Answer:
The magnitude of a torque about a fixed axis is calculated by finding the lever arm to the point where the force is applied and using the relation |→τ|=r⊥F | τ → | = r ⊥ F , where r⊥ is the perpendicular distance from the axis to the line upon which the force vector lies.
Explanation:
:)
In transverse waves, there is no _________ motion.
A. Perpendicular
B. Vertical
C. Horizontal
D. Up and down
In a transverse wave, the disturbance are carried forward and the particles are undergoing to and fro motion. Hence in transverse waves, there is no horizontal motion.
A wave can be described as a disturbance that travels through a medium from one location to the other location without transporting any matter.
There are two types of matter,
(i) Transverse wave
(ii) Longitudinal wave
In a transverse wave, the particles of the medium move in a direction perpendicular to the direction of propagation of the wave. That means, the particles undergo to and fro motion about their mean position and moves in the direction of the wave propagation.
Examples are:
Radio wavesLight wavesWater waves when a stone is dropped in the pondWhereas longitudinal waves undergo back and forth motion with respect to the mean position.
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HELP PLS
The minimum frequency for the photoelectric effect of a zinc plate is 9.7 × 10^14 Hz. If a green photon with a wavelength of 532nm strikes the plate, will electrons be emitted? Show your work to support your answer.
yes electrons will be emitted with the kinetic energy of
[tex]30.87 \times 10 { }^{ - 19} j[/tex]
what is photoelectric effect?
In photoelectric effect, the electrically charged particles are released from or within a material when it absorbs electromagnetic radiation.
what is kinetic energy?
It is a form of energy that an object or a particle has by reason of its motion. If work, which transfers energy, is done on an object by applying a net force, the object speeds up and thereby gains kinetic energy.
Given:
wavelength,λ
[tex] = 5.32 \times 10 {}^{ - 8} m[/tex]
Frequency
[tex] = 9.7 \times {10}^{14} [/tex]
Einstein's photoelectric equation
€= w + KE
€ = hc/ λ
[tex] = \frac{6.63 \times {10}^{ - 34} \times 3 \times {10}^{8} } {5.32 \times 10 {}^{ - 8} } [/tex]
[tex]€= 3.73 \times {10}^{ - 18} [/tex]
w=h.f
[tex] = 6.63 \times {10}^{ - 34} \times 9.7 \times {10}^{14} [/tex]
[tex] = 6.43 {10}^{ - 19} j[/tex]
KE = € - W
[tex]37.3 \times {10}^{ - 19} - 6.43 \times {10}^{ - 19} [/tex]
[tex]kE = 30.87 \times {10}^{ - 19} [/tex]
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Explain the mechanism by which an open fracture could result in shock.
Answer:
an open fracture contains some sort of water which if it comes in contact with electrons could result to a shock
A force of 570 N keeps a certain ideal spring stretched at a distance of 0.700 m.
A). What is the potential energy of the spring when it is stretched 0.700 m?
B). What is its potential energy when it is compressed 8.00 cm?
Answer:
399j and 456j
Explanation:
(a)spring energy= force * distance
spring energy=570 * 0.700= 399 joules
(b) convert 8.00 cm to m we have 0.08m
E =f * s
E=570 *0.08= 456j
The potential energy of the spring when it is stretched 0.700 m would be 199.5 Joules, and the potential energy when it is compressed 8.00 cm would be 2.60 Joules.
What is the spring constant?The spring constant is used to define the stiffness of the spring, the greater the value of the spring constant stiffer the spring and it is more difficult to stretch the spring.
The mathematical relation for calculating the spring constant is as follows
F = - Kx
As given in the problem, if a force of 570 N keeps a certain ideal spring stretched at a distance of 0.700 m.
k = 570 / 0.7
k = 814.28 N / m
The potential energy stored in spring when it is stretched 0.700 m
E = 1/2 kx²
=0.5×814.28×0.7²
= 199.5 Joules
The potential energy stored in spring when it is stretched 8 cm
E = 1/2 kx²
=0.5×814.28×0.08²
=2.60 Joules
Thus, the potential energy of the spring when it is stretched 0.700 m would be 199.5 Joules, and the potential energy when it is compressed 8.00 cm would be 2.60 Joules.
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Two drums are rolling down a hill. The drums are the same size and mass.
Drum #1 has most of its mass concentrated at the rim, while drum #2 has
most of its mass concentrated in the center. Which of the following
statements are correct? Select all that apply.
Drum #1 will reach the bottom of the hill first because its moment of inertia is
greater.
Drum #1 will have a greater center of mass speed and reach the bottom of the
hill first.
Drum #2 will have a greater center of mass speed and reach the bottom of the
hill first.
Drum #2 will reach the bottom of the hill first because its moment of inertia is
smaller.
Hi there!
Drum #2 will have a greater center of mass speed and reach the bottom of the hill first.
The moment of inertia can be thought of as inertia for rotation.
If mass is concentrated at the rim, the drum has a GREATER moment of inertia compared to if the mass is more concentrated towards the center.
Using the Rotational Equivalent of Newton's Second Law:
[tex]\Sigma \tau = I\alpha[/tex]
**Sum of torques = Moment of inertia * angular acceleration
From this equation, we know that if 'I' increases, 'α' decreases, and thus, the speed of the object's center of mass decreases and it will reach the bottom later.
Therefore, drum #2 with the smaller moment of inertia (mass concentrated at the center) will have a greater angular acceleration ⇒ greater center of mass speed ⇒ read the bottom first.
A jet of water squirts out horizontally from a hole near the bottom of the tank, as seen in the figure.
If the hole has a diameter of 3.13 mm, what is the height, h, of the water level in the tank? Assume that x = 1.33 m and y = 1.72 m.
The height of the water level in the water tank is 0.011 m.
What is the time taken by a fluid particle to reach the ground?From Newtown's equation of motion, y=U×t+(1/2)gt²As, initial velocity (U) is zero, t= 2y/gt = (2× 1.72)/9.8 = 0.35 s
What's the velocity along x direction?Velocity along x direction= x × t
= 1.33 × 0.35
= 0.46 m/s
What's the height of water level in the tank?As per Bernoulli's theorem, 1/2 × ρ × v² = ρ × g× h
=> h = v²/2g = 0.46²/(2×9.8)
= 0.011 m
Thus, we can conclude that the height of water level is 0.011m.
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An object with a mass of m = 122 kg is suspended by a rope from the end of a uniform boom with a mass of M = 74.9 kg and a length of l = 8.77 m. The end of the boom is supported by another rope which is horizontal and attached to the wall as shown in the figure.
Calculate the tension in the horizontal rope. (The horizontal and the vertical ropes are not connected to each other. They are both independently attached to the end of the boom.)
The the tension in the horizontal rope is 7,019.4 N.
What is tension?
Tension is described as the pulling force transmitted axially by the means of a string, a cable, chain, or similar object, or by each end of a rod.
Tension can also be described as the action-reaction pair of forces acting at each end of said elements.
The unit of tension is Newton (same unit as force, since tension is also a force).
Tension in the horizontal ropeThe tension in the horizontal rope is calculated as follows;
Apply the principle of torque;
T(L/2) cosθ = Mg (L/2) sinθ + mg L sinθ
T = (M + 2m)g sinθ/cosθ
T = (M + 2m)g tanθ
let θ = 66⁰ (this value should be given in the question)
T = (M + 2m)g tanθ
T = (74.9 + 2 x 122)(9.8)(tan 66)
T = 7,019.4 N
Thus, the the tension in the horizontal rope is 7,019.4 N.
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what is elecric field line
A vector field and a starting position inside the field define the locus as a "field line." We have electric field lines for the electric fields.
What do you mean by electric field line?In general, an electric field line is a curve drawn with each point's tangent pointing in the direction of that point's net field. An arrow on the curve is obviously required to designate the direction of the electric field from the two potential directions provided by a tangent to the curve. A field line is a space curve or a three-dimensional curve.The vector gets shorter as you move away from the origin and always points radially outward because the electric field varies as the inverse of the square of the distance that points from the charge.The density of the lines indicates the size of the field. This indicates that the location with a high density of field lines has a stronger electric field due to the charged substance. The electric field is weaker in the area where the density of these lines is low.The electric field can be depicted by joining these vectors to form a line.The direction of an imaginary line called an electric field line at any place must match the direction of the field there.In general, a field line is a curve drawn so that each point's tangent points in the direction of the net field.To learn more about the electric field, refer to:
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4 Four objects are stiuated along the y axis as follow: a 20 kg object is at +3 m, a 3 kg object is at +2.5 m, a 2.5 kg object is at origin, and a 4 kg object is at -5 m. What is the center of mass of these objects?
Answer: 1.348 meters
Explanation: Although the sign is missing from the location of the 4.00 kg object, it is assumed to be positive. The net moment of all the objects about the center of mass must be zero. Let the center of mass be on the y axis at a point c . Adding the four moments together, we get:
(2.00)(3.00−c)+(3.00)(2.50−c)+(2.50)(0−c)+(4.00)(0.500−c)=0
6.00−2.00c+7.50−3.00c+0−2.50c+2.00−4.00c=0
11.5c=15.50
c= 1.348 metres
The center of mass is on the y axis at y = 1.348 metres.
A transverse mechanical wave is traveling along a string lying along the x-axis. The displacement of the string as a function of position and time, y(x,t), is described by the following equation:
[tex]y(x,t)=0.0480[/tex]×[tex]sin(5.40x-128t)[/tex]
where x and y are in meters and the time is in seconds.
1. What is the wavelength of the wave?
2. What is the velocity of the wave? (Define positive velocity along the positive x-axis.)
3. What is the maximum speed in the y-direction of any piece of the string? (Give a positive answer for speed.)
The wavelength of the wave is 1.16m and the velocity is 23.64m/s.
To find the answer, we have to know more about the Transverse waves.
How to find different parameters of a wave?The displacement of the string as a function of position and time, y(x,t), when the wave traveling along a string lying along the x-axis is given as,[tex]y(x,t)=0.048sin(5.40x-128t)[/tex]
Comparing this with the general form of wave equation, we get,[tex]amplitude, a=0.048m\\wave vector, k=5.40\\angular frequency,w=128Hz[/tex]
We have to find the wavelength of the wave, for this, we have the expression as,[tex]k=\frac{2\pi }{wavelength} \\\\wavelength=\frac{2\pi }{k} =\frac{2*3.14}{5.40} \\\\wavelength=1.16m[/tex]
We have to find the velocity of the wave,[tex]v=frequency*wavelength\\2\pi f=w, thus,\\f=\frac{w}{2\pi } =\frac{128}{2*3.14}=20.38s^{-1}\\\\v=1.16*20.38=23.64m/s[/tex]
Thus, we can conclude that, the wavelength of the wave is 1.16m and the velocity is 23.64m/s
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Which diagram best represents the relationship between these terms?
Quantum
Mechanics
Uses Solid-
State Physics
Has
Applications
Crystallography
how much power is radiated as a sound from a band whose intensity is 1.6x10-3 w/m2 at a distance of 12m
2.89watts.
What is meant by sound intensity?The average rate at which sound energy moves across a unit area normal to a given direction is used to determine a sound's intensity. This rate is generally stated in ergs per second per square centimeter.Decibels are the units used to measure sound intensity, often known as sound power or sound pressure. The decibel (dB) unit is named after Alexander Graham Bell, who also created the audiometer and the telephone. An audiometer is a tool to gauge a person's hearing capacity for various noises.Our ability to measure the flow of sound energy as a time-averaged vector quantity makes sound intensity measuring an effective method. We can identify sound sources and tell direct sound from reverberant sound in a room using the characteristics of sound intensity.How much power is radiated as a sound from a band whose intensity is 1.6x10-3 w/m2 at a distance of 12m:
Formula: [tex]I\frac{P}{4\pi r^{2} }[/tex]
I=1.6x10-3 w/m2
r=12m
[tex]I\frac{P}{4\pi r^{2} }[/tex]
[tex]P=I4\pi r^{2}[/tex]
[tex]=(1.6x10-3\frac{W}{m^{2} } ) (4\pi (12m)^{2} )[/tex]
The power is radiated as a sound from a band whose intensity is 1.6x10-3 w/m2 at a distance of 12m [tex]=2.89watts.[/tex]
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Respond to the following prompts in your initial post:
1. Is Felisha's argument sound or unsound? Use the concepts discussed in your textbook: a valid
structure, true premises, and a sound or unsound argument.
2. Using the fallacies discussed in chapter 11 of your book, identify one fallacy (by name) in
Felisha's argument and explain why this fallacy is an illogical way to argue her conclusion.
3. Describe a time when you successfully argued a point of view and explain why you believe
you were successful.
Based on the textbook, Felisha's argument is known to be unsound because not all the premises that were given was true.
2. She stated that the “The Cowboys are popular and using only their huge fan base to tell is not right and if they are are better as she claim, why are they not the best but she stated that they are among the best.
3. A time when when i successfully argued a point of view was during my high school debate on the topic that doctors are better than lawyers and i gave a lot of valid reasons why the world cannot do without doctors.
What is fallacies and its types?The term fallacies are seen as flawed or deceptive and false kind of arguments that is known to be be proven wrong with the aid of reasoning.
Note that there are two key types of fallacies which are the formal fallacy and an informal fallacy.
Therefore, Based on the textbook, Felisha's argument is seen as an unsound argument because not all the premises that were given was true and they were not standard enough.
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is power and voltage the same thing yes or no
Which of the following statements are true about gravity? Check all that
apply.
A. Gravity exists between two objects that have mass.
B. Gravity exists in the whole universe.
C. Gravity doesn't exist between Earth and the sun.
D. Gravity is a force that pulls two objects together.
E. Gravity exists only on Earth.
SUBMIT
Answer:
Gravity exist between two objects that have mass
In traveling to the Moon, astronauts aboard the Apollo spacecraft put spacecraft into a slow rotation to distribute the Sun's energy evenly (so one side would not become too hot). At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. Think of the spacecraft as a cylinder with a diameter of 8.5 m rotating about its cylindrical axis.
a)Determine the angular acceleration of the ship.
Express your answer using two significant figures.
b)Determine the radial component of the linear acceleration of a point on the skin of the ship 9.5 min after it started this acceleration.
Express your answer to two significant figures and include the appropriate units.
c)Determine the tangential component of the linear acceleration of a point on the skin of the ship 9.5 min after it started this acceleration.
Express your answer to two significant figures and include the appropriate units.
The angular acceleration is 4.44*[tex]10^{-5} rev/s^{2}[/tex] , radial component is 0.016 m/[tex]s^{2}[/tex], tangential component is 0.9347*[tex]10^{-5} m/s^{2}[/tex].
Angular acceleration,
ω=1/60=0.016 rev/s
[tex]\alpha[/tex]=0.016/(6*60)=4.44*[tex]10^{-5} rev/s^{2}[/tex]
The angular acceleration is 4.44*[tex]10^{-5} rev/s^{2}[/tex]
Radial component of the linear acceleration=[tex]\alpha_{r}[/tex]
v=ωr=0.016*4.75=0.076 m/s
[tex]\alpha_{r}[/tex]=0.076 /4.75=0.016 m/[tex]s^{2}[/tex]
The tangential component = [tex]\alpha_{t}[/tex]=4.44*[tex]10^{-5} rev/s^{2}[/tex]/4.75=0.9347*[tex]10^{-5} m/s^{2}[/tex]
Angular accelerationThe temporal rate at which angular velocity changes is known as angular acceleration. Due to the fact that there are two different types of angular velocity—spin angular velocity and orbital angular velocity—there are also two different types of angular acceleration, referred to as spin angular acceleration and orbital angular acceleration, respectively. The terms "orbital angular acceleration" and "spin angular acceleration" describe the angular acceleration of a point particle about a fixed origin and, respectively, the angular acceleration of a rigid body about its center of rotation.
The unit of measurement for angular acceleration is the angle per unit time squared, or, in SI units, radians per second squared. It is typically denoted by the symbol alpha ().
In traveling to the Moon, astronauts aboard the Apollo spacecraft put spacecraft into a slow rotation to distribute the Sun's energy evenly (so one side would not become too hot). At the start of their trip, they accelerated from no rotation to 1.0 revolution every minute during a 12-min time interval. Think of the spacecraft as a cylinder with a diameter of 8.5 m rotating about its cylindrical axis.
a)Determine the angular acceleration of the ship.
Express your answer using two significant figures.
b)Determine the radial component of the linear acceleration of a point on the skin of the ship 9.5 min after it started this acceleration.
Express your answer to two significant figures and include the appropriate units.
c)Determine the tangential component of the linear acceleration of a point on the skin of the ship 9.5 min after it started this acceleration.
Express your answer to two significant figures and include the appropriate units.
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1. What type of waves can only travel through a medium?
Answer:
A mechanical wave can only travel through a medium.
The gravitational force exerted by the Sun on the Earth holds the Earth in an orbit around the Sun. Let us assume that the orbit is perfectly circular. The work done by this gravitational force during a short time interval in which the Earth moves through a displacement in its orbital path is (a) zero (b) positive (c) negative (d) impossible to determine
The work done by this gravitational force during a fast time interval in which the Earth drives through a displacement in its orbital path is (a) zero.
What is the unit of gravitational force?Gravitational Force
The kilogram force (kgf) is a gravitational unit of force. The force exercised by the earth on a body of mass 1 kg is regarded as 1 kgf. Force = Mass × Acceleration. 1 kgf = 9.8 N.
The gravitation force and perpendicular to the path of movement
hence angle between gravitational force [ F ]and displacement (d)=90°
work done (W)= F d cos 90°
= 0
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A 100 N force pulls a box but it doesn’t move. How much work is done?
A. 0 J
B. 100 J
C. 50 J
D. Not enough info
Answer:
A
Explanation:
Work = force * distance
= 100 n * 0 = 0 work done
Drag each tile to the correct location.
Gas cloud 1 is likely to form a star. Gas cloud 2 is not. Based on this information, match the given conditions with each cloud.
Its temperature stays well
below 14 million Kelvin.
its volume shrinks and density
increases due to gravity.
It is spread out, with a greater volume and
lesser concentration of elements.
Its hydrogen atoms retain their electrons.
gas cloud 1
Its temperature surpasses
14 million Kelvin.
Its hydrogen atoms shed their electrons.
gas cloud 2
The most appropriate conditions that matches Gas cloud 1 include the following:
"Its volume shrinks and density increases due to gravity.""Its hydrogen atoms shed their electrons.""Its temperature surpasses 14 million Kelvin."The most appropriate conditions that matches Gas cloud 2 include the following:
"Its hydrogen atoms retain their electrons.""Its temperature stays well below 14 million Kelvin.""It is spread out, with a greater volume and lesser concentration of elements."What is a star?A star can be defined as a giant astronomical object that contains a luminous sphere of plasma and two (2) main hot gases (hydrogen and helium), and it is bounded together by its own gravitational force.
The conditions of a gas cloud.Since Gas cloud 1 is likely to form a star, the most appropriate conditions that matches it include the following:
"Its volume shrinks and density increases due to gravity.""Its hydrogen atoms shed their electrons.""Its temperature surpasses 14 million Kelvin."Since Gas cloud 2 is not likely to form a star, the most appropriate conditions that matches it include the following:
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If a frying pan has a heat capacity of 500.j∘c and it absorbs 25,000 j of heat, what will be the change in temperature in degrees celsius?
Answer:
50° C change
Explanation:
25000 J / (500 J/ °C) = 50 ° C
light has a frequency of about 6 x1014 Hz.
Answer:
The visible light frequency is 400 THz to 700 THz, approximately. A THz is a Terahertz, which is a unit of frequency equal to one trillion Hertz.
• An object of mass 2.0 kg moves in uniform circular motion on a horizontal friction less table. The radius of the circle is 0.75 m and the centripetal force is 10.0 N. The work done by this force when the object moves through one-half of a complete revolution is
Answer:
23.562
Explanation:
First it is good to work out the circumference:
2 pi r
2 pi .75
circumference = 4.7124
Next we need half of this because it is half a resolution. This will be our distance travelled.
half = 2.3562
word done = force x distance
work done = 10 x 2.3562
work done = 23.562
(I didn't see the need for mass...)
Which of the following is correct concerning the uncontrolled burn phase?
Group of answer choices
The uncontrolled burn phase is characterized by uncontrolled combustion in a cylinder until fuel accumulated during ignition delay is burned.
This is also called the flame propagation phase.
Many points in the combustion chamber will simultaneously reach the threshold values required for ignition, and multiple flame fronts will move through the air-fuel mixture.
(All three statements are correct.)
The option that is the correct one concerning the uncontrolled burn phase is:
The uncontrolled burn phase is characterized by uncontrolled combustion in a cylinder until fuel accumulated during ignition delay is burned.What is uncontrolled combustion?
Uncontrolled Combustion is known to be the the time and place in which a kind of an ignition will stop and it is said to be never fixed by anything in regards to the compression ignition engine as seen in SI engines.
Note that the four Stages of combustion are:
1. Pre-flame combustion
2. Uncontrolled combustion
3. Controlled combustion and
4. After burning
Hence, The uncontrolled burn phase is characterized by uncontrolled combustion in a cylinder until fuel accumulated during ignition delay is burned as all the fuel need to burn out.
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i. Which of the following formula gives definition of relative density? d d B. A. C. d water at 4°C d d mercury at 4°C D. d water at 40°C d d alcohol at 4°C
Answer:
water at 4°c that's abnormal stage of water
The velocity of a body is given by the equation v= a + bx, where 'x' is displacement. The unit of b is .......
Answer:
s^ -1 ( or 1/sec)
Explanation:
Velocity is given in units of displacement / sec
like feet /sec or m/sec
so b would have units of s^-1
(or perhaps a more general term would be time^-1)
A fisherman and his young son are in a boat on a small pond. Both are wearing life jackets. The son is holding a large helium filled balloon by a string, holding a significant part of his weight. Consider each action below independently and indicate whether the level of the water in the pond, Rises, Falls, is Unchanged or Cannot tell.
The son pops the helium balloon.
The fisherman knocks the tackle box overboard and it sinks to the bottom.
The son finds a cup and bails some water out of the bottom of the boat
The fisherman lowers himself in the water and floats on his back.
The fisherman lowers the anchor and it hangs one foot above the bottom of the pond. (the anchor is initially inside the boat)
The son gets in the water, looses his grip on the string, letting the balloon escape upwards.
(a) The son pops the helium balloon (unchanged)
(b) The fisherman knocks the tackle box overboard and it sinks to the bottom (rises)
(c) The son finds a cup and bails some water out of the bottom of the boat (falls)
(d) The fisherman lowers himself in the water and floats on his back (unchanged)
(e) The fisherman lowers the anchor and it hangs one foot above the bottom of the pond (rises)
(f) The son gets in the water, looses his grip on the string, letting the balloon escape upwards (rises).
Displaced volume of water in the pond
According to Archimedes principle, when a body is partially or completely immersed in a fluid, it experiences an upthrust which is equal to weight of to fluid displaced.
F = ρVg
V = F/ρg
where;
V is volume of water displacedρ is density of the immersed objectg is acceleration due to gravityWhen an object with a significant weight is dropped into the pond, the level of water in the pond will rise and vice versa.
The son pops the helium balloonThe water level in the pond will be Unchanged, since the weight of the balloon is almost insignificant.
Fisherman knocks the tackle box overboard and it sinks to the bottomThe water level will rise because the weight of the tackle box is significant.
Son finds a cup and bails some water out of the bottom of the boatThe water level will fall since some volume of water is being removed.
Fisherman lowers himself in the water and floats on his backThe water level will be unchanged, since nothing new is added into the pond.
Fisherman lowers the anchor and it hangs one foot above the bottom of the pondThe water level will rise because the anchor will displace some volume of water upwards when it is dropped inside the pond.
Son gets in the water, looses his grip on the string, letting the balloon escape upwards.The water level will rise, because the balloon will displace the water upwards when it escape upwards.
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2. Two particles P and Q are shot vertically up. T
Particle P is first up with a velocity 40ms-¹. After
4s, particle Q is also shot up. Find 01 -
(a) where the two particles meet, if at the point of
meeting, P has velocity of 15ms™¹.
(b) the velocity with which Q is shot. (g = 10ms-²)
(000)(9)
(a) The position where particle Q and P meet is 68.75 m.
(b) The velocity with which particle Q is shot is 15 m/s.
Time at which the two particles meet each otherThe time elapsed before the two particles meet is calculated as follows;
Distance Q - Distance P = Distance between them
Distance traveled by particle P:Trise = (V - V₀)/g
Trise = (0 - 40) / -10
Trise = 4.0 s
Hmax = V₀t + 0.5gt²
Hmax = 40 x 4 - (0.5)(10)4²
Hmax = 80 m.
P is falling when Q is moving up:h = Hmax - (V² - V₀²)/2g
h = 80 - ((15)²- 0) / 20
h = 68.75 m.
Thus, the position where particle Q and P meet is 68.75 m
Tfall = (V - V₀)/g = (15-0) / 10
Tfall = 1.5 s
Fall time. = Rise time for Q.
Distance traveled by particle Q:h = V₀t + 0.5gt²
h = 80 - 68.75
h = 11.25
V₀ x 1.5 - 5(1.5)² = 11.25
V₀ x 1.5 - 11.25 = 11.25
V₀ x 1.5 = 22.5
V₀ = 22.5 / 1.5
V₀ = 15 m/s
Thus, the velocity with which particle Q is shot is 15 m/s.
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(a) Convert 45.0° to radians.
_______ rad
(b) Convert 13.0 rad to revolutions.
________ rev
(c) Convert 76.5 rpm to rad/s.
__________ rad/s
**Remember that there are 2 in one revolution, and 60 seconds in 1 minute. rad/s
(a) Converting 45.0° to radians is 0.785 radian.
(b) Converting 13.0 rad to revolutions is 2.1 rev.
(c) Converting 76.5 revolution per minute to rad/s is 8.02 rad/s.
Degrees to radianTo convert 45.0 degrees to radians, we use the following method;
180⁰ = π radians
45⁰ = ?
= (45 x π)/180
= 0.785 radian
Radian to revolutions2π radians = 1 rev
13 radians = ?
= (13)/(2π)
= 2.1 rev
Revolution per minute to radians per second= 76.6 rev/min x 2π rad/rev x 1 min/60 s
= 8.02 rad/s
Thus, converting 45.0° to radians is 0.785 radian.
Converting 13.0 rad to revolutions is 2.1 rev.
Converting 76.5 revolution per minute to rad/s is 8.02 rad/s.
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Three professional wrestlers are fighting over a champion’s belt, and each exerts a force on the belt. Wrestler 1 exerts a force F1=40.0 N in the +x-direction, wrestler 2 exerts a force F2=80.0 N in the negative y-direction, and wrestler 3 exerts a force F3=60.0 N at an angle of 36.9° counterclockwise (anticlockwise) from the +x-direction.
The resultant force of the three professional wrestlers on the championship belt is 98.35 N.
Component of the forces in x - direction
The component of the forces in x -direction is calculated as follows;
Fx = 40 N + 60(cos 36.9)
Fx = 40 N + 47.98 N
Fx = 87.98 N
Component of the forces in y - directionThe component of the forces in y -direction is calculated as follows;
Fy = -80 N + 60(sin 36.9)
Fy = -43.95 N
Resultant forceR = √Fx² + Fy²
R = √( 87.98² + 43.95²)
R = 98.35 N
Thus, the resultant force of the three professional wrestlers on the championship belt is 98.35 N.
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