The magnitude of the radial acceleration of the car 10m/sec²
Given Velocity v = 50m/sec
Diameter D = 500m
Radius r = 250m
Acceleration a = [tex]v^{2}[/tex]/r = 2500/250 = 10m/sec²
The rate of change in an object's velocity with respect to time is known as acceleration in mechanics. In vector quantities, accelerations exist (in that they have magnitude and direction). [1] [2] The direction of the net force that is acting on an object determines its acceleration. Newton's Second Law[3] states that the sum of the effects of two causes determines the size of an object's acceleration:
The net balance of all external forces acting on that thing — magnitude is directly proportional to this net resulting force; that object's mass, depending on the materials out of which it is built — magnitude is inversely proportional to the object's mass.
Meter per Second Squared (m/s2) is the SI unit for acceleration. displaystyle, mathrm, tfrac, ms2, and
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a constant horizontal force is applied to a block initially at rest on a flat frictionless surface. after the block has traveled a distance d, its speed is v. by the time it has traveled an additional distance 8d, how fast is it moving?
It is moving with a speed of 3v.
What is the straightforward meaning of velocity?The primary indication of an object's position and speed is its velocity. It is the distance that an item travels in one unit of time. The displacement of such item in one unit of time is the definition of velocity.
How to calculate velocity of block?Given, initial velocity, u = 0
velocity at distance d = v
by applying the concept of equation of motion,
v² = u² + 2as
v² = 0+2a×d
a = v²/2d
now, velocity at distance 8d, v°² = v² + 2a×8d
v°² = v² + 2×v²/2d×8d
v°² = v² + 8v²
v° = √9v²² = 3v
It is moving with a speed of 3v.
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A bowling ball rolls without slipping up a ramp that slopes upward at an angle β to the horizontal. treat the ball as a uniform, solid sphere, ignoring the finger holes.
a. What is the acceleration of the center of mass of the ball?
b. What minimum coefficient of static friction is needed to prevent slipping?
The acceleration of the center of mass of the ball is a =g*sin(β)/1.4 and K=tanβ is the absolute minimum of the static friction coefficient.
A sort of opposition force known as frictional force attempts to counteract the motion of the body by acting on the surface of the body. Newton is its unit (N). It is described mathematically as the sum of the normal reaction and the coefficient of friction.
(a) A solid sphere rolling uphill has the equation of motion
M*g sinβ-(2/5)M*a = M*a, where an is the acceleration of the center of mass and mgcosβ = R.
We know that the static friction F=μR
By rearranging above formulas we get
2/5M*a + M*a = Mgsinβ
7/5a = gsinβ
Then a = gsinβ/1.4
(b) In the meantime, the normal force or maximum static friction force is equal to kmgcosβ, where k is the static friction's minimum coefficient. To prevent slippage, the frictional force must be less than the maximum static friction force.
Equating the two terms, we get: mgsinβ = kmgcosβ, k = (sinβ/cosβ) = tanβ.
As a result, k=tanβ is the lowest static friction coefficient.
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Do all waves have a backs and fourth pattern of motion
Yes all waves have the back and forth pattern of motion.
What are waves?A wave is described as a propagating dynamic disturbance of one or more quantities that can be periodic, in which case those quantities oscillate repeatedly about an equilibrium value at some frequency.
Waves come in major types which are :
longitudinal waves transverse waves.Transverse waves are like those on water, with the surface going up and down, and longitudinal waves are like of those of sound, consisting of alternating compressions and rarefactions in a medium.
All types of waves have the same fundamental properties of reflection, refraction, diffraction and interference, and all waves have a wavelength, frequency, speed and amplitude.
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A constant net force of 520n is applied onto a 180kg oil drum. If this force causes the drum to accelerate up to a speed of 3.0m/s from rest, how far did the drum go?
the oil drum traveled a distance of approximately 1.56 meters.
To find the distance that the oil drum traveled, we need to use the equation for average acceleration:
d = (vf^2 - vi^2) / 2a
where d is the distance traveled, vf is the final velocity, vi is the initial velocity, and a is the acceleration.
In this case, we are given that the final velocity is 3.0 m/s, the initial velocity is 0 m/s, and the acceleration is 520 N / 180 kg = 2.89 m/s^2. Substituting these values into the equation, we get:
d = (3.0^2 - 0^2) / 2 * 2.89
= 9 / 5.78
= 1.56 m
Therefore, the oil drum traveled a distance of approximately 1.56 meters.
what is the energy required to change the temperature of 3 kg of water from 26 oc to 64 oc? remember, that the specific heat 4186 j/kgc. answer only in numbers to the nearest whole number.
The energy required to change the temperature from 26°C to 64°C is 47500 J.
Heat is a form of energy that can be transferred from one object to another due to different temperatures.
The heat required to raise the temperature is expressed by the equation:
Q = m.c.ΔT
Q: Heat (Joules)
m: mass (kg)
ΔT: temperature change (°C)
c: specific heat (J/kg°C)
In the given question mass are 3 kg and the temperature change from 26°C to 64°C. (the specific heat is 4186 J/kg°C)
Q = m.c.ΔT
Q = 3 x 4186 x (64°C - 26°C)
Q = 12588 x 38°C
Q = 47720 J ≈ 47500 J
So, the energy required to change the temperature is 47500 J.
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In the original Milgram study, what percentage of participants displayed complete compliance, administering shocks of 450 volts ____ that they believed were lethal.
In the original Milgram study, what percentage of participants displayed complete compliance, administering shocks of 450 volts About 40% that they believed were lethal.
Overview on original Milgram studyThe Milgram experiment(s) on conformity to authoritative persons were a series of social psychology research carried out by Yale University psychologist Stanley Milgram. The willingness of 40 research participants, males from various occupations and educational levels, to follow orders from an authority figure that conflicted with their own moral values was examined.
The volunteers were led to believe that they were taking part in a different experiment in which they had to administer electric shocks to a "learner." If these electric shocks had been real, they would have increased over time to lethal levels.
Unexpectedly, the experiment revealed that a very high percentage of the lab rats would fully comply with the instructions, with every person reaching 300 volts and 65% reaching the full 450 volts.
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A bicyclist increases her speed from 4. 0 m/s to 6. 0 m/s. The combined mass of the bicyclist and the bicycle is 55 kg. How much work did the bicyclist do in increasing her speed?.
The kinetic energy of the horse and rider is equal to 1/2 (mass)(speed)2. 440 joules are equal to KE = 1/2 (55 kg) (4 m/s) at 4.0 m/s. KE = 1/2 (55 kg) (6 m/s) at a speed of 6.0 m/s. 2, or 990 joules. She added 550 joules to her own and her vehicle's kinetic energy.
In Example, what is mass?The proportion of substances involved in any item and body serves as the most accurate definition of weight. We see mass in everything around us. Taking a table, chair, your bed, a football, and a glass as examples.
In simple form, what is mass?The quantity of matter or other constituents that make up an item is its mass. It is measured in kilograms, which can be shortened to kg. It's critical to keep in mind that mass and weight are two distinct concepts.
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Two blocks A and B of masses 5 kg and 1 kg are connected with the help of massless strings
The system is just at the verge of slipping. The coefficient of static friction between the block A and surface below it is
Answer:
The coefficient of friction between all contact surfaces is 0.4. The force, necessary to move the block B with constant velocity, will be (g = 10 m/s)
The coefficient of friction between all contact surfaces is 0.4. The force, necessary to move the block B with constant velocity, will be (g = 10 m/s).
In which condition block B moves?Two blocks A and B of masses 5 kg and 1 kg are connected with the help of massless strings and the system is just at the verge of slipping. The coefficient of static friction between the block A and surface below it is necessary to move the block B.
Static friction is the friction that exists between two surfaces that are not trying to move over each other and which must be overcome before one object starts moving the other.
Two blocks are static equilibrium indicates that the force acting on both blocks is equal.
The frictional force acting on block A is calculated as follows:
Frictional force = coefficient of static friction * normal reaction
Normal reaction on Block A = 30 * 9.8
The coefficient of static friction between block A and the surface = 0.55
Frictional force = 30 * 9.8 * 0.55
Force on Block B = 161.7
Mass of Block B = 161.7 / 9.8
Mass of Block = 18 kg
Therefore, The coefficient of friction between all contact surfaces is 0.4. The force, necessary to move the block B with constant velocity, will be (g = 10 m/s).
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apid change of a magnetic field induces a. a magnetic field of greater magnitude. b. a magnetic field of the same magnitude. c. an electric field. d. nothing.
Faraday is credited with discovering that a fluctuating magnetic field causes a current to flow.
According to Faraday's Law, a current whose magnitude depends on the rate of change of the magnetic field will flow when the strength of a magnetic field changes within a loop of wire. A shifting magnetic field causes an induced current. The induced current is accompanied by an induced emf. Without a battery in the circuit, a current can be generated. The induced emf can be described using Faraday's law of induction. According to Faraday's law, an electromotive force is created when the magnetic flux or magnetic field varies over time.
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When nitrogen and hydrogen gas combine to make ammonia, the chemical equation looks like this:
2N2 + 3H2 => 2NH3
If the hydration energy of 2N2 + 3H2 is equal to + 2251.3 kJ/mol and the lattice energy of 2NH3 is equal to -2343.52 kJ/mol, what is the total energy change of this reaction and is the reaction endothermic or exothermic?
Specific heat capacity of a substance is the amount of heat required to raise the temperature by one degree Celsius of one gram of a substance. Therefore, the total energy change of this reaction is -4,594.82 kJ/mol and reaction is exothermic reaction.
What is Enthalpy?Enthalpy term is basically used in thermodynamics to show the overall energy that a matter have. Mathematically, Enthalpy is directly proportional to specific heat capacity of a substances.
ΔH = Hp - Hr
Hp = energy of the product or lattice energy = -2343.52 kJ/mol
Hr = energy of the reactant or hydration energy= 2251.3 kJ/mol
substituting all the given values in the above equation, we get
ΔH = -2343.52 kJ/mol - 2251.3 kJ
ΔH = -4,594.82 kJ/mol
Since the sing of energy is negative, so reaction is exothermic reaction.
Therefore, the total energy change of this reaction is -4,594.82 kJ/mol and reaction is exothermic reaction.
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the reason a moving object slows down is that its force of motion gradually runs out. true false
The reason a moving object slows down is that its force of motion gradually runs out is false.
If no unbalanced force applies to an object, its momentum stays constant. According to Newton's Second Law, if an object is subjected to an unbalanced force, it will move with a constant speed.
What does momentum actually mean?
The product of a particle's mass and velocity is momentum. Momentum is a vector quantity that has both magnitude and direction. The force exerted on a particle is equated to the time rate of change of momentum by Isaac Newton's second equation of motion.
What does the word "momentum" mean?
illustration of momentum
whenever you throw a ball at a person and it hits him in the face. It shows how challenging it would have been to put a stop to the situation. In the air, a baseball is swooping. There is a big truck moving. a gun of this type shot a bullet.
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Which one of the following is true, according to Newton’s laws of motion? Ignore friction.A. A sports utility vehicle (SUV) hits a stationary motorcycle. Since it is stationary, the motorcycle sustains a greater force than the SUV does.B. A semitrailer truck crashes all the way through a wall. Since the wall collapses, the wall sustains a greater force than the truck does.C. Sam (18 years old) and his sister (9 years old) go ice skating. They push off against each other and fly apart. Sam flies off with the greater acceleration.D. Two astronauts on a space walk are throwing a ball back and forth between each other. In this game of catch the distance between them remains constant.E. None of the above is true, according to the third law.
Option A is a true. An SUV strikes a motorcycle that is standing still. The motorcycle can withstand more force than the SUV since it is stationary.
Every time one object applies force to another, the other object applies an equal and opposing force to the first. His third law argues that there is an equal and opposite reaction to every action (force) in nature. If you push a truck and a vehicle with the same amount of effort, the car will accelerate faster than the truck since it is lighter. Due to the full shopping cart's greater bulk compared to the empty one, it is simpler to push one than the other.
In the early stages of having enough grip, engineers frequently discuss "power to weight ratio" because this impacts acceleration. Since it takes longer (more time) to accelerate a heavier car with the same amount of power to go the same distance, more fuel is consumed.
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A wire can be broken by applying load of 200N. The force required to break another wire of the same length and same material, but double in diameter is
The force needed to break another wire of the same length and material but twice the diameter is 200N.
Because the wires are made of the same material, their modulus of elasticity must be the same.
As a result, the ratio of longitudinal stress to longitudinal strain (Young's Modulus of Elasticity) must be the same. Now, the strains in both wires must be the same before they break.
Therefore,
stress = Young's modulus × strain,
both wires must be the same.
Because the second wire has a diameter twice that of the first, its area of cross section is four times that of the first. As a result, in order to generate the same stress, the force applied to the second wire must be four times that applied to the first wire.(since stress = force/cross section area).
Thus, the force required to break the second wire is 4200=800N.
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if 54 j of work is needed to stretch a spring from 10 cm to 16 cm and another 90 j is needed to stretch it from 16 cm to 22 cm, what is the natural length (in cm) of the spring? cm
The natural length of the spring is 4cm.
Solution:
15/9 = 19k - ka/13k - ka
15/9 = 19 - a/13 - a
195 - 15a = 171 - 9a
24 = 6a
a = 4cm
The term equilibrium length is sometimes used to describe stationary modal distributions. H. Length of multimode optical fiber required to achieve static mode distribution from given excitation conditions. Spring Balance The balance length of a spring is the length when no force is acting.
This is the natural state of spring. Spring constant A measure of elasticity. There is a point where the force and weight of the spring are equal and the directions are opposite. This point is called the equilibrium position. If the masses are in different positions, a net force called the restoring force is directed toward the equilibrium position.
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determine the shear v at a section b between a and c and the moment m at the support a.
The shear force V at A is 7.21 kN, between A and C is 4.01 kN, and the moment M at the support A is -7.22 kN.m
Consider forces acting along y direction:
∑Fy = 0
Ra + Rc = 1.4 + 1.8 .... equation (1)
Take a moment of A ie:
∑Ma = 0
1.4 x 3.1 + 1.8 x 1.6 + 1.8 + Rc = 0
Rc = 4.01kN (left direction)
From equation (1)
Ra + Rc = 1.4 + 1.8
Ra - 4.01kN = 1.4 + 1.8
Ra = 1.4 + 1.8 + 4.01
Ra = 7.21 kN
Consider free body diagram of portion BC: (see in the picture)
Shear force calculation:
Vb= 4.01kN
Consider free body diagram of portion AC:(see in the picture)
Taking a moment of A ie..
∑Ma = 0
Ma + 4.01 x 1.8 = 0
Ma + 7.22kN.m = 0
Ma = -7.22kN.m
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A 40.0-kilogram child exerts a 100.-newton force on a 50.0-kilogram object. the magnitude of the force that the object exerts on the child is: ________
The magnitude of the force that the object exerts on the child is 100N.
Describe Newton's third law of motion.According to Newton's third law of motion, every action has an equal and opposite reaction. In other words, both an action and a reaction are equal and opposed.
The Newton's third is defined mathematically as;
Fa = Fb
where;
Fa is the applied force.
Fb is the response that the object goes through.
The reaction of the object, or the upward force exerted on the child by the object, is 100 N in the opposite direction if the child applies 100 N of force to the object.
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you hang a 65.0 kg mass from an ideal spring having negligible mass. the mass stretches the spring 0.180 m. the mass is now pulled down 0.050 m and released. the period of oscillation of the mass is
The force constant of the spring is 3.53 * 10^3 N/m, the period of oscillation of the fish is 0.115 s and the maximum speed it will reach is 0.869 m/s
Hook's law states that:
where F is the force applied on the spring, k is the spring constant, x is the stretching of the spring.
In this problem, we have
Solving the equation for k, we find the spring constant: k = 3539 N/m
The period of oscillation of a spring-mass system is
T= 2π√M/K
In this case,
m = 65.0 kg
T=2π√(65/3539) = 0.869s
k = 3539 N/m
Substituting into the formula, the period of oscillation of the mass is 0.869 sec.
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what happens to the volume of a marshmallow when you squeeze it? group of answer choices increases decreases remains constant
When you squeeze marshmallow its volume decreases.
Mass remains constant
ρ = m/v ,So density increases as volume decreases.
The amount of three-dimensional space that is occupied is measured by volume. [1] It is frequently measured quantitatively using SI-derived units (such the cubic meter and litre) or by other imperial or US-standard units. Volume and length (cubed) are related concepts. The volume of a container is typically understood to be the capacity of the container, i.e., the amount of fluid (gas or liquid) that the container might store, rather than. the amount of space. the container. itself occupies.
Volume was first determined using naturally occurring vessels of a comparable shape and later with standardized containers. Arithmetic formulas make it simple to determine the volume of several straightforward three-dimensional shapes. Integral calculus can be used to determine the volumes of more complex shapes.
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you do more work on yourself against gravity when you run up the stairs than when you walk slowly. true false
False; running up stairs really requires less exertion against gravity than leisurely walking up them.
Gravity, which means "weight" in Latin, is a basic interaction in physics that causes all objects with mass or energy to be attracted to one another. By far the weakest of the four basic interactions, gravity is 1038 times weaker than the strong interaction, 1036 times weaker than the electromagnetic force, and 1029 times weaker than the weak interaction. As a result, it has no discernible impact on the level of subatomic particles. The motion of planets, stars, galaxies and even light are all governed by gravity, which is the most important interaction between things at the macroscopic level.
On Earth, gravity imparts weight to tangible objects, and the Moon's gravity is what causes sublunar tides in the seas.
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One of the most efficient heat engines ever built is a coal-fired steam turbine in the Ohio River valley, operating between 1870 C and 430 C. (a) What is its maximum theoretical efficiency? (b) The actual efficiency of the engine is 42.0%. How much mechanical power does the engine deliver if it absorbs 1.40×10 ^5 J of energy each second from its hot reservoir?
Maximum theoretical efficiency is 67.2%.
What is Maximum theoretical efficiency?
The utmost efficiency that a heat engine may achieve when working
between two temperatures is known as the Carnot Efficiency.
The degree of heat that the high temperature reservoir runs at ( T Hot ).
The degree of heat in the low temperature reservoir ( T Cold ).
The two temperatures in the case of a car are:
the temperature of the engine's combustion gases ( T Hot ).
The temperature at which the engine's gases are released ( T Cold ).
The maximum theoretical efficiency of this engine is the efficiency of a Carnot engine connected between the same two reservoirs, found from Equation
e C=1− T h
Substitute numerical values:
e C =1− 2143.15
703.15
=0.672
=67.2%
Maximum theoretical efficiency is 67.2%.
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an alpha particle is to be taken apart in the following steps. give the energy (work) required for each step: (a) remove a proton, (b) remove a neutron, and (c) separate the remaining proton and neutron.
Two protons and two neutrons are securely linked together to form composite particles known as alpha particles.
What are Mcq's alpha particles?An elementary particle is a He nucleus, which consists of two protons and two neutrons. A particle with two protons has two units of charge. Four mass units of a particle are equal to two protons and two neutrons. As a result, 4He2 is the symbol for a particle.
How many protons and electrons are present in each alpha particle?Since an alpha particle is the same as a helium atom that has had its two electrons removed, it has two protons and two neutrons. No electrons are present in an alpha particle, hence the two protons' positive charge cannot be balanced.
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in which substance in the table does the speed of light have the value 2.292×108m/s?
The speed of light in ice at 20°C has the value 2.92 × 10⁸ m/s.
We know the expression for refractive index of a medium as,
Refractive index n = velocity of light in vacuum / velocity of light in a medium
It does not have units as it is a ratio.
Given that,
Velocity of light in a medium is 2.92 × 10⁸ m/s.
We know the speed of light in vacuum is 3 × 10⁸ m/s.
The refractive index n = (3 × 10⁸)/(2.92 × 10⁸) = 1.31
The substance with the refractive index 1.31 is ice at 20°C.
Thus, the required substance is ice.
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what is the minimum distance, in au and in miles, for an object to be considered a potentially hazardous object?
An object must have a MOID of 0.05 AU or less in order to be considered a potentially hazardous object. This distance is equivalent to 4.65 million miles. Objects with a MOID between 0.05 and 0.25 AU are considered Near Earth Objects and could potentially become potentially hazardous object (PHOs) in the future.
A potentially hazardous object (PHO) is an asteroid or comet that has an orbital path that comes close enough to Earth to pose an impact hazard. The minimum distance that an object must be from Earth to be considered a PHO is defined by the International Astronomical Union (IAU). The IAU defines a PHO as an object whose Minimum Orbit Intersection Distance (MOID) with Earth's orbit is 0.05 AU or less.
In astronomical units (AU), the minimum distance for an object to be considered a PHO is 0.05 AU. An AU is equivalent to the average distance from Earth to the Sun, or about 93 million miles. Therefore, the minimum distance for an object to be considered a PHO is about 4.65 million miles.
The MOID is the closest approach an object can make to Earth’s orbit. The MOID of an asteroid or comet is calculated based on its orbital elements, such as its semi-major axis and eccentricity. An object with a MOID of 0.05 AU or less is considered to have a close enough approach to Earth’s orbit to pose an impact hazard.
The IAU also defines an object as a “Near Earth Object” (NEO) if its MOID is between 0.05 and 0.25 AU. NEOs are objects that could potentially come close enough to Earth to cause an impact hazard, but are not considered to be PHOs because the risk is not as high.
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ssm what is the spring constant of a spring that stores 25 j of elastic potential energy when compressed by 7.5 cm?
The spring constant for a spring that can store 25J of elastic potential energy when compressed by 7.5 cm is 8.9*10³ N/m.
given,
energy stored in the spring = E = 25J
compressed distance = x = 7.5cm = 0.075m
E = 1/2 * kx²
K = 2E/x²
= 8.9*10³ N/m
The energy that an item retains due to its position in relation to other objects, internal tensions, electric charge, or other reasons is known as potential energy in physics.
Potential energy can take many different forms. Some examples are an object's gravitational potential energy, the elastic potential energy of a stretched spring, and the electric potential energy of an electric charge in an electric field. The joule, denoted by the letter J in the International System of Units (SI), is the unit of energy.
Although it has connections to the Greek philosopher Aristotle's concept of potentiality, the word "potential energy" was first used in the 19th century by the Scottish engineer and scientist William Rankine.
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determine the horizontal velocity va of a tennis ball at a so that it just clears the net at b.
Upon calculation the horizontal velocity of the tennis ball at A so that is just clears the net at B is found to be 39.7 ft/s
This question can be solved using newton's equation of motion.
Equations of motion in physics are equations that explain how a physical system behaves in terms of how its motion changes over time. The behavior of a physical system is described in further detail by the equations of motion as a collection of mathematical functions expressed in terms of dynamic variables. Typically, these variables are time and geographical coordinates, but they might also have momentum components.
Applying newton's equation of motion in vertical direction,
[tex]s_{y}= s_{0y} +ut+\frac{1}{2}gt^{2}+ut[/tex]
Here, u= 0
[tex]s_{y}=3ft\\ s_{0y}=7.5ft[/tex]
g= -32.2 fts⁻²
Putting in equation
3= 7.5+0-[tex]\frac{1}{2}[/tex]×32.2×[tex]t^{2}[/tex]
t= 0.5287 seconds
Applying newtons's equation in horizontal direction
[tex]s_{x}=s_{0x}+u_{x}t[/tex]
Here,
[tex]s_{x}= 21 ft\\s_{0x}= 0\\ t= 0.5287 seconds[/tex]
21= 0+[tex]u_{x}[/tex]×0.5287
[tex]u_{x}= 39.72 ft/s[/tex]
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write a statement about the relationship between the diameter of a pipe and the speed of the fluid flowing through it.
Through the equation of Continuity, The diameter of the pipe and the speed of the fluid are inversely proportional to each other.
According to the equation of Continuity,
Area multiplied by velocity results in a constant., A*v = Constant
Thus, the Area or diameter is inversely proportional to the speed or flow of the fluid.
The cross-sectional area of the pipe has an inverse relationship with flow velocity at any given flow rate.
Higher flow rates result from smaller pipes; slower speeds result from larger pipes. According to the continuity equation, we can increase the volume flow rate, or the velocity of the fluid passing through the pipe, by reducing the pipe's diameter. The fluid velocity is unaffected by the pipe's length, whether it is longer or shorter.
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The curved rod has a radius of 5 ft. If a force of 60 lb acts at its end as shown, determine the moment of this force about point C.
The moment of this force about point C is 267.7lb.ft
According to the information provided in the aforementioned query,
The provided data are,
A curved rod has a radius of 5 feet.
The force act on the end of a curved rod is 60lb.
We have to determine the moment of this force about point C?
Position vector from C to A is;
[tex]& \vec{r}_{C A}=\vec{r}_A-\vec{r}_C[/tex]
Substitute the value in above we get,
[tex]& \Rightarrow \vec{r}_{C A}=\left(5 \sin 60^{\circ} \hat{j}+5 \cos 60^{\circ} \hat{k}\right)-(5 \hat{k}) \\& \Rightarrow \vec{r}_{C A}=4.33 \hat{j}-2.5 \hat{k}[/tex]
Position vector from A to B is;
[tex]& \vec{r}_{A B}=\vec{r}_B-\vec{r}_A[/tex]
Substitute the value in above we get,
[tex]& \Rightarrow \vec{r}_{A B}=(7 \hat{i}+7 \hat{j})-\left(5 \sin 60^{\circ} \hat{j}+5 \cos 60^{\circ} \hat{k}\right) \\& \Rightarrow \vec{r}_{A B}=7 \hat{i}+2.67 \hat{j}-2.5 \hat{k}[/tex]
Force in vector form;
[tex]& \vec{F}=(F)\left[\frac{\vec{r}_{A B}}{\left|r_{A B}\right|}\right][/tex]
Substitute the value in above we get,
[tex]& \Rightarrow \vec{F}=(60)\left[\frac{7 \hat{i}+2.67 \hat{j}-2.5 \hat{k}}{\sqrt{7^2+2.67^2+2.5^2}}\right] \\& \Rightarrow \vec{F}=53.178 \hat{i}+20.284 \hat{j}-18.992 \hat{k}[/tex]
Moment about C will be;
[tex]& \vec{M}_C=\vec{r}_{C A} \times \vec{F}[/tex]
Substitute the value in above we get,
[tex]& \Rightarrow \vec{M}_C=\left|\begin{array}{ccc}\hat{i} & \hat{j} & \hat{k} \\0 & 4.33 & -2.5 \\53.178 & 20.284 & -18.992\end{array}\right| \\& \Rightarrow \vec{M}_C=-\mathbf{3 1 . 5} \hat{\mathbf{i}}-\mathbf{1 3 2 . 9} \hat{\mathbf{j}}-\mathbf{2 3 0 . 3 \hat { \mathbf { k } }}[/tex]
Therefore the Magnitude will be;
[tex]& M_C=\sqrt{(-31.5)^2+(-132.9)^2+(-230.3)^2} \\& \Rightarrow M_C=\mathbf{2 6 7 . 7} \mathrm{lb.ft}[/tex]
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Note:- The correct question would be as bellow.
The curved rod has a radius of 5 ft. If a force of 60 lb acts at its end as shown, determine the moment of this force about point C.
Johnny finds it difficult to play catch on a planet Binu because the planets escape speed is only 5.00m/s and if jonny throws the ball too hard, it flies away. If planet Binu has a mass of 1.56x10^15kg, what is the radius
Answer:
Approximately [tex]4.16 \times 10^{3}\; {\rm m}[/tex] (or equivalently, [tex]4.16\; {\rm km}[/tex]) assuming this planet is spherical.
Explanation:
Let [tex]m[/tex] denote the mass of the ball. If the speed of the ball is [tex]v[/tex], the kinetic energy of the ball will be [tex](\text{KE}) = (1/2)\, m\, v^{2}[/tex].
Assume that the planet is spherical. Let [tex]r[/tex] denote the radius of the planet. Let [tex]M[/tex] denote the mass of this planet, and let [tex]G[/tex] denote the gravitational constant.
On the surface of this planet, the gravitational potential energy [tex](\text{GPE})[/tex] of this ball will be [tex](\text{GPE}) = (-G\, M\, m) / (r)[/tex]. (Note the negative sign. The ball is trapped inside the gravitational field of the planet, and it takes energy input to bring the ball out of this field.)
The ball is at its escape speed [tex]v_{e}[/tex] if the sum of [tex](\text{KE})[/tex] and [tex](\text{GPE})[/tex] at the surface of the planet is [tex]0[/tex]. In other words:
[tex](\text{KE}) + (\text{GPE}) = 0[/tex].
[tex]\begin{aligned}\frac{1}{2}\, m\, v^{2} + \frac{- G\, M\, m}{r} = 0\end{aligned}[/tex].
Rewrite this equation and solve for radius [tex]r[/tex].
[tex]\begin{aligned}\frac{G\, M\, m}{r} = \frac{1}{2}\, m\, v^{2}\end{aligned}[/tex].
[tex]\begin{aligned}r &= \frac{v^{2}}{2\, G\, M}\end{aligned}[/tex].
[tex]\begin{aligned}r &= \frac{2\, G\, M}{{v_{e}}^{2}} \\ &= \frac{2\, (6.67 \times 10^{-11}\; {\rm m^{3}\cdot kg^{-1} \cdot s^{-2})\, (1.56 \times 10^{15}\; {\rm kg})}}{(5.00\; {\rm m\cdot s^{-1}})^{2}} \\ &\approx 8.32 \times 10^{3}\; {\rm m}\end{aligned}[/tex].
A car and a truck traveling in opposite directions left washington, d. C. The car traveled 19 miles per hour faster than the truck, and at the end of 8 hours the vehicles were 1448 miles apart. What was the average speed of each vehicle?.
The car traveled at an average speed of 97 miles per hour and the truck traveled at an average speed of 78 miles per hour.
What is average speed?Average speed is a measure of the distance traveled over time, or the rate at which someone or something is moving. It is calculated by dividing the total distance traveled by the total amount of time it took to travel that distance. For example, if a person runs one mile in five minutes, their average speed is 12 miles per hour (mph).
To calculate this, we must use the equation:
Distance = Rate x Time
For the car: 1448 = (97 + 19) x 8
For the truck: 1448 = (78 - 19) x 8
Therefore, the car traveled at an average speed of 97 mph and the truck traveled at an average speed of 78 mph.
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ta photon absorbed by an electron will give up more energy to the electron if the photon.A. TrueB. False
If a photon's frequency is greater when it is absorbed by an electron, the electron will gain more energy.
Is an electron a photon?Two fundamental quantum-mechanical particles, photons and electrons, have entirely distinct characteristics. The e is an elementary particle found in every atom, whereas the photon is a sort of subatomic particle that serves as an energy carrier.
A photon—is it only light?The basic unit of light would be both commonplace and surprising. Others may just refer to what scientists refer to that as photons as light. Particles are the tiniest electro magnetism packets known as quanta of light.
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