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
define motion also justify that rest and motion are related terms
Answers
Answer;
Motion: A body is said to be in motion if it changes its position with respect to its surroundings.
Explanation:
Rest and motion are the relative terms because they depend on the observer's frame of reference. So if two different observers are not at rest with respect to each other, then they too get different results when they observe the motion or rest of a body .
one example for each. Rest: If a body does not change its position with respect to its surroundings, the body is said to be at rest. ... Motion: A body is said to be in motion if it changes its position with respect to its surroundings.
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
Two long, straight wires are parallel and 10 cm apart. One carries a current of 2.0 A, the other a current of 5.0 A. If the two currents flow in opposite directions, what is the magnitude and direction of the force per unit length of one wire on the other
Answers
Answer:
The magnitude and direction of the force per unit length of one wire on the other is 2 x 10⁻⁵ N/m, attractive force.
Explanation:
Given;
distance between the two parallel wires, r = 10 cm = 0.1 m
current in the first wire, I₁ = 2A
current in the second wire, I₂ = 5 A
The force per unit length on each wire can be calculated as;
[tex]\frac{F}{L} = \frac{\mu_oI_1I_2}{2\pi r}[/tex]
where;
μ₀ is permeability of free space = 4π x 10⁻⁷ m/A
[tex]\frac{F}{L} = \frac{\mu_oI_1I_2}{2\pi r} \\\\\frac{F}{L} = \frac{4\pi*10^{-7}*2*5}{2\pi *0.1} \\\\\frac{F}{L} = 2 *10^{-5} \ N[/tex]/ m
The direction of the force between the two wires is attractive since the current in the two wires are in opposite direction.
Therefore, the magnitude and direction of the force per unit length of one wire on the other is 2 x 10⁻⁵ N/m, attractive force.
A machine takes 0.5 seconds to move a brick 1 meter and put 100 Joules of energy into it. (hint: Power is the amount of energy transferred or converted per unit time. Or we say power is work done per unit time. LaTeX: P\:=\:\frac{W}{t}P = W t) This machine would expend more power in this action if it:
Answers
Answer:
200 Watts.
Explanation:
Power is defines as the amount of work expended per unit time. Mathematically, it is expressed as Power = Workdone/Time
Given parameters
Energy used up 100Joules
Distance moved by brick = 1 meters
Time taken by the machine = 0.5 secs
Power can also be written as Energy/Time
Required
We need to calculate the amount of power used up.
Power = 100J/0.5s
Power = 100/(1/2)
Power = 100 * 2/1
Power = 200Watts.
This shows that the machine would expend 200Watts of power
PLEASE HELP ASAP. IT'S URGENT
Answers
Answer:
Q1 acceleration = 16m/s²
Q2 Net force = 9N North
Explanation:
Q1 Using the formula F=ma
Q2 R = F1 + F2
When we double the distance between a source of light and the
surface on which it falls, the amount of illumination on the surface
decreases to
(what fraction) of the
original illumination.
Answers
The amount of lighting on a surface drops to (1/4) of the initial illumination when the distance between a light source and the surface it falls on is doubled.
What is illumination?The amount of light or luminous flux that falls on a surface is known as illumination. It is expressed as lux or lumens per square meter.
The square of the distance has an inverse relationship with the light intensity;
[tex]\rm I = \frac{1}{r^2}[/tex]
Where,
I is the light intensity
r is the distance
Let r is the distance and I is the sound intensity for case 2;
r' = 2r
[tex]\rm I' = \frac{1}{(2r)^2} \\\\ I' = \frac{1}{4r^2} \\\\ I' = \frac{I}{4}[/tex]
When we double the distance between a source of light and the surface on which it falls, the amount of illumination on the surface decreases to(1/2) of the original illumination.
Hence the value of the fraction is 1/4.
To learn more about the illumination refer;
https://brainly.com/question/20160684
#SPJ2
a 6 letter word a way of explaining an object or event using a set of facts
Answers
Explanation:
A theory is a way of explaining an object or event using a set of facts.
A 24 cm radius aluminum ball is immersed in water. Calculate the thrust you suffer and the force. Knowing that the density of aluminum is 2698.4 kg / m3
Answers
Answer:
W =1562.53 N
Explanation:
It is given that,
Radius of the aluminium ball, r = 24 cm = 0.24 m
The density of Aluminium, [tex]d=2698.4\ kg/m^3[/tex]
We need to find the thrust and the force. The mass of the liquid displaced is given by :
[tex]m=dV[/tex]
V is volume
Weight of the displaced liquid
W = mg
[tex]W=dVg[/tex]
So,
[tex]W=dg\times \dfrac{4}{3}\pi r^3\\\\W=2698.4\times 10\times \dfrac{4}{3}\times \pi \times (0.24)^3\\\\W=1562.53\ N[/tex]
So, the thrust and the force is 1562.53 N.
Two trains run in the opposite direction with speeds of v1 = 15 m / s and v2 = 20 m / s. A passenger on the first train (the one on v1) notes that train 2 takes 6 s to pass on its side. What is the length of the second train? (The passenger is supposed to be immobile looking through the window)
Answers
Answer:
210 m
Explanation:
The speed of train 2 relative to train 1 is 15 m/s + 20 m/s = 35 m/s.
It takes 6 seconds for the train to pass, so the length of the train is:
(35 m/s) (6 s) = 210 m
1. A note has a wavelength of 0.77955 m. If the speed of sound is 343.00 m/s, what pitch is this note? 2. A note has a wavelength of 0.52028 m. If the speed of sound is 343.00 m/s, what pitch is this note? please no funny answers
Answers
Answer:
1.) 440 Hz
2.) 659.3 Hz
Explanation:
1.) Given parameters are:
wavelength = 0.77955 m.
speed of sound = 343.00 m/s
Frequency = speed/ wavelength
Substitute speed and wavelength into the formula
Frequency = 343/ 0.77955
Frequency = 439.99
Frequency = 440 Hz approximately
2.) The parameters given are:
wavelength = 0.52028 m.
speed of sound = 343.00 m/s
Using the same formula
Frequency = speed/wavelength
Substitute all the parameters into the formula
Frequency = 343 / 0.52028
Frequency = 659.3 Hz approximately
The pitch of a note depends on the frequency of the sound waves.
The pitch of a sound increases as the frequency of the sound waves increases.
Answer:
1.) 440 Hz
2.) 659.3 Hz
Explanation:
1.) Given parameters are:
wavelength = 0.77955 m.
speed of sound = 343.00 m/s
Frequency = speed/ wavelength
Substitute speed and wavelength into the formula
Frequency = 343/ 0.77955
Frequency = 439.99
Frequency = 440 Hz approximately
2.) The parameters given are:
wavelength = 0.52028 m.
speed of sound = 343.00 m/s
Using the same formula
Frequency = speed/wavelength
Substitute all the parameters into the formula
Frequency = 343 / 0.52028
Frequency = 659.3 Hz approximately
The pitch of a note depends on the frequency of the sound waves.
The pitch of a sound increases as the frequency of the sound waves increases.
A spherical mirror gives an image magnified 5 times at a distance 5 m. determine whether the mirror is convex or concave? How much will be the focal length of the mirror?
Answers
Answer:
1. Concave mirror.
2. 4.17 m or 417 cm.
Explanation:
The following data were obtained from the question:
Object distance (u) = 5 m
Magnification (M) = 5
Focal length (f) =..?
1. Identification of the mirror.
To determine whether or not the mirror is concave or convex, we must first of all calculate the image distance.
This can be obtained as follow:
Object distance (u) = 5 m
Magnification (M) = 5
Image distance (v) =.?
Magnification (M) = image distance (v) /object distance (u).
M = v/u
5 = v/5
Cross multiply
v = 5 x 5
v = 25 m
Since the image distance obtained is positive, the mirror is said to be a concave mirror.
2. Determination of the focal length of the mirro.
This can be obtained as follow:
Object distance (u) = 5 m
Image distance (v) = 25 m
Focal length (f) =...?
1/f = 1/v + 1/u
1/f = 1/25 + 1/5
1/f = 0.04 + 0.2
1/f = 0.24
Cross multiply
f x 0.24 = 1
Divide both side by 0.24
f = 1/0.24
f = 4.17 m
Converting the focal length of cm, we have:
1 m = 100 cm
Therefore, 4.17 m = 4.17 x 100 = 417 cm
Therefore, the focal length of the mirror is 4.17 or 417 cm.
The following passage has not been edited. There is an error in each line. Write the
incorrect word and the correction in your answer sheet against the correct question
number. The first one has been done as an example. ( 1 x 4 = 4 )
Community service sensitize people to Error: sensitize ; Correction: sensitizes
other‟s needs and supports inclusive (a) Error: _______ ; Correction: ______
development to the underprivileged (b) Error: _______ ; Correction: ______
sections with society. Courses about social (c) Error: ______ ; Correction: _______
work prepares frontline workers to (d) Error: _______ ; Correction: ______
Answers
Answer:
(a) Error: Other's ; Correction: Others'
(b) Error: to ; Correction: for
(c) Error: with ; Correction: of
(d) Error: prepares ; Correction: prepare
Explanation:
a) The error is in the word "other's" as the position of apostrophe is wrong, so the correct word will be "others'", it shows plural nouns.
b) The error is in the word "to", so the correct word will be "for" as for is use to talk about a purpose.
c) The error is in the word "with" and the correct word will be "of" as of indicates relationships between other words including things that made of other things.
d) The error is in the word "preapres" and the correct word will be "prepare".
Select the correct answer.
According to the Universal Law of Gravitation, every object attracts every other object in the universe. Why can’t you feel the force of attraction between you and Mars?
A.
There is no force of attraction between you and Mars.
B.
Your mass is too low.
C.
Mars is a larger planet than Earth.
D.
Mars is a long distance away.
Answers
Answer:
D. Mars is a long distance away
b. i. In a hydraulic press, a force of 200N is applied to master piston of area 25cm. If
the press is designed to produce a force of 5000N, determine the area of the slave
piston.
(4marks)
Answers
Answer:
625 cm²
Explanation:
The pressure is the same on both pistons.
F/A = F/A
200 N / 25 cm² = 5000 N / A
A = 625 cm²
A diver releases an air bubble of volume 3.0 cm3 from a depth of 18 m below the surface of a lake, where the temperature is 9.0 ∘C. Part A What is the volume of the bubble when it reaches just below the surface of the lake, where the temperature is 22 ∘C?
Answers
Answer:
Explanation:
We shall apply gas law formula to get the solution .
P₁ V₁ / T₁ = P₂ V₂ / T₂
P₁ = 10⁵ + 18 x 10³ x 9.8 where 10⁵ Pa is atmospheric pressure at surface
= 1.764 x 10⁵ + 10⁵
= 2.764 x 10⁵
2.764 x 10⁵ x 3 / ( 273 + 9 ) = 10⁵ x V₂ / ( 273 + 22 )
V₂ = 8.67 cm³
Please answer this question
Answers
Explanation:
m = kg. v=m/s. g=m/s^2. h= m
>>1/2mv^2=mgh
>>1/2mv^2=mgh>> kg*(m/s)^2= kg*m/s^2*m
>>1/2mv^2=mgh>> kg*(m/s)^2= kg*m/s^2*m>>kg m^2/s^2=kg m^2/s^2 the fraction 1/2 won't be able to make any changes to to the dimensional expression of energy i.e half of energy is still energy therefore you can neglect the number .
>>kg m^2/s^2=kg m^2/s^2
>>J= J
Given a volume of 1000. сm of an ideal gas at 300. K, what volume would it occupy at a temperature of 600. K?
Answers
Answer:
2000 cm³
Explanation:
Assuming the pressure is constant:
V / T = V / T
1000 cm³ / 300 K = V / 600 K
V = 2000 cm³
Iron man wears an awesome ironsuit.He is flying over high current carrying wire. Will he be affected?
Answers
Answer:
According to super hero logic , nothing will happen to him.
But according to science , yes he will get current shock but good news is that he wouldn't get elected until he is in contact with the wires.
He may / may not be affected but his suit will be damaged for sure as it is made of metal.
HOPE THIS HLEP AND PLSSSSS MARK AS BRAINLIEST AND THNXX :)
A ray of light is projected into a glass tube that is surrounded by air. The glass has an index of refraction of 1.50 and air has an index of refraction of 1.00. At what minimum angle will light in the glass tube be totally reflected at the glass/air interface?
Answers
Answer:
θ = 41.8º
Explanation:
This is an internal total reflection exercise, the equation that describes this process is
sin θ = n₂ / n₁
where n₂ is the index of the incident medium and n₁ the other medium must be met n₁> n₂
θ = sin⁻¹ n₂ / n₁
let's calculate
θ = sin⁻¹ (1.00 / 1.50)
θ = 41.8º
Let us treat a helicopter rotor blade as a long thin
rod, as shown in Fig. 8–49. (a) If each of the three rotor
helicopter blades is 3.75 m long and has a mass of 135 kg,
calculate the moment of inertia of the three rotor blades
about the axis of rotation. (b) How much torque must the
motor apply to bring the blades from rest up to a speed
of 6.0 rev/s in 8.0 s?
Rotor
Answers
Answer:
(a) 1900 kg m²
(b) 8950 Nm
Explanation:
(a) The moment of inertia of a rod about its end is I = ⅓mL².
For 3 rods of mass m = 135 kg and length L = 3.75 m, the total moment of inertia is:
I = 3 (⅓ (135 kg) (3.75 m)²)
I = 1900 kg m²
(b) Net torque = moment of inertia × angular acceleration
∑τ = Iα
First, find the angular acceleration.
ω₀ = 0 rad/s
ω = 6.0 rev/s (2π rad/rev) = 37.7 rad/s
t = 8.0 s
α = (37.7 rad/s − 0 rad/s) / 8.0 rad/s = 4.71 rad/s²
∑τ = Iα
∑τ = (1900 kg m²) (4.71 rad/s²)
∑τ = 8950 kg m² / s²
∑τ = 8950 Nm
Fill in the blanks in the following statements:
1. A parsec is defined as the distance from the Sun which would result in a parallax of_____ arcsecond as seen from Earth when observed 6 months apart.
2. One parsecs is about_____light years.
3. The more distant a star, the_____its parallax.
4. The statement "we can measure stellar parallax for most stars in our galaxy" is_____.
5. The closest stars have parallaxes smaller than______arcsecond.
6. The first successful measurements of stellar parallax were made by______in year______for the star named.
7. Star Fred has parallax four times greater than star Bob. Star Fred is______times______then star Bob.
Answers
Answer:
Explanation:
1. A parsec is defined as the distance from the Sun which would result in a parallax of_TWO____ arcsecond as seen from Earth when observed 6 months apart.
2. One parsecs is about_3.3____light years
3. The more distant a star, the_LESS ____its parallax.
4. The statement "we can measure stellar parallax for most stars in our galaxy" is__TRUE .___.
5. The closest stars have parallaxes smaller than_.002 _____arcsecond.
6. The first successful measurements of stellar parallax were made by_Friedrich Bessel_____in year_1838_____for the star named.
7. Star Fred has parallax four times greater than star Bob. Star Fred is__4____times_nearer_____than star Bob.
The angle of incidence of a ray of light striking an equilateral triangular prisms ABC of refracting angle 60o is 40o. Calculate:
(i)the angle of refraction at the first face
(ii)the angle of emergence
Answers
Answer:
1: the refracted angle in the first face is equal to the incident angle that is 60degrees
2. Emergence Angle is 42degrees
Explanation:
Pls see attached file
calculate the energy dissipated by an electric iron which draws a current of 5A from a240v power supply for 25minutes
Answers
Explanation:
Given,
I = 5 A
V = 240 V
T = 25 mins = 1500 sec
Now,
Energy dissipated = IVT= 5×240×1500 = 1800000 J
The graph shows a wave that oscillates with a frequency of 60 Hz. Based on the information given in the diagram, what is the speed of the wave?
Answers
Answer:
900 cm/s or 9 m/s.
Explanation:
Data obtained from the question include the following:
Length (L) = 30 cm
frequency (f) = 60 Hz
Velocity (v) =.?
Next, we shall determine the wavelength (λ).
This is illustrated below:
Since the wave have 4 node, the wavelength of the wave will be:
λ = 2L/4
Length (L) = 30 cm
wavelength (λ) =.?
λ = 2L/4
λ = 2×30/4
λ = 60/4
λ = 15 cm
Therefore, the wavelength (λ) is 15 cm
Now, we can obtain the speed of the wave as follow:
wavelength (λ) = 15 cm
frequency (f) = 60 Hz
Velocity (v) =.?
v = λf
v = 15 × 60
v = 900 cm/s
Thus, converting 900 cm/s to m/s
We have:
100 cm/s = 1 m/s
900 cm/s = 900/100 = 9 m/s
Therefore, the speed of the wave is 900 cm/s or 9 m/s.
Increase in Space Suit Pressure 0.0/3.0 points (graded) If the pressure in a space suit increases, how will each of the following be affected? Flexilibity will: Increase Decrease Stay the same unanswered The required pre-breathe time will: Increase Decrease Stay the same unanswered The mass of the suit will: Increase Decrease Stay the same
Answers
Answer:
Flexibility Increases
Pre-breathe time decreases
Mass of suit decreases.
Explanation:
Spacesuits are designed for space shuttles when a person goes to explore the galaxy. The spacesuits shuttle era are pressurized at 4.3 pounds per inch. The gas in the suit is 100% of oxygen and there is more oxygen to breathe when the altitude of 10,000 is reached. This will decrease the breathing time and mass of suit.
Complete all four parts. 15 points. Will give brainliest! Show work!
Answers
Answer:
A. 5.08 secs.
B. 10.16 secs.
C. 126.50 m.
D. 373.36 m
Explanation:
Data obtained from the question include the following:
Initial velocity (u) = 65 m/s
Angle of projection θ = 50°
A. Determination of the time taken to reach the peak.
Initial velocity (u) = 65 m/s
Angle of projection θ = 50°
Acceleration due to gravity (g) = 9.8 m/s²
Time (t) =.?
t = u•Sine θ/g
t = (65 × Sine 50) /9.8
t = 5.08 secs.
B. Determination of the total time spent by the ball in air.
Time (t) taken to reach the peak = 5.08 secs.
Total time (T) spent by the ball in air =?
T = 2t
T = 2 × 5.08
T = 10.16 secs
Therefore, the total time spent by the ball in air is 10.16 secs.
C. Determination of the maximum height.
Initial velocity (u) = 65 m/s
Angle of projection θ = 50°
Acceleration due to gravity (g) = 9.8 m/s²
Maximum height (H) =..?
H = u²•Sine² θ / 2g
H = 65² × (Sine 50)² / 2 × 9.8
H = 4225 × (Sine 50)² /19.6
H = 126.50 m
Therefore, the maximum height reached by the ball is 126.50 m.
D. Determination of the horizontal distance travelled by the ball.
Initial velocity (u) = 65 m/s
Angle of projection θ = 50°
Acceleration due to gravity (g) = 9.8 m/s²
Horizontal distance (R) =..?
R = u²•Sine 2θ / g
R = 65² × Sine (2×30) / 9.8
R = (4225 × Sine 60) / 9.8
R = 373.36 m
Therefore, the horizontal distance travelled by the ball is 373.36 m
a) A conductor carrying a current I = 12.5 A is directed along the positive x axis and perpendicular to a uniform magnetic field. A magnetic force per unit length of 0.110 N/m acts on the conductor in the negative y direction. Determine the magnitude of the magnetic field in the region through which the current passes.
Answers
Answer:
8.8 mT
Explanation:
Current through the conductor = 12.5 A
Magnetic force per unit length on the wire = 0.110 N/m
Recall that the magnetic force per unit length on a current carrying conductor is in a uniform magnetic field is
[tex]\frac{F}{l}= IBsin\alpha[/tex]
where B is the magnetic field magnitude
[tex]I[/tex] is the current in the conductor
α is the angle the conductor makes with the magnetic field ( since it is perpendicular in this case, α is 90°)
imputing values into the equation, we'll have
0.11 = 12.5 x B x sin 90°
but sin 90° = 1, therefore, we have
0.11 = 12.5B
B = 0.11/12 = 8.8 x 10^-3 T
or rather = 8.8 mT
3.) [15 points] A physics teacher is on the west side of a small lake and wants to swim across and up at a point directly across from his starting point. He notices that there is a current in the lake and
that a leaf floating by him travels 4.2m [S] In 5.0s. He is able to swim 1.9 m/s in calm water,
(a) What direction will he have to swim in order to arrive at a point directly across from his position?
Answers
Answer:
The teacher should swim in a direction 29.24° North of East
Explanation:
Given that the there is a water current across the lake, and the physics teacher intends to swim directly across the lake, the direction the physics teacher will have to swim is found as follows;
The speed of the water current is given by the speed of the floating leaf traveling with the water current
Distance traveled by the leaf = 4.2 m South
Time of travel of the leaf = 5.0 s
Speed of leaf = 4.2/5 = 0.84 m/s = Speed of the water current
Swimming peed of the teacher, v = 1.9 m/s
To swim directly across the lake, the teacher has to swim slightly in the opposite direction of the water current, the y-component of the teacher's swimming speed should be equal to and opposite that of the speed of the water current.
Y-component of v = v×sin(θ), where θ is the angle of the direction, the teacher should swim
Therefore;
1.9 × sin(θ) = 0.84
sin(θ) = 0.84/1.9 = 0.44
θ = 26.24°
That is the teacher should swim in a direction 29.24° North of East.
To cross the lake the teacher has to swim in a direction 29.24° North of the East
Finding the direction of speed required:
The speed of the water current can be derived from the speed of the floating leaf :
The distance traveled by the leaf L = 4.2 m South
Time taken T = 5s
So, the speed of the leaf is:
u = 4.2/5
u = 0.84 m/s South
So, the speed of the current is 0.84 m/s South
Now, it is given that the speed of the teacher is, v = 1.9 m/s East
To cross the lake the speed of the teacher must be in a Northeast direction so that the North component of the speed of the teacher cancels out the speed of the current which is directed towards the South.
Let, the speed of the teacher makes an angle of θ from the EAST.
So, the North component is given by:
v(north) = vsinθ
it must be equal to the speed of the current:
vsinθ = u
1.9 × sinθ = 0.84
sinθ = 0.84/1.9
sinθ = 0.44
θ = 26.24°
The teacher should swim in a direction 29.24° North of East.
Learn more about vector components:
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PLEASEEE HELP, thank you :)
Answers
Answer:
The answer is B.
Explanation:
Given that the current (Ampere) in a series circuit is same so we can ignore it. We can assume that the total voltage is 60V and all the 3 resistance are different, 20Ω, 40Ω and 60Ω. So first, we have to find the total resistance by adding :
Total resistance = 20Ω + 40Ω + 60Ω
= 120Ω
Next, we have to find out that 1Ω is equal to how many voltage by dividing :
120Ω = 60V
1Ω = 60V ÷ 120
1Ω = 0.5V
Lastly, we have to calculate the voltage at R1 so we have to multiply by 20 (R1) :
1Ω = 0.5V
20Ω = 0.5V × 20
20Ω = 10V
If the absolute pressure inside the bottom of a container open to the atmosphere and filled with an unknown substance is 300 Pa. And the height of the container is 800.0 cm. What is the density of the substance?
Answers
Answer:
2.5 kg/m³
Explanation:
Absolute pressure = gauge pressure + atmospheric pressure
P = Pg + Pa
The gauge pressure caused by the weight of a fluid is called the static pressure. It is equal to the density of the fluid × acceleration due to gravity × depth of the fluid,
Pg = ρgh
Therefore:
P = ρgh + Pa
300 Pa = ρ (10 m/s²) (8.00 m) + 100 Pa
ρ = 2.5 kg/m³