The momentum during the collision is conserved. Hence, the total initial momentum is equal to the total final momentum. Therefore, the initial velocity of the car with a mass of 3250 Kg was, 2.05 m/s.
What is momentum?Momentum of a body is the product of its mass and velocity. Momentum is a vector quantity having both magnitude and direction.
The momentum during a collision is conserved. Thus,the sum of initial momentum of the colliding bodies is equal to the final momentum of the combined mass.
Given that, mass of car 1 = 2150 Kg
velocity = 10 m/s
Momentum = mass × velocity.
= 10 m/s × 2150 Kg = 21500 kg m/s.
Mass of car 2 = 3250 kg
the combined mass = 3250 + 2150 = 5400 Kg
final velocity = 5.22 m/s
final velocity = 5400 Kg × 5.22 = 28188 kg m/s .
momentum of car 1 + momentum of car 2 = 281888 kg m/s
21500 kg m/s + (3400 Kg × V) = 281888 kg m/s
v = 2.05 m/s.
Therefore, the initial velocity of the car with a mass of 3250 Kg is 2.05 kg m/s.
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Your question is incomplete. But your complete question probably was:
A 2150 kg car, moving east at 10.0 m/s, collides and joins with a 3250 kg car. The cars move east together at 5.22 m/s. What was the initial speed of car with 3250 kg mass.
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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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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a line in the spectrum of atomic mercury has a wavelength of 255 nm. when mercury emits a photon of light at this wavelength, the frequency of this light is
The frequency of light is 1.18 × 10^15Hz
Wavelength = 255m
The frequency of light is the number of cycles of the light wave that pass a given point in a specified amount of time. Light waves are electromagnetic waves that are characterized by their frequency, which is measured in hertz (Hz).
Calculating the frequency -
f = c/ λ
where c is the speed of light and λ is the wavelength
Thus,
c = 3 × 10^18 m/s
λ = 255 × 1/ 10^9
= 255 × 10^7
Substituting the values in the formula -
= 3 × 10^18 / 255 × 10^7
= 1.18 × 10^15
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sn]]a dentist's drill accelerates from rest at 770 rad/s2 for 2.01 s. during its angular acceleration, how many revolutions has the drill turned?
The 14976.31 revolutions has the drill turned.
What is acceleration?
The rate of change in velocity is known as acceleration. Acceleration typically signals a change in speed, though this is not always the case. Because of the shifting direction of its velocity, an item moving on a circular path at a constant speed is still accelerating.
What is revolutions ?
When two objects orbit one other, there is a revolution. For instance, once every month, the Moon makes its way around the Earth.
Drill is initially rest ( w₀) = 0
Angular velocity = 814 rad/ s²
time = 4.84 sec
Equation of motion
Ф= w₀t ∝ 1/2∝ t²
where,
∝ = angular acceleration
we want to find no. of revolution which is write as
no.of radiation = distance travelled / 2π
Ф= (0) ( 4.84) + 1/2 (814) ( 4.84)²= 0+ ( 407) (4.84)²
n= Ф/ 2π = 1534.2192/ 2π= 14916.31
n= 14976.31
Therefore, 14976.31 revolutions has the drill turned.
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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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A 48 cm long metal rod is oriented horizontally in a uniform magnetic field with magnetic flux density of 340 g. The magnetic field is directed vertically down into the ground. The metal rod is moved with a speed of 13 m/s in a horizontal direction perpendicular to the length of the rod. Neglect the magnetic field of earth at the location of this apparatus. Determine the potential difference induced in the rod. Calculate the answer in the units of v. Write your answer in decimal form with three digits to the right of the decimal point (e. G. 5. 374); do not write any units
The potential difference induced in the rod is approximately -6.912 v. In general, the potential energy of an object is equal to the work done to move the object to its current position, against the forces acting on it.
Potential energy is a form of energy that an object possesses due to its position in a gravitational field or due to its configuration. It is the energy that an object has due to its position in a system, rather than its motion.
The potential difference induced in the rod is given by Faraday's law of electromagnetic induction:
ΔV = -(BLv)
where B is the magnetic flux density, L is the length of the rod, and v is the speed at which the rod moves through the magnetic field.
Plugging in the given values, we have:
ΔV = -(340 g * 48 cm * 13 m/s)
Converting the length to meters and the magnetic flux density to teslas, we have:
ΔV = -(0.34 T * 0.48 m * 13 m/s)
= -6.912 v
So the potential difference induced in the rod is approximately -6.912 v.
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For the circuit of Fig.30.17 in the textbook, let C = 12.0nF , L = 23.0mH , and R = 78.0? .
Part A
Calculate the oscillation frequency of the circuit once the capacitor has been charged and the switch has been connected to point a
Part B
How long will it take for the amplitude of the oscillation to decay to 10.0% of its original value?
Part C
What value of R would result in a critically damped circuit?
Part A
The oscillation frequency of the circuit after the capacitor is charged and the switch is connected to point a:
given:
C = 12.0 nF = 12 x 10⁻⁹ F
L = 23.0mH = 2,3 x 10⁻² H
R = 78.0
f = ω/2π
Where ω is the corner frequency of the circuit and is given as:
ω = [tex]\sqrt{\frac{1}{LC} - \frac{R^2}{4L^2} }[/tex]
ω = [tex]\sqrt{\frac{1}{(12x10^{9-})(2.3 x 10^{-2})} - \frac{78^2}{4 (23x10^{-2})^2} }[/tex]
ω = [tex]\sqrt{\frac{1}{276 x 10^{-12}} -\frac{6084}{4761 x10^6} }[/tex]
ω = [tex]\sqrt{3.6 x 10^9 - 2.8 x 10^6}[/tex]
ω = 5.99 x 10⁴
f = ω/2π
f = 5.99 x 10⁴/2(3.14)
f = 0,9545 x 10⁴
f = 9545 Hz
So, the frequency of the circuit is 9545 Hz
Part B
The amplitude of the circuit can be expressed as a function of time, and it is expressed in the form.
A(t)= A₀e[tex]__{-Rt/2L}[/tex]
Here, A₀ is the amplitude when time, t = 0, we need to find the time it takes the oscillation to damp into 10%.
A(t) = 10%A = 0.10
0.1A₀ = A₀e[tex]__{-Rt/2L}[/tex]
0.1 = e[tex]__{-Rt/2L}[/tex]
Taking natural log on both sides and rearranging the variables, we get
t = -2LIn(0.1)/R
t = -2(2,3 x 10⁻²)(-2.3)/78.0
t = 1.35 x 10⁻³ s
So, the time taken for the oscillation to damp to 10% is 1.35 s
Part C
The critical damping of the circuit occurs when
R² = 4L/C
R = [tex]\sqrt{\frac{4L}{C} }[/tex]
R = 2768.87 Ω
So, the critical damping occurs for R = 2768.87 Ω
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A dog sits 1.50 m from the center of a merry-go-round and revolves at a tangential speed of 1.80 m/s. If the dog’s mass is 18.5 kg, what is the magnitude of the centripetal force on the dog?
Answer: Fc = 39.96 N
Explanation:
Fc = (mv^2)/r
Fc = (18.5 kg * (1.80 m/s)^2)/(1.50 m)
Fc = 39.96 N
question 6 a 5 m chain with density 2 kg/m hangs off the roof of a building. how much work is required to pull the chain to the roof?
A 5 m chain with density 2 kg/m hangs off the roof of a building. 10 joules work is required to pull the chain to the roof.
The lowest amount of thermodynamic work, or energy, required to transfer an electron from a solid to a point in the vacuum immediately outside the solid surface is known as the work function (sometimes spelled workfunction). Here, the term "immediately" refers to a final electron position that is, on an atomic scale, far from the surface but still too close to the solid to be affected by ambient electric fields in the vacuum. The work function is a property of the material's surface rather than a characteristic of the substance in its bulk (depending on crystal face and contamination). When two dissimilar conductors are in complete equilibrium with one another, the space between them will have an embedded electric field due to the fact that relies on the material surface (electrically shorted to each other, and with equal temperatures). The work function refers to moving an electron many nanometers away from the surface so that the force between the electron and the surface's image charge may be disregarded. The electron must also be close to the surface in relation to any change in the surface structure, such as a change in the material composition, a surface coating, or a reconstruction, as well as the closest edge of a crystal facet.
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what makes the earth different from the other worlds that might have life in the solar system (and easier to detect from far away) is that only earth .
The solar system has a biosphere on its surface where photosynthesis can take place.
What is Biosphere?
The biosphere, usually referred to as the ecosphere, is the sum of all ecosystems on the planet. The area where life exists on Earth is another name for it. According to certain descriptions, the biosphere is practically a closed system in terms of matter, with few inputs and outputs.
The biosphere, according to the broadest definition of biophysiology, is the ecological system that encompasses all living things and their relationships, including their interactions with the lithosphere, geosphere, hydrosphere, and atmosphere.
It is generally believed that the biosphere began to evolve at least 3.5 billion years ago, beginning with a process of biopoiesis (which means life formed spontaneously from non-living matter, such as simple organic molecules) or biogenesis (which means life created from living stuff).
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A vector has initial point at (3, –5) and terminal point at (–2, 3). what are the characteristics of this vector? the magnitude is startroot 13 endroot, and the direction angle is about 58°. the magnitude is startroot 13 endroot, and the direction angle is about 122°. the magnitude is startroot 89 endroot, and the direction angle is about 58°. the magnitude is startroot 89 endroot, and the direction angle is about 122°.
The magnitude of this vector is 9.43 and the direction angle of the vector is 58°.
The initial point and the terminal point of the vectors are (3 - 5) and (-2, 3) respectively.
The characteristics of the vector mainly includes the magnitude and the direction of the angle of the vector.
The magnitude of this vector will be given by,
M = √((-2-3)²+(3+5)²)
M = √(25+64)
M = √89
M = 9.43
The direction angle of this vector with the x-axis will be given by,
Tan A = (8/-5)
Tan A = -1.6
A = 58°.
The direction angle of this vector is 58 degree.
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Answer: D. The magnitude is StartRoot 89 EndRoot, and the direction angle is about 122°.
Explanation:
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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a 10 kg mass is given an initial speed of 10 m/s up a 30o incline plane with coefficient of friction 0.50. calculate the maximum distance it moves up the incline plane.
The maximum distance it moves up the incline plane is 5.47m.
Maximum distance, velocity of mass v = 0
Final kinetic energy, Kf = 1/2 m[tex]v^{2}[/tex] = 1/2 × 10 ×[tex]10^{2}[/tex] = 500j
W = ΔK = Kf - Ki
-mgdcosθμ - mgsinθd = 0 - 500j
mgd(μcosθ + sinθ) = 500j
d = 5.47m
Regardless of the starting or ending point, distance can be defined as the amount of space an object has covered. How much ground an object has covered while moving is referred to as the scalar quantity known as distance. It is the object's overall change in position, or "how far out of place an object is," that is described by the vector quantity displacement. An object's total path traveled can be used to measure distance. As an illustration. The total distance covered by an automobile is 13 km if it drives 5 km east, 8 km north, and then back again.
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a mouse in a maze scurries 41 cm south and then takes a 90-degree turn and scurries 64 cm west to get a piece of cheese. find the mouse's displacement.
Answer:
76 cm southwest
Explanation:
The displacement of the mouse is 76.01 cm along south-west at an angle 57.35° with south direction.
What is displacement?In mechanics, displacement refers to the distance that a particle or body moves in a particular direction. Generally, point masses are used to describe particles and bodies. This means that, without sacrificing generality, bodies can be thought of as having all of their mass concentrated in a single mathematical point.
The mouse scurries 41 cm south and then takes a 90-degree turn and scurries 64 cm west.
Hence, magnitude of resultant displacement = √( 41² + 64²) cm = 76.01 cm.
The direction of displacement is along south-west with an angle with south direction= tan⁻¹(64/41) = 57.35°.
Hence, the displacement of the mouse is 76.01 cm along south-west at an angle 57.35° with south direction.
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Weighing a Bacterium Scientists are using tiny, nanoscale cantilevers 4 micrometers long and 500 nanometers wide-essentially miniature diving boards-as a sensitive way to measure mass. The cantilevers oscillate up and down with a frequency that depends on the mass placed near the tip, and a laser beam is used to measure the frequency. A single E. coli bacterium was measured to have a mass of 710 femtograms = 7.10×10−16 kg with this device, as the cantilever oscillated with a frequency of 17.1 MHz .
Treating the cantilever as an ideal, massless spring, find its effective force constant.
If we consider the cantilever to be a perfect, massless spring, then K = 5.952N/m is its effective force constant.
How does science define force?The meaning of the term "force" is obvious. At about this point, it's perfectly permissible to describe a force as shoving or pulling. An object doesn't "have a force in it" or "contain a force." A force is applied to one thing by another.
Why is force such a big deal?A force can be a push or a pull, and it affects how we go about our daily lives because we can't open or close items, raise our legs or arms or accomplish a lot more without it.
BriefingNumerous E coli bacteria, m = 7.10 × 10⁻¹⁶
frequency =17.1 MHz
frequency of vibration, F = 1/2π√K/M
17.1×10⁶= 1/2π√K/ 7.10 × 10⁻¹⁶
K/ 7.10 × 10⁻¹⁶ = 7.10 ×10¹⁵
K = 5.952N/m
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what is the approximate value of tc for an ideal bose gas at a density of 125 kg/m3, the density of liquid 4he? take m
The approximate value of tc for an ideal bose gas at a density of 125 kg/m3 is 8.3 * 10¹⁹ K
[tex]P_{c} = \frac{2mkt^{3/2} }{4 pi h^{2} } * (2.612)\frac{\sqrt{pi} }{2}[/tex]
[tex]125 kg/m^{3} = \frac{2(6.65*10^{-24})(1.38*10^{-23})^{3/2} }{4pi^{2}(1.05*10^{-34}} *(2.612)\ \frac{sqrt{pi}}{2}[/tex]
Tc = 8.3 * 10¹⁹ K
The substance's mass per unit of volume is its density (also known as specific mass or volumetric mass density). The Latin letter D can also be used to represent density, however the most common sign is (the lower case Greek letter rho). Mass divided by volume is the definition of density in mathematics, where is the density, m is the mass, and V is the volume. Density is sometimes loosely described as weight per unit volume, although this definition is incorrect technically; the term "specific weight" is more appropriate. An example of this is in the US oil and gas business.
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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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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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a spring with a force of 2.9 n / m has a relaxed 0.85 m distance, when a 0.5 kg mass is attached it stretches to 1.65 m. what is the elastic potential energy?
The calculated answer is 1.96kg * m \s2\s /2. The energy that is stored when a force is used to deform an elastic object is known as elastic potential energy.
Until the force is released and the object springs back to its original shape, doing labor in the process, the energy is retained. The object may be compressed, stretched, or twisted during the deformation. Since you are aware of the spring constant k, which is 144 N/m, and the spring stretch from equilibrium position x, which is 16.5 cm, or 0.165, you can use the equation
PE = 2 1 kx 2
= 2 1144(.165) 2
to determine the potential energy of the spring.
This, if you prefer SI terms, is kg * m 2 /s2, or 1.96 Joules.
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what maximum power can be radiated by a 13 cmcm -diameter solid lead sphere? assume an emissivity of 1.
Maximum power can be radiated by a 13 cm diameter solid lead sphere
is 232W
The melting point of lead, which is T = 328°c, is the highest temperature that can be raised.
The sphere's area is A = D2.
Using the maximum radiated power as a baseline and by inserting the values of the numbers:
P = 1.56 × [tex]10^{-8}[/tex] × 0.1² ×601³ = 232W
Energy transfer or conversion rate expressed as power. One joule per second, or one watt, is the definition of power in the International System of Units. Power is referred to as activity in some ancient writings. Scalar quantities include power.
Power is related to other factors; for instance, the power required to move a ground vehicle is calculated as the product of the vehicle's velocity, its aerodynamic drag, and the traction force on its wheels. The torque that a motor produces is multiplied by the angular velocity of its output shaft to produce the output power of the motor. Similarly, the power dissipated in an electrical component of a circuit is the sum of its current and voltage across the element.
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wave interference occurs for a. sound waves. b. light waves. c. water waves. d. all of the above choices are correct. e. none of the above choices are correct
Wave interference occurs for: sound waves, light waves. water waves. all the given option is correct.
What is Wave Interference?
The result of two or more waves colliding is interference. Depending on how the peaks and troughs of the overlapping waves line up, they may add up or may partially or completely cancel one another. The interference definition states that it is
The occurrence when two or more waves combine to generate a new wave with a bigger, smaller, or same amplitude.
The medium adopts a form as a result of the net influence of the two distinct waves due to wave interference. Let's use the example of two pulses with the same amplitude moving in opposite directions in the same medium to better comprehend.
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when ultraviolet light with wavelength of 370.0 nm falls on certain metal surface, the maximum kinetic energy of the emitted photoelectrons is measured to be 1.40 ev. find the work function (binding energy) of the metal (in ev). (10 pts.)
The work function of the metal is 2.25 eV.
The work function, or binding energy, of a metal is the minimum energy required to remove an electron from the surface of the metal. In this case, the maximum kinetic energy of the emitted photoelectrons is 1.40 eV, which means that the energy required to remove the electron from the metal was at least 1.40 eV.
To find the work function of the metal, we can use the following equation:
Work function (eV) = Photon energy (eV) - Maximum kinetic energy of photoelectrons (eV)
Plugging in the values given in the problem, we get:
Work function (eV) = Photon energy (eV) - 1.40 eV
The energy of a photon can be calculated using the equation:
Photon energy (eV) = hc / wavelength (m)
Where h is the Planck constant (6.626 x [tex]10^{-34}[/tex] J × s), c is the speed of light (2.998 x [tex]10^{8}[/tex] m/s), and wavelength is the wavelength of the photon in meters.
Plugging in the values and converting the wavelength to meters, we get:
Photon energy (eV) = (6.626 x [tex]10^{-34}[/tex] J × s) × (2.998 x [tex]10^{8}[/tex] m/s) / (3.70 x [tex]10^{-7}[/tex] m)
= 3.65 eV
Substituting this value back into the first equation, we get:
Work function (eV) = 3.65 eV - 1.40 eV
= 2.25 eV
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i need the answer for this one
Answer:
120 N.
Explanation:
This can be calculated using Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma).
In this case, the mass of the object is 60 kg, and its acceleration is 2 m/s^2. so,the net force acting on the object is 60 kg * 2 m/s^2 = 120 N.
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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The electric potential along the x-axis is V=100e?2x/mV, where x is in meters.Part AWhat is Ex at x=1.0m?Express your answer as an integer and include the appropriate units.
27.23 V/m it the electric field strength at a distance 1.0m from origin in x direction.
given V=100[tex]e^-^2^x[/tex]
What is electric field?The physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them, is known as an electric field (or E-field).
formula of electric field in term of electric potential is given by:
[tex]E_x[/tex] = [tex]-\frac{dV}{dx}[/tex]
=> - d(100[tex]e^-^2^x[/tex] )/dx
=>200[tex]e^-^2^x[/tex]
so [tex]E_x=[/tex] 200[tex]e^-^2^x[/tex] ----- (i)
now we have to find electric field strength at point x=1m
so putting the value of x in in equation (i) we get
[tex]E_x=[/tex] 200[tex]e^-^2[/tex]
=> 200/(2.71*2.71)
=>27.23
so electric field strength at point x=1 is 27.23 V/m
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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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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.
a man 1.9 m tall is standing 4.0 m from the edge of the barn. will he be hit by the snowball?
The man will not be hit by the snowball as it passes well above him without touching him.
(a) The length of time in the air is determined by vertical motion.
ax = 0
ay = 9.8 m/s²
vx = v₀ cosθ₀ = 7 cos 40° = 5.36 m/s
vy = v₀ sinθ₀ = 4.5 m/s
Distance from the ground is given as s = 14 m, so,
14 = 4.5 t + (1/2 × 9.8 × t²)
4.9 t² + 4.5 t - 14 = 0
The positive root of t = 1.29 s
The horizontal distance, vx t + (1/2 × ax × t²) = 6.91 m
(b) We know, x - x₀ = vx t + (1/2 × ax × t²)
As ax = 0,
t = (x - x₀)/vx = 4/5.36 = 0.746 s
During this time, the snowball travels a horizontal distance
y - y₀ = vy t + (1/2 × ay × t²) = 6.08 m
Hence, 14 - 6.08 = 7.9 m above the ground and the snowball passes above the man without hitting him.
The question is incomplete. The complete question is '(a) A snowball rolls off a barn roof that slopes downward at an angle of 40°. The edge of the roof is 14.0 m above the ground and the snowball has a speed of 7.00 m/s as it rolls off the roof. How far from the edge of the barn does the snowball strike the ground if it doesn't strike anything else while falling?
(b) A man 1.9 m tall is standing 4.0 m from the edge of the barn. Will he be hit by the snowball?'
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the north celestial pole is 35∘ above your northern horizon. this tells you that you are at:
You are at latitude 35∘ N , if the north celestial pole is 35∘ above your northern horizon . The north celestial pole is a point where all stars can be seen from the northern hemisphere.
All of the stars visible from the Northern Hemisphere spin about the North Celestial Pole in the sky. North Street Polaris stays virtually immobile in the sky and all the stars in the northern sky appear to revolve around it because it is almost directly aligned with the Earth's axis of rotation "above" the North Pole, the north celestial pole. This spot in the sky is virtually exactly where ar, also known as Polaris, is located.
The reasonably brilliant Pole Star is located extremely close to the North Celestial Pole, making it simple to detect it in the night sky. But there are no observable stars near the South Celestial Pole. All of the stars in the sky are centred on the North Celestial Pole.
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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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