Answer:
Explanation:
Apply the law of conservation of energy
[tex]KE_i+PE_i=KE_f+PE_f[/tex]
[tex]Gm_1m_2[\frac{1}{r_f} -\frac{1}{r_1} ]=\frac{1}{2} (m_1v_1^2+m_2v_2^2)[/tex]
from the law of conservation of the linear momentum
[tex]m_1v_1=m_2v_2[/tex]
Therefore,
[tex]Gm_1m_2[\frac{1}{r_f} -\frac{1}{r_1} ]=\frac{1}{2} (m_1v_1^2+m_2v_2^2)[/tex]
[tex]=\frac{1}{2} [m_1v_1^2+m_2[\frac{m_1v_1}{m_2} ]^2]\\\\=\frac{1}{2} [m_1v_1^2+\frac{m_1^2v_1^2}{m_2} ]\\\\=\frac{m_1v_1^2}{2} [\frac{m_1+m_2}{m_2} ][/tex]
[tex]v_1^2=[\frac{2Gm_2^2}{m_1+m_2} ][\frac{1}{r_f} -\frac{1}{r_1} ][/tex]
Substitute the values in the above result
[tex]v_1^2=[\frac{2Gm_2^2}{m_1+m_2} ][\frac{1}{r_f} -\frac{1}{r_1} ][/tex]
[tex]=[\frac{2(6.67\times 10^-^1^1)(107)^2}{27+107} ][\frac{1}{26} -\frac{1}{41}] \\\\=1.6038\times 10^-^1^0\\\\v_1=\sqrt{1.6038\times 106-^1^0} \\\\=1.2664 \times 10^-^5m/s[/tex]
B) the speed of the sphere with mass 107.0 kg is
[tex]v_2=\frac{m_1v_1}{m_2}[/tex]
[tex]=[\frac{27}{107} ](1.2664 \times 10^-^5)\\\\=3.195\times 10^-^6m/s[/tex]
C) the magnitude of the relative velocity with which one sphere is
[tex]v_r=v_1+v_2\\\\=1.2664\times 10^-^5+3.195\times10^-^6\\\\=15.859\times10^-^6m/s[/tex]
D) the distance of the centre is proportional to the acceleration
[tex]\frac{x_1}{x_2} =\frac{a_1}{a_2} \\\\=\frac{m_2}{m_1} \\\\=3.962[/tex]
Thus,
[tex]x_1=3.962x_2[/tex]
and
[tex]x_2=0.252x_1[/tex]
When the sphere make contact with eachother
Therefore,
[tex]x_1+x_2+2r=41\\x_1+0,252x_1+2r=41\\1.252x_1+2r=41\\x_1=32.747-1.597r[/tex]
And
[tex]x_1+x_2+2r=41\\3.962x_2+x_2+2r+41\\4.962x_2+2r=41\\x_2=8.262-0.403r[/tex]
The point of contact of the sphere is
[tex]32.747-1.597r=8.262-0.403r\\\\r=\frac{24.485}{1.194} \\\\=20.506m[/tex]
(A) The speed of the sphere of 27 kg is [tex]1.2664 \times 10^{-5} \;\rm m/s[/tex].
(B) The speed of sphere of mass 107 kg is [tex]3.195 \times 10^{-6} \;\rm m/s[/tex].
(C) The magnitude of the relative velocity with which one sphere is approaching to the other is [tex]15.85 \times 10^{-6} \;\rm m/s[/tex].
(D) The distance from the initial position of the center of the 27.0 sphere is 20.506 m.
Given data:
The mass of sphere 1 is, [tex]m_{1} = 27.0 \;\rm kg[/tex].
The mass of sphere 2 is, [tex]m_{2} = 107.0 \;\rm kg[/tex].
The radius of each spheres are, r = 0.10 m.
The distance between the centers of each sphere is, d = 41.0 m.
(A)
In this part, we can apply the conservation of energy to find the speed at given distance of 26.0 m. So,
Total energy at initial = Total energy at final
[tex]\dfrac{Gm_{1}m_{2}}{r_{f}}-\dfrac{Gm_{1}m_{2}}{r_{i}}=\dfrac{1}{2}(m_{1}v^{2}_{1}+m_{2}v^{2}_{2})[/tex]
Now, as per the conservation of momentum,
[tex]m_{1}v_{1}=m_{2}v_{2}\\\\v_{2}=\dfrac{m_{1}v_{1}}{m_{2}}[/tex]
Therefore,
[tex]\dfrac{Gm_{1}m_{2}}{r_{f}}-\dfrac{Gm_{1}m_{2}}{r_{i}}=\dfrac{1}{2}(m_{1}v^{2}_{1}+m_{2} \times [m_{1}v_{1}/m_{2}]^{2})\\\\\\\dfrac{Gm_{1}m_{2}}{r_{f}}-\dfrac{Gm_{1}m_{2}}{r_{i}}=\dfrac{m_{1}v^{2}_{1}}{2} \times (\dfrac{m_{1}+m_{2}}{m_{2}})[/tex]
Modifying as,
[tex]v^{2}_{1}=[\dfrac{2Gm^{2}_{2}}{m_{1}+m_{2}}] \times [\dfrac{1}{r_{f}}-\dfrac{1}{r_{i}}][/tex]
Substitute the values in the above result
[tex]v^{2}_{1}=[\dfrac{2 \times 6.67 \times 10^{-11} \times 107^{2}}{27+107}] \times [\dfrac{1}{26}-\dfrac{1}{41}]\\\\v_{1}=\sqrt{1.6038 \times 10^{-5}}\\\\v_{1}=1.2664 \times 10^{-5} \;\rm m/s[/tex]
Thus, the speed of the sphere of 27 kg is [tex]1.2664 \times 10^{-5} \;\rm m/s[/tex].
(B)
The sphere with mass 107 kg is calculated as,
[tex]v_{2}=\dfrac{m_{1}v_{1}}{m_{2}}\\\\v_{2}=\dfrac{27 \times 1.2664 \times 10^{-5} \;\rm m/s }{107}\\\\v_{2}=3.195 \times 10^{-6} \;\rm m/s[/tex]
Thus, the speed of sphere of mass 107 kg is [tex]3.195 \times 10^{-6} \;\rm m/s[/tex].
(C)
The magnitude of the relative velocity with which one sphere is
[tex]v_{r} = v_{1} +v_{2}\\\\v_{r} =( 1.2664 \times 10^{-5})+ (3.195 \times 10^{-6})\\\\v_{r}=15.85 \times 10^{-6} \;\rm m/s[/tex]
Thus, the magnitude of the relative velocity with which one sphere is approaching to the other is [tex]15.85 \times 10^{-6} \;\rm m/s[/tex].
(D)
The distance of the centre is proportional to the acceleration,
[tex]\dfrac{x_{1}}{x_{2}}=\dfrac{m_{2}}{m_{1}}\\\\\\\dfrac{x_{1}}{x_{2}}=\dfrac{107}{27}\\\\\\\dfrac{x_{1}}{x_{2}}=3.962\\\\\\x_{1}=3.962 \times x_{2}[/tex]
As per the given problem,
[tex]x_{1}+x_{2}+2R = d\\\\3.962x_{2}+x_{2}+(2R) = 41 \\\\x_{2} = 8.262-0.403R[/tex]
And,
[tex]x_{1}=0.252x_{2}\\\\x_{1}=0.252 \times (8.262-0.403R)\\\\x_{1}=32.747-1.597R[/tex]
Then for point of contact of the sphere:
[tex]x_{1} = x_{2}\\\\32.747-1.597R = 8.262-0.403R\\\\R =20.506 \;\rm m[/tex]
Thus, the distance from the initial position of the center of the 27.0 sphere is 20.506 m.
Learn more about the conservation of linear momentum here:
from the initial position of the center of the 27.0 sphere
Un atleta de 70 kg de masa que ha efectuado un salto de altura cae una vez que ha
sobrepasado el listón, identifica y dibuja las fuerzas que actúan sobre el atleta cuando:
a)En el momento que está impulsándose en el suelo.
b)Va cayendo. ¿Qué tipo de movimiento tiene en este caso?
c)Al chocar con la colchoneta.
Answer:
a) the elastic force of the pole directed upwards and the force of gravity with dissects downwards
Explanation:
The forces on the athlete are
a) at this moment the athlete presses the garrolla against the floor, therefore it acquires a lot of elastic energy, which is absorbed by the athlete to rise and gain potential energy,
therefore the forces are the elastic force of the pole directed upwards and the force of gravity with dissects downwards
b) when it falls, in this case the only force to act is batrachium by the planet, this is a projectile movement for very high angles
c) When it reaches the floor, it receives an impulse that opposes the movement created by the mat. The attractive force is the attraction of gravity.
What is the answer to the question?
Answer:
Explanation:
The y component is measured by the horizontal component and the vertical component. Together they determine the magnitude of the vector. In this case, the y or vertical component is found by using the sine function.
Formula
Sin(angle) = vector resultant / y component component.
Givens
angle = 42 degrees.
vector = 419 degrees
Solution
sin(42) = y / 419 Multiply both sides by 419
419 * sin(42) = 419 * y / 419
y = 419 * 0.6691
y = 280.37
Note
The vector is pointing downward so technically the vertical component should be negative. I'm not sure what to tell you to answer. I would try - 280.37, but if the computer marks you wrong, try 280.37 (no minus sign).
A child in an inner tube is bobbing up and down in the ocean and notices that after a wave crest passes, four more crests pass in a time of 38.4 s and the distance between the crests is 32 m. If possible, determine the following properties for the wave. (If not possible, enter IMPOSSIBLE.)(a) Period (s)(b) Frequency (Hz)(c) Wavelength (m)(d) Speed ( m/s)(e) Amplitude (m)
Answer:
Explanation:
Given:
Four more crests pass in a time of 38.4 s and the distance between the crests is 32 m.
We have to determine five terms.
Lets start with one-one basis.
a.
Period = Time taken by a wave to pass though.
⇒ [tex]P = \frac{Total\ time}{No.\ of\ waves}[/tex]
⇒ [tex]P = \frac{38.4}{4}[/tex]
⇒ [tex]P=9.6 s[/tex]
b.
Frequency = Reciprocal of time period in Hertz.
⇒ [tex]f=\frac{1}{T}[/tex]
⇒[tex]f=\frac{1}{9.6}[/tex]
⇒ [tex]f=0.104 Hertz[/tex]
c)
Wavelength = Distance between two consecutive trough and crest.
⇒ [tex]\lambda = 32 m[/tex]
d.
Speed (v) = Product of frequency and wavelength.
⇒ [tex]v=f\times \lambda[/tex]
⇒ [tex]v=0.104\times 32[/tex]
⇒[tex]v = 3.33 ms^-1[/tex]
e)
Amplitude = The maximum displacement or half the distance from crest to trough.
⇒ Here it can't be determined.
⇒ Impossible.
Josh has a helium-filled balloon. He wants to calculate the speed of his balloon as it rises to the ceiling. What two measurements should he take to calculate the average speed of his balloon?
Answer:Distance and time
Explanation:
We know that average speed is the ratio of distance traveled by the particle over the time taken
So average velocity of balloon is
[tex]v_{avg}=\frac{\text{Distance}}{\text{Time taken}}[/tex]
So, Josh should note the distance traveled by balloon and time taken in doing so.
The two measurements required by Josh to calculate the average speed of the helium-filled balloon are distance and time.
The average speed of an object signifies and explains the total distance an object travels within a specified time. The average speed is a scalar quantity since it doesn't have a definite direction.
The average speed can be estimated if the measurement of the distance and time is being known because of its formula:
[tex]\mathsf{v_{avg} = \dfrac{distance}{time}}[/tex]
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A uniform rod of length l and mass m rests on supports at its ends. The right support (white triangle) is quickly removed. a) What is the force from the left support immediately thereafter? A uniform rod of length 2r and moment of inertia rests on top of two supports, each of which is a distance d away from the center where is a constant. The right support (white triangle) is quickly removed. b) What is the force from the left support immediately thereafter?
Answer:
Explanation:
For solving this question we will be using Newton's second law of motion in 2 different formats.
F = ma and [tex]\tau = I\alpha[/tex]
Here F = net external force applied on the body
m = mass of the body
a = acceleration of the centre of mass of the body
[tex]\tau[/tex] = net external torque on the body
I = moment of inertia of the body about given axis
[tex]\alpha[/tex] = angular acceleration of the body
These are 2 forms of Newton's second law of motion first one is from transnational motion and second for rotational motion.
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A car goes by 20 m/sec for 3 minutes. Find traveled distance?
21. If € = 8.0 V, at what rate is the emf providing energy to the circuit shown?
15 2
10 22
12 V
+
1022.
a. 8.4 W
b. 7.6 W
C.5.6 W
d. 11 W
e. 2.0 W
Answer:
c. 5.6 W
Explanation:
We can write the Kirchoff's voltage law (KVL) equations for the circuit using i1 for the clockwise current in the left loop, and i2 for the clockwise current in the right loop. Then the circuit equations are ...
i1 (10 +10) -i2(10) = 12
-i1(10) +i2(10 +15) = 8
Using Cramer's rule to find i2, we have ...
i2 = (12(-10) -8(20))/((-10)(-10) -(25)(20)) = -280/-400 = 0.7
The power supplied by the Emf is ...
(8 V)(0.7 A) = 5.6 W . . . . . matches choice C
When an object is placed within the focal length of a convex lens, the image appears on the same side as the object itself. This situation is shown below. In this situation, which of the following statements is true?
Answer:
the image formed is virtual, this means that it is the prolongations of the rays that form the image. It is straight and magnified by the quantity
Explanation:
In a lens there is a relationship between the focal length, the distance to the object and to the image given by the constructor equation
1 / f = 1 / o + 1 / i
where is the focal length, or and i are the distance to the object and the image respectively.
In the case presented, the object is within the focal length, so the image formed is virtual, this means that it is the prolongations of the rays that form the image. It is straight and magnified by the quantity
m = - i / o
Answer:A
Explanation:Got it right :)
Although electromagnetic waves can always be represented as either photons or waves, in the radio part of the spectrum we typically do not discuss photons (like we do in the visible) because they are at such a low energy. Nevertheless, they exist. Consider such a photon in a radio wave from an AM station has a 1545 kHz broadcast frequency.
Required:
What is the energy, in joules, of the photon?
Answer:
E = 1.02 x 10⁻²⁷ J
Explanation:
The energy of a photon is given by the Plank's formula. The formula is given as:
E = hυ
where,
E = Energy of Photon = ?
h = Plank's Constant = 6.626 x 10⁻³⁴ J.s
υ = Frequency of the Wave = 1545 KHz = 1545000 Hz
Therefore, we can find the energy of photon in the given radio wave from an AM station, by substituting the known values in Plank's formula.
E = (6.626 x 10⁻³⁴ J.s)(1545000 Hz)
E = 1.02 x 10⁻²⁷ J
The energy of a photon, in a radio wave from an AM station has a 1545 kHz broadcast frequency, is found to be E = 1.02 x 10⁻²⁷ J
The energy , in joules, of the photon should be considered as the E = 1.02 x 10⁻²⁷ J.
Plank formula:The energy of a photon should be like
E = hυ
where,
E = Energy of Photon = ?
h = Plank's Constant = 6.626 x 10⁻³⁴ J.s
υ = Frequency of the Wave = 1545 KHz = 1545000 Hz
Now
E = (6.626 x 10⁻³⁴ J.s)(1545000 Hz)
E = 1.02 x 10⁻²⁷ J
hence, The energy , in joules, of the photon should be considered as the E = 1.02 x 10⁻²⁷ J.
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A 50-kilogram object in outer space is attracted to a nearby planet with a
force of 400 newtons. What is the object's acceleration? *
Answer: 8m/s^2
Explanation:
By Newton's second law we have that.
F = m*a
Where F is force, m is mass and a is acceleration.
We know that m = 50kg and F = 400N
400N = 50kg*a
a = (400/50) m/s^2 = 8m/s^2
A motorcycle has a speed of 30 m / s. After braking, it decelerates with constant deceleration A = -3.0 m / s ^ 2
Calculates its speed after 3.0 s
[tex]a = \displaystyle\frac{v-u}{t}[/tex]
[tex]-3 = \displaystyle\frac{v - 30}{3}[/tex]
[tex]v -30 = -9[/tex]
[tex] v = 21 m/s[/tex]
Answer:21
Explanation:
For each of the situations described below, the object considered is undergoing some changes. Among the possible changes you should consider are:
(Q) The object is absorbing or giving off heat.
(T) The object's temperature is changing.
(U) The object's internal energy is changing.
(W) The object is doing mechanical work or having work done on it.
(C) The objects chemical energy is changing.
For each of the situations described below, identify which of the four changes are taking place and write as many of the letters Q T U W C (or none) as are appropriate.
1. A cylinder with a piston on top contains a compressed gas and is sitting on a thermal reservoir (a large iron block). After everything has come to thermal equilibrium, the piston is moved upward somewhat (very slowly). The object to be considered is the gas in the cylinder.
Q T U W C
2. Consider the same cylinder as in part 1, but it is wrapped in styrofoam, a very good thermal insulator instead of sitting on a heat reservoir. The piston is pressed downward (again, very slowly), compressing the gas. The object to be considered is the gas in the cylinder.
Q T U W C
3. An ice cube sitting in the open air is melting.
Q T U W C
4. A mixture of two moles of hydrogen gas and one mole of oxygen gas in a thermally insulated vessel is subjected to small spark (contributing negligible energy) and converts to water vapor.
Q T U W C
Explain your reasoning for each of these cases.
Answer:
1.) Q T U W
Explanation:
1.) QTUW
2.) UW
3.) QU
4.) QTUC
According to first law of thermodynamics
dU = Q - W
Where
dU = change in internal energy
Q = heat added
W = work done by the system
2.) UW
Work is been done on the system. The pressure will surely distort the internal energy of the system
Pressure = Force/area.
3.) QU
The melting process begins because the air temperature around the ice cubes is warmer
The solid ice particles absorb heat energy from the warmer air, giving the particles energy and enabling them to move away from one another.
4.) Chemical reaction can be exothermic or endothermic which involves absorption or release of heat. Since it is subjected to small spark, there is definitely a change in internal energy.
In this exercise we have to have knowledge about thermodynamics in order to identify the alternatives that are correctly classified, so we can say that:
1.) QTUW
2.) UW
3.) QU
4.) QTUC
According to first law of thermodynamics:
[tex]dU = Q - W[/tex]
Where:
dU = change in internal energyQ = heat addedW = work done by the system1.) The first alternative corresponds to:
The object is absorbing or giving off heat.The object's temperature is changing.The object's internal energy is changing.The object is doing mechanical work or having work done on it.In other words QTUW.
2.) The second alternative corresponds to:
The object's internal energy is changing.The object is doing mechanical work or having work done on it.Work happen been finished ahead of the system. The pressure will without doubt deform the internal strength of bureaucracy:
[tex]Pressure = Force/area[/tex]
In other words UW.
3.) The third alternative corresponds to:
The object is absorbing or giving off heat.The object's internal energy is changing.The softening process begins cause the air coldness of some degree around the frozen water cubes happen warmer The complete frozen water particles take in heat strength from the warmer air, bestowing the piece energy and allowing to happen them to move out each one.
In other words QU.
4.) The fourth alternative corresponds to:
The object is absorbing or giving off heat.The object's temperature is changing.The object's internal energy is changing.The objects chemical energy is changing.Chemical reaction maybe exothermic or endothermic that involves assimilation or release of heat. Since it happen commit small spark, skilled happen certainly a change in within strength.
In other words QTUC
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Use the graph to answer the questions.
Based on the graph, what happens to current as resistance increases?
This type of graph shows which type of relationship between the two variables?
What would be a reasonable estimate for current at a resistance of 50 Ω?
Answer:
1) Decreases
2) Inverse Proportionality
3) 1 A
Explanation: Just Did Em'
Answer:
Decreases
Inverse Proportionality
1 A
Explanation:
correct on quiz EDGE2021
what did the biologist wear on his first date ?
Answer:
Calvin Cycles
Explanation:
This is a popular joke. Is this an answer choice for your question?
resonance occurs in an AC series circuit when which of the following condition is met ?
A,Resistant equal compactive resistance
B, comparative resistance equal zero
C, resistance equals inductive resistance
Answer:
capacitive reactance equals inductive reactance
ASAP answer right and I will do a giveaway
Explanation:
Ans 1 ) As the gravity of a planet increases, there will be increase in thickness of atmosphere around that planet. The gravitational force of the planets holds the bulks of molecules of atmosphere (as gas will need higher escape velocity).
Ans 2) Mars is the easier planets among all other planets in our solar system as it lies in habitable zone and it as a moderate gravity (where live can survive). Well, there's lot of resources too.
Thanks for asking
Answer:
ghujg
Explanation:
The minute hand on a watch is 2.00 cm cm in length. What is the displacement vector of the tip of the minute hand Part A From 8:00 to 8:20 a.m.? Express vector Δ r ⃗ Δr→ in the form Δ r x ΔrxDeltar_x , Δ r y ΔryDeltar_y , where the x and y components are separated by a comma. Δ r ⃗ Δr→ = nothing cm SubmitRequest Answer Part B From 8:00 to 9:00 a.m.? Express vector Δ r ⃗ Δr→ in the form Δ r x ΔrxDeltar_x , Δ r y ΔryDeltar_y , where the x and y components are separated by a comma.
Answer:
Check the explanation
Explanation:
Kindly check the attached image below to see the step by step explanation to the question above.
Two radio antennas A and B radiate in phase. Antenna B is a distance of 140 m to the right of antenna A. Consider point Q along the extension of the line connecting the antennas, a horizontal distance of 40.0 m to the right of antenna B. The frequency, and hence the wavelength, of the emitted waves can be varied.
a) What is the longest wavelength for which there will be destructive interference at point ?
b) What is the longest wavelength for which there will be constructive interference at point ?
Explanation:
a) 120m
b) since Q is the first order constructive interference, the distance between mid point of antennas and Q is 0.5 wavelengths (appear in A-Level question). so the wavelength should be (2)(30) =60m
60m
a) Fill in the blanks in the following paragraph to correctly describe the nucleus of an atom.
_______ and _________ are the two types of nucleons that make up a nucleus. The __________ force exists between _________ in the nucleus because of their charge. Because it is repulsive, this force tends to make a nucleus __________. However, the __________ force acts between protons, between neutrons, and between protons and neutrons. This force helps to make a nucleus __________, because it is always attractive.
Answer:
Protons and Neutrons are the two types of nucleons that make up a nucleus. The electrostatic force exists between protons in the nucleus because of their charge. Because it is repulsive, this force tends to make a nucleus unstable. However, the strong nuclear force acts between protons, between neutrons, and between protons and neutrons. This force helps to make a nucleus stable, because it is always attractive.
Explanation:
The nucleus of an atom contains two types of particles, protons and neutrons. Proton has a positive charge, while neutron has no charge. The protons have a repulsive electrostatic force between each other, due to like charges. Due to this repulsive force protons tend to scatter away making the nucleus unstable. In order to overcome this, a force inside the nucleus binds these protons and neutrons together. This attractive force is called strong nuclear force. This force acts on very short ranges.
An atom is made up of nucleus and electrons orbitting the nucleus. The correct words are proton, neutron, electrostatic force, protons, unstable, nuclear, stable respectively.
Nucleus:
It is composed of Protons and Neutrons. Protons are potsitively charged , hence repulse each other which makes the nucleus unstable.
Nucleons held together by Strong nucleur force because it is the strongest force of universe.
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A set of pulleys is used to lift a piano weighing 1,000 newtons. The piano is lifted 3 meters in 120 seconds. How much power was used?
Answer:
25 watts
Explanation:
Power=work/time
work=force x distance
1000 × 3
=3000 Joules
power= 3000/120
=25 watts
If A set of pulleys is used to lift a piano weighing 1,000 newtons. The piano is lifted 3 meters in 120 seconds. Then the power used is equal to 25 watts.
What is power?Power is the rate at which work is done or energy is transferred. It is a physical quantity that measures how quickly energy is used or transformed.
P=W/s
Where W= work done in joules.
s= time in seconds.
Power is typically measured in watts (W), which is equivalent to joules per second (J/s). In simple terms, power can be defined as the amount of work done or energy transferred per unit of time.
Here in the question,
To calculate the power used to lift the piano, we need to use the formula:
Power = Work / Time
The work done in lifting the piano is given by:
Work = Force x Distance
Where
Force = the weight of the piano, which is 1,000 newtons,
Distance = the height to which it is lifted, which is 3 meters.
Then, the work done is:
Work = 1,000 N x 3 m = 3,000 joules
The time taken to lift the piano is 120 seconds.
Now we can substitute these values in the formula for power:
Power = Work / Time
Power = 3,000 joules / 120 seconds
Power = 25 watts
Therefore, the power used to lift the piano is 25 watts.
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Josh calculated that the speed of his balloon travelling a distance of 10m was 2m/s. What was the length of time?
The surface tension of water was determuned in a laboratory by using the drop weight method. 100 drops were released from a burette the inner diameter of whose opening is 1.8mm. The mass of the droplets was 3.78g dertermine the surface tension of the water and comparing it with the tabulatef value
Answer:
The surface tension of the water is 6.278×10⁻² N/m
error = 13.65%
Explanation:
The surface tension of water is given by
[tex]$ \gamma = \frac{F}{L} $[/tex]
Where F is the force acting on water and L is the length over which is force is acted.
We are given the mass of 100 droplets of water
M = 3.78 g
n = 100
The mass of 1 droplet is given by
[tex]m = \frac{M}{n} \\\\m = \frac{3.78}{100}\\\\m = 0.0378 \: g \\\\m = 3.780\times10^{-5} \: kg[/tex]
The force acting on a single droplet of water is given by
[tex]F = m \cdot g[/tex]
Where m is the mass of water droplet and g is the acceleration due to gravity
[tex]F = 3.780\times10^{-5} \cdot 9.81[/tex]
[tex]F = 3.708\times10^{-4} \: N[/tex]
The circumferential length of the droplet is given by
[tex]L = \pi \cdot d[/tex]
Where d is the diameter
[tex]L = \pi \cdot 1.88\times10^{-3}\\\\L = 5.906 \times10^{-3} \: m[/tex]
Now we can find out the required surface tension of the water
[tex]\gamma = \frac{3.708\times10^{-4} }{5.906 \times10^{-3}} \\\\\gamma = 0.06278\: N/m\\\\\gamma = 6.278 \times10^{-2} \: N/m\\\\[/tex]
Therefore, the surface tension of the water is 6.278×10⁻² N/m
The tabulated value of the surface tension of water at 20 °C is given by
[tex]$ \gamma_t = 0.0727 \: N/m $[/tex]
The percentage error between tabulated and calculated surface tension is given by
[tex]$ error = \frac{\gamma_t - \gamma }{\gamma_t} $[/tex]
[tex]$ error = \frac{ 0.0727 - 0.06278}{0.0727} \times 100\% $[/tex]
[tex]$ error = 13.65 \%[/tex]
A parallel plate capacitor is attached to a battery which stores 3 C of charge. A dielectricmaterial is inserted to fill the gap. There is now 9 C of charge stored.1. What is the dielectric constant of the material?2. As a fraction of the original how much energy is stored in the capacitor after thedielectric is inserted?3. If we pull the dielectric half way out how much charge is stored on the capacitor?Hint:we could imagine our capacitor now as 2 in parallel, each with half the area and onewith the dielectric.
Answer:
A) 3
B) fraction is 2/1 = 2
C) 3 C
Explanation:
Initial capacitance with air U is 3 C
Final charge with dielectric Ud material is 9 C
Dielectric constant = capacitance with dielectric/capacitance with air
= 9/3 = 3
Since it is connected to a battery, the potential difference at the plate will be constant.
P.d = V
Also energy stored in a capacitor is given as 0.5CV^2
For capacitance with air, energy is 0.5 x 3 x V^2 = 9V^2
For capacitance with dielectric, energy is 0.5 x 9 x V^2 = 18V^2
Fraction of energy stored in capacitance with dielectric to that with air is 18V^2/9V^2 = 2
From C = eA/d
Where C is the capacitance,
e is the dielectric constant
A is the area of the dielectric
d is the distance between plates of the capacitor.
For initial, assuming the distance to be of unit distance, area will be given as
9 = (3 x A)/1
9 = 3A
A = 2 m^2. If we pull dielectric half way out, area becomes
C = (3 x 1)/1
C = 3 C
Instead of moving back and forth, a conical pendulum moves in a circle at constant speed as its string traces out a cone (see figure below). One such pendulum is constructed with a string of length
L =10.7 cm and bob of mass 0.344 kg. The string makes an angle = 5.58° with the vertical.
(a) What is the radial acceleration of the bob?
magnitude
(b) What are the horizontal and vertical components of the tension force exerted by the string on the bob? (Assume radially inward to be the positive x axis and vertically upward to be the
positive y axis. Express your answer in vector form.)
T= N
Answer:
a
The radial acceleration is [tex]a_c = 0.9574 m/s^2[/tex]
b
The horizontal Tension is [tex]T_x = 0.3294 i \ N[/tex]
The vertical Tension is [tex]T_y =3.3712 j \ N[/tex]
Explanation:
The diagram illustrating this is shown on the first uploaded
From the question we are told that
The length of the string is [tex]L = 10.7 \ cm = 0.107 \ m[/tex]
The mass of the bob is [tex]m = 0.344 \ kg[/tex]
The angle made by the string is [tex]\theta = 5.58^o[/tex]
The centripetal force acting on the bob is mathematically represented as
[tex]F = \frac{mv^2}{r}[/tex]
Now From the diagram we see that this force is equivalent to
[tex]F = Tsin \theta[/tex] where T is the tension on the rope and v is the linear velocity
So
[tex]Tsin \theta = \frac{mv^2}{r}[/tex]
Now the downward normal force acting on the bob is mathematically represented as
[tex]Tcos \theta = mg[/tex]
So
[tex]\frac{Tsin \ttheta }{Tcos \theta } = \frac{\frac{mv^2}{r} }{mg}[/tex]
=> [tex]tan \theta = \frac{v^2}{rg}[/tex]
=> [tex]g tan \theta = \frac{v^2}{r}[/tex]
The centripetal acceleration which the same as the radial acceleration of the bob is mathematically represented as
[tex]a_c = \frac{v^2}{r}[/tex]
=> [tex]a_c = gtan \theta[/tex]
substituting values
[tex]a_c = 9.8 * tan (5.58)[/tex]
[tex]a_c = 0.9574 m/s^2[/tex]
The horizontal component is mathematically represented as
[tex]T_x = Tsin \theta = ma_c[/tex]
substituting value
[tex]T_x = 0.344 * 0.9574[/tex]
[tex]T_x = 0.3294 \ N[/tex]
The vertical component of tension is
[tex]T_y = T \ cos \theta = mg[/tex]
substituting value
[tex]T_ y = 0.344 * 9.8[/tex]
[tex]T_ y = 3.2712 \ N[/tex]
The vector representation of the T in term is of the tension on the horizontal and the tension on the vertical is
[tex]T = T_x i + T_y j[/tex]
substituting value
[tex]T = [(0.3294) i + (3.3712)j ] \ N[/tex]
The radical acceleration of the bob is 0.9575 m/s². The horizontal and vertical components of the tension force exerted by the string on the bob are 0.329 N and 3.37 N respectively.
Taking the vertical component of the tension where the weight mass is balanced, then:
T sin θ = mg
[tex]\mathbf{T = \dfrac{mg}{sin \theta}}[/tex]
However, the centripetal force of the system is given by the horizontal component of the tension which can be expressed as:
T cos θ = m[tex]\mathbf{a_r}[/tex]
Making [tex]\mathbf{a_r}[/tex] the subject, we have:
[tex]\mathbf{a_r = \dfrac{Tcos \theta }{m}}[/tex]
replacing the value of tension (T), we have:
[tex]\mathbf{a_r = \dfrac{ \dfrac{mg}{sin \theta}cos \theta }{m}}[/tex]
[tex]\mathbf{a_r=g tan \theta}[/tex]
where;
angle θ = 5.58°[tex]\mathbf{a_r=9.8 m/s^2 \times tan 5.58}[/tex]
[tex]\mathbf{a_r=9.8 m/s^2 \times 0.0977}[/tex]
[tex]\mathbf{a_r=0.9575 \ m/s^2}[/tex]
Thus, the radical acceleration of the bob is 0.9577 m/s²
On the positive x-axis, the horizontal component of the tension force is:
[tex]\mathbf{T_x =Tcos \theta}[/tex]
[tex]\mathbf{T_x =ma_r}[/tex]
[tex]\mathbf{T_x =0.344 \ kg \times 0.9575 \ m/s^2}[/tex]
[tex]\mathbf{T_x =0.329 \ N}[/tex]
On the positive y-axis, the vertical component of the tension force is:
[tex]\mathbf{T_y =Tsin \theta}[/tex]
[tex]\mathbf{T_y =mg}[/tex]
[tex]\mathbf{T_y=0.344 \ kg \times 9.8 \ m/s^2}[/tex]
[tex]\mathbf{T_x =3.37 \ N}[/tex]
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Whenever using a microscope slide, you should always:
A.
check for cracks or chips in the glass.
B.
make sure it is clean.
C.
handle it with care.
D.
all of these
Answer:
D.
all of these.......
A parachutist is falling with terminal velocity. Which of the following statement is not correct?
a) Gravitational potential energy is converted into kinetic energy of the air
b) G.P.E is converted into K.E of the parachutist
c) G.P.E is converted into thermal energy of the air
d) G.P.E is converted into thermal energy of the parachutist
Answer: D i think
Explanation:
the difference between how lenses and mirrors interact with light
Answer:
Light when strikes mirror, it bounces off where as it transmits through a lens. A mirror is glass with lustrous metal coated at its back. Light reflects off a mirror and image is formed behind it.
Explanation:
A manufacturing firm has hired your company, Acoustical Consulting, to help with a problem. Their employees are complaining about the annoying hum from a piece of machinery. Using a frequency meter, you quickly determine that the machine emits a rather loud sound at 1100 Hz. After investigating, you tell the owner that you cannot solve the problem entirely, but you can at least improve the situation by eliminating reflections of this sound from the walls. You propose to do this by installing mesh screens in front of the walls. A portion of the sound will reflect from the mesh; the rest will pass through the mesh and reflect from the wall.How far should the mesh be placed in front of the wall for this scheme to work?
Answer: 7.7cm
Explanation:
If i want to set up destructive interference, meaning that the reflection will be half (½) of the wavelength out of phase, or the distance is ¼ of a wavelength.
v.s = Speed of sound = 340 m/s ( some books may use 343 m/s, this change varies due to change in temperature and humidity.)
f = 1100 hz
λ = v.s / f
λ = 340 m/s / 1400 Hz
λ = .3091 m
Recall that the distance is ¼ of the wavelength,
.3091/4 = 0.0773 m
Distance used would be = 7.7 cm
Two astronauts of equal mass are holding on to each other and moving at a speed of 30 m/s. They push off of each other and one of the astronauts moves in the same direction as the two were initially moving but at 60 m/s. The velocity of the second astronaut is
Answer:
Zero
Explanation:
A Chinook salmon can jump out of water with a speed of 6.50 m/s . How far horizontally can a Chinook salmon travel through the air if it leaves the water with an initial angle of =30.0° with respect to the horizontal? (Let the horizontal direction the fish travels be in the + direction, and let the upward vertical direction be the + direction. Neglect any effects due to air resistance.)
Answer:
3.73m
Explanation:
What we are asked to find is the range covered by the fish. This is given by the following equation (1). Range can simply be defined as the horizontal distance covered by a body whose motion freely under gravity is in two dimensions. The motion of the fish is in two dimensions, the vertical dimension and the horizontal dimension.
[tex]R=\frac{u^2sin2\theta}{g}.........(1)[/tex]
where u = 6.5m/s is the initial velocity, g is acceleration due to gravity which is taken as [tex]9.8m/s^2[/tex] and [tex]\theta=30.0^o[/tex].
Substituting these values into equation (1), we obtain the following;
[tex]R=\frac{6.5^2sin2(3)}{9.8}\\R=\frac{42.25sin60}{9.8}\\\\R=\frac{36.59}{9.8}\\R=3.73m[/tex]
The range should be 3.73m.
Important information:A Chinook salmon can jump out of water with a speed of 6.50 m/s . The initial angle of =30.0°
The range refers to the horizontal distance i.e. covered by a body whose motion freely under gravity should be in two dimensions. It can be the vertical dimension and the horizontal dimension.
calculation of the range:[tex]= 6.5sin^2\div 9.8\\\\= 36.59 \div 9.8[/tex]
= 3.73m
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