.3 x 10⁻¹¹)
V = 27.2 volts
V = 2.7 x 10¹ volts
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What is the maximum height that the water would reach in the internal network of a building, without the use of a pump, if the pressure at the sidewalk level is 1.3 kgf/cm2? (density of water 1000 kg/m3)
The maximum height to be reached by the water at the given pressure is 13 m.
Maximum height reached by the water
The maximum height to be reached by the water is calculated as follows;
P = ρgh
where;
P is the pressure of the waterρ is the density of the waterg is acceleration due to gravityh is the maximum height1 kgf/cm² = 98066.5 Pa = 98066.5 N/m²
1.3 kgf/cm² = 127486 N/m²
h = P/ρg
h = (127486)/(1000 x 9.8)
h = 13 m
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Which of these must be the same on both
sides of a balanced chemical equation?
A the number of atoms
B
the number
C the number
D the number of solids, liquids, and gases
of compounds
of molecules
Answer:
the total number of atoms of each element present is the same on both sides of the equation. (if I remember correctly)
A roller coaster has a mass of 450 kgIt sits at the top of a hill with height 49 m. If it drops from this hill, how fast is it going when it reaches the bottom? Assume there is no air resistance or friction.)
The speed of the roller coater at the bottom of the hill is 31 m/s.
Speed of the roller coater at the bottom of the hill
Apply the principle of conservation of mechanical energy as follows;
K.E(bottom) = P.E(top)
¹/₂mv² = mgh
v² = 2gh
v = √2gh
where;
v is the speed of the coater at bottom hillh is the height of the hillg is acceleration due to gravityv = √(2 x 9.8 x 49)
v = 31 m/s
Thus, the speed of the roller coater at the bottom of the hill is 31 m/s.
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Hellowww..... =)
What is atomic number ?..
Answer:
The atomic number is the number of protons in an element
Farsightedness is corrected with a ___ lens.
Farsightedness is corrected with a convex lens. The correct answer is a convex lens.
The center and edges of a convex lens alternate in thickness. Convergence or focus of the light rays caused by the passage of light through a convex lens aids in projecting the picture onto the retina of the eye. As a result, the person can see items in their immediate surroundings more clearly and the greater focus length of the eye is balanced.
In order to have a positive focal length, a convex lens must be thicker in the middle and narrower in the corners. A convex lens causes light to bend inward and towards its center as it travels through it. By bending the light, the focal point is brought closer to the lens and helps to focus the incoming light rays.
Hence, farsightedness is corrected with a convex lens. The correct answer is a convex lens.
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Under normal conditions the human heart converts about 13.0 J of chemical energy per second into 1.30 W of mechanical power as it pumps blood throughout the body. (a) Determine the number of Calories required to power the heart for one day
The energy (in calories) required to power the heart for one day is 268.32 Cal
How to convert 1 day to seconds1 day = 24 h
24 h = 24 × 60 = 1440 mins
1440 mins = 1440 × 60 = 86400 s
Thus,
1 day = 86400 s
How to determine the energy (in calories) for 1 day (86400 s)From the question given,
1 s = 13 J
Therefore,
86400 s = 86400 × 13
86400 s = 1123200 J
Divide by 4186 to express in calories
86400 s = 1123200 / 4186
86400 s = 268.32 Cal
Thus, the energy needed to power the heart for 1 day is 268.32 Cal
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Complete question
Under normal conditions the human heart converts about 13.0 J of chemical energy per second into 1.30 W of mechanical power as it pumps blood throughout the body. (a) Determine the number of Calories required to power the heart for one day given that 1 Calorie equals 4186
Two forces F1=20N and F2=30N are acting on an object as shown in figure: F1=20N F2=30N (i) Find the net force acting on the object? (ii) State the direction of the net force acting on the object? (iii) If the body still does not move under the application of these forces, what can be the possible reason for this? Identify the name of this extra force and its direction. Two forces F1 = 20N and F2 = 30N are acting on an object as shown in figure : F1 = 20N F2 = 30N ( i ) Find the net force acting on the object ? ( ii ) State the direction of the net force acting on the object ? ( iii ) If the body still does not move under the application of these forces , what can be the possible reason for this ? Identify the name of this extra force and its direction .
The net force is the 10N force and its direction is towards F2 force.
What is resultant force?The resultant force or the net force is the actual force that acts on a body. We are told that the two forces act in opposite directions hence the net force is F2 - F1 = 30 N - 20 N = 10 N.
ii) The direction of this net force is going to be towards the 30N force.
iii) If the body does not move under the application of these forces then the F1 force must be reinforced by another force which balances it against the F2 force.
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Two loudspeakers, 3.5 m apart and facing each other, play identical sounds of the same frequency. You stand halfway between them, where there is a maximum of sound intensity. Moving from this point toward one of the speakers, you encounter a minimum of sound intensity when you have moved 0.15 m . Assume the speed of sound is 340 m/s .
a. What is the frequency of the sound?
b. If the frequency is then increased while you remain 0.15 m from the center, what is the first frequency for which that location will be a maximum of sound intensity?
For the given question the answer to the first part is that frequency of sound will be 404.76 Hz. and answer to the second part will be that the initial frequency for which that place will have the highest level of sound intensity
Given, the speed of sound 340 m/s
a) L1 + L2 = 3.5 m
and Ld = | L1 - L2 | = ( 1.75 + 0.21 ) - (1.75 - 0.21 ) = 1.96 - 1.54 = 0.42 m
Ld = λ/2
λ = 2Ld = 2×0.42 = 0.84 m
and finally,
f = v/λ
f = 340/0.84
f = 404.76 hertz
Frequency came out to be 404.76 hertz in this case
b) For the first frequency
0.42 = λ
f = v/λ
f = 340 / 0.42
f = 809.52 Hertz
Frequency came out to be 809.52 Hertz in this case.
To conclude with we can say that the Frequency of the sound in case on came out to be 404.76 hertz which is approximately 405 Hz after applying all the concepts and calculations, in second case first frequency for which that location will be a maximum of sound intensity came out to be 809.52 Hertz after applying all the concepts and calculations.
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A solid, homogeneous sphere with of mass of M = 2.35 kg and a radius of R = 12.9 cm is resting at the top of an incline as shown in the figure.
The height of the incline is h = 1.29 m, and the angle of the incline is θ = 20.1°. The sphere is rolled over the edge very slowly. Then it rolls down to the bottom of the incline without slipping.
What is the total kinetic energy (translational plus rotational kinetic energy) of the sphere when it reaches the bottom of the incline?
The total kinetic energy of the sphere when it reaches the bottom of the incline is 44.57 J.
Total kinetic energy of the sphereThe total kinetic energy of the sphere = translational + rotational kinetic energy.
Translational kinetic energyK.E = ¹/₂mv²
K.E(bottom) = P.E(top) = mgh
K.E = (2.35)(9.8)(1.29)
K.E = 29.71 J
Rotational kinetic energyK.E(rot) = ¹/₂Iω²
K.E(rot) = ¹/₂I(v²/R²)
where;
I is rotational kinetic energyI = ¹/₂MR²
K.E(rot) = ¹/₂( ¹/₂MR²)(v²/R²)
K.E(rot) = ¹/₄Mv²
K.E(rot) = ¹/₄M(2gh)
K.E(rot) = ¹/₂Mgh
K.E(rot) = ¹/₂(29.71) = 14.855 J
Total kinetic energy = 29.71 + 14.855 = 44.57 J
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