Suppose that you are navigating a spacecraft far from other objects. The mass of the spacecraft is 1.5×10
5
kg. The rocket engines are shut off, and you're coasting along with a constant velocity of
v
i
=⟨0,22,0⟩km/s. As you pass location
r
i
=⟨13,16,0⟩km, you briefly fire side thruster rockets, so that your spacecraft experiences a net force of
F
=⟨60000,0,0⟩N for 3.2 s. The ejected gases have a mass that is small compared to the mass of the spacecraft. You then continue coasting with the rocket engines turned off. What will be the components of your position vector an hour later? Start by finding the x component, r
f,x
. Answer in units of m. Answer in units of m. 009 (part 2 of 3 ) 10.0 points Find r
f,y
. Answer in units of m. Answer in units of m. 010 (part 3 of 3 ) 10.0 points Find r
f,z
. Answer in units of m. Answer in units of m.
Answers
The components of the position vector of the spacecraft an hour later are:- x component (r_f,x): 13460.8 m
- y component (r_f,y): 7.92 × \(10^7\) + 16000 m
- z component (r_f,z): 0 m
To find the components of the position vector of the spacecraft an hour later, we need to consider the initial velocity and the net force experienced during the firing of the side thruster rockets.
Given:
- Mass of the spacecraft: 1.5 ×\(10^5\) kg
- Initial velocity: v_i = ⟨0, 22, 0⟩ km/s
- Initial position: r_i = ⟨13, 16, 0⟩ km
- Net force during firing: F = ⟨60000, 0, 0⟩ N
- Firing duration: 3.2 s
First, let's convert the given quantities to SI units. Since the answer is required in meters, we will convert kilometers to meters.
Mass of the spacecraft: 1.5 × \(10^5\) kg
Initial velocity: v_i = ⟨0, 22, 0⟩ km/s = ⟨0, 22000, 0⟩ m/s
Initial position: r_i = ⟨13, 16, 0⟩ km = ⟨13000, 16000, 0⟩ m
Net force during firing: F = ⟨60000, 0, 0⟩ N
Now,
let's calculate the change in velocity during the firing of the thruster rockets using Newton's second law: Δv = (F/m) * Δt
Where:
- Δv is the change in velocity
- F is the net force
- m is the mass of the spacecraft
- Δt is the firing duration
Δt = 3.2 s
m = 1.5 × \(10^5\) kg
F = ⟨60000, 0, 0⟩ N
Δv = (⟨60000, 0, 0⟩ N) / (1.5 × \(10^5\) kg) * (3.2 s)
Δv = ⟨0.128, 0, 0⟩ m/s
Now,
let's find the final velocity by adding the change in velocity to the initial velocity: v_f = v_i + Δv
v_f = ⟨0, 22000, 0⟩ m/s + ⟨0.128, 0, 0⟩ m/s
v_f = ⟨0.128, 22000, 0⟩ m/s
To find the final position, we can use the equation of motion:Δr = v_f · Δt
Where: - Δr is the change in position
- v_f is the final velocity
- Δt is the time interval
Δt = 1 hour = 3600 seconds
Δr = ⟨0.128, 22000, 0⟩ m/s · (3600 s)
Δr = ⟨460.8, 7.92 × \(10^7\), 0⟩ m
Finally, let's find the final position by adding the change in position to -
- the initial position: r_f = r_i + Δr
r_f = ⟨13000, 16000, 0⟩ m + ⟨460.8, 7.92 ×\(10^7\), 0⟩ m
r_f = ⟨13460.8, 7.92 ×\(10^7\) + 16000, 0⟩ m
Therefore,
the components of the position vector of the spacecraft an hour later are:- x component (r_f,x): 13460.8 m
- y component (r_f,y): 7.92 × \(10^7\) + 16000 m
- z component (r_f,z): 0 m
Note: The y component has been simplified by adding the values, but the x and z components remain the same as they are in the same direction as the initial position.
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Related Questions
Sushant went on an educational trip to a village. There he found a potter making pots. He found that the soil used for making pots was different from normal soil. Name the soil and also tell its characteristics.
Answers
The soil used for making pots by potters is commonly known as "Potter's Clay" or "Potter's Soil."
Characteristics of Potter's Clay:
1. Plasticity: Potter's clay has high plasticity, which means it can be easily molded and shaped into different forms without cracking or breaking.
2. Cohesiveness: It exhibits good cohesion, allowing the clay particles to stick together when moistened, forming a workable material.
3. Fine Particle Size: Potter's clay consists of fine particles that contribute to its plasticity and workability.
4. High Water Retention: It has the ability to retain water, which helps maintain the moisture content necessary for the clay to be shaped and formed.
5. Low Shrinkage: Potter's clay exhibits low shrinkage when it dries or undergoes firing, ensuring minimal distortion or cracking during the drying and firing processes.
6. Good Bonding Properties: The clay particles have the ability to bond together, creating a strong and durable structure once fired.
7. Good Porosity: After firing, the clay retains some porosity, allowing the pot to breathe and allowing for the exchange of air and moisture.
Stars appear to move in the sky because______
Answers
Answer:
Stars appear to move in the sky because earth rotates on its axis.
Explanation:
Stars appear to move in the sky because of Earth's rotation on its axis. As Earth rotates, it creates the illusion that the stars are moving in the opposite direction across the sky. This movement is similar to how objects appear to move past us when we are driving down the road. The stars themselves do not actually move, but our perspective from Earth makes it seem as though they are. This movement, along with the changing position of the sun, creates the patterns and movements that we see in the sky throughout the day and night.
A ship is 425 m from a perpendicular cliff at the coast. The ship's siren is sounded and an echo is heard after 2,5 s. Calculate the speed of sound from the data supplied.
Answers
The speed of sound when a echo is heard 2.5 s later is 340 m/s.
What is an echo?An echo is a sound that is repeated due to the reflection of a sound wave in a medium.
To calculate the speed of light from the data supplied, we use the formula below.
Formula:
v = 2d/t...................... Equation 1Where:
v = Speed of soundd = Distance of the from the cliff = 425 mt = Time taken to hear the echo = 2.5 sSubstitute these values into equation 1
v = (2×425)/2.5v = 340 m/sHence, the speed of sound is 340 m/s.
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A state trooper’s car sends out a radar signal
at a frequency of 14.6 GHz.
Find the wavelength of this signal. The
wave speed is 2.998 × 108 m/s.
Answer in units of m.
Answers
The wavelength of the signal of the state trooper's car sending a radar signal at a frequency of 14.6 GHz is 2.05 × 10⁻² m.
What is wavelength?Wavelength is the separation between two consecutive waves corresponding points. When two points or particles are referred to be "corresponding points," it means that they are both in the same phase and have completed exactly the same portions of their periodic motion.
Wavelength is typically measured from crest to crest or from trough to trough in transverse waves (waves with points vibrating at right angles to the direction of their advance); from compression to compression or from rarefaction to rarefaction in longitudinal waves (waves with points vibrating in the same direction as their advance).
The following equation describes how a wave's frequency and speed are related to its wavelength:
λ =\(\frac{v}{f}\)
where,
λ is the wavelength
v is the speed of the wave
f is its frequency
The radio signal of the car has a frequency of:
f= 14.6GHz = 14.6 × 10⁹ Hz
and a speed of:
v = 2.998 × 10⁻² m/s
Substituting the values:
λ = 2.02 × 10⁻² m
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Which of the following does light demonstrate?
A. Both particle and wave characteristics
B. Particle characteristics only
C. Neither particle nor wave characteristics
D. Wave characteristics only
Answers
Answer:
A
Explanation:
Light has both wave and particle characteristics. It behaves as wave in examples such as Reflection, refraction, diffraction, interference. It behaves as a particle in photoelectric effect, compton's effect etc. Light is an example of wave-particle duality.
Light demonstrate both particle and wave characteristics. It can be understood by photo electric effect .
What is light?Light behaves like a particle in some phenomenon , for example photoelectric effect and like wave in some phenomenon , for example reflection and refraction , in this wave light has dual nature.
What is Photoelectric effect ?Emission of photo electrons due to incidence of light on a surface, is called photo electric effect. For it the energy of the incident light should be greater than the work function of the material on which light incidents.
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When 4050 joules of heat were applied to 150g of aluminum, the final temperature was 50 degree Celsius. What was the initial temperature? Take specific heat capacity of aluminum as 900J/kg degree Celsius.
Answers
Answer:
\(\boxed {\boxed {\sf 20 \textdegree C}}\)
Explanation:
We are asked to find the initial temperature of aluminum. We will use the following formula.
\(q= mc \Delta T\)
Where q is the heat energy, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature, which is also the difference between the final and initial temperature.
\(q= mc (T_f-T_i)\)
We know the heat energy applied is 4050 Joules, the mass is 150 grams, the final temperature is 50 degrees Celsius and the specific heat is 900 Joules per kilogram degree Celsius.
We must convert the mass to kilograms because the specific heat is in kilograms. 1 kilogram contains 1000 grams.
\(\frac { 1 \ kg }{1000 g }\)\(150 \ g *\frac{ 1 \ kg }{1000 g } = 150 * \frac {1}{1000} \ kg = 0.150 \ kg\)Substitute all the known values into the formula.
q= 4050 J m= 0.150 kg c = 900 J/g °C \(T_f\)= 50°C\(4050 \ J = (0.150 \ kg )(900 \ J/kg \textdegree C)(50 \textdegree C -T_i)\)
We are solving for the initial temperature, so we must isolate the variable \(T_i\)It is being multiplied by 0.150 kilograms and 900 Joules per kilogram degree Celsius. The inverse operation of multiplication is division, so we divide by both values.
\(\frac {4050 \ J}{ (0.150 \ kg )(900 \ J/kg \textdegree C)}= \frac{(0.150 \ kg )(900 \ J/kg \textdegree C)(50 \textdegree C -T_i)}{(0.150 \ kg )(900 \ J/kg \textdegree C)}\)
\(\frac {4050 \ J}{ (0.150 \ kg )(900 \ J/kg \textdegree C)}=(50 \textdegree C -T_i)}\)
The units of Joules and kilograms cancel.
\(\frac {4050 }{ (0.150 )(900 \ \textdegree C)}=(50 \textdegree C -T_i)}\)
\(\frac {4050}{135} \textdegree C = (50 \textdegree C -T_i)\)
\(30 \textdegree C = (50 \textdegree C -T_i)\)
50 degrees Celsius is being added to \(-T_i\). The inverse operation of addition is subtraction. Subtract 50 degrees Celsius from both sides.
\(30 \textdegree C - 50 \textdegree C= 50 \textdegree C - 50 \textdegree C - T_i\)
\(-20 \textdegree C = -Ti\)
\(T_i\) is being multiplied by -1. The inverse operation of multiplication is division. Divide both sides by -1.
\(\frac {-20 \textdegree C}{-1}= \frac{-T_i}{-1}\)
\(20 \textdegree C = T_i\)
The initial temperature of the aluminum was 20 degrees Celsius.
What is wheel. and axle? Explain its structure with the help of a diagram
Answers
Answer:
The wheel and axle consist of a round disk, known as a wheel, with a rod through the centre of it, known as the axle. This system uses angular momentum and torque to do work on objects, typically against the force of gravity. The wheel and axle simple machine is closely related to gears.
Explanation:
what is a microwave?
Answers
Answer:
an electromagnetic wave with a wavelength in the range 0.001–0.3 m, shorter than that of a normal radio wave but longer than those of infrared radiation. Microwaves are used in radar, in communications, and for heating in microwave ovens and in various industrial processes.
The primary magnetic flux through a coil is increasing. The induced magnetic field is in the opposite direction as the primary field.TRUE
FALSE
Answers
Answer: True
Explanation: Lenz's law - the induced magnetic field is always in such a direction as to oppose the change producing it.
The given statement "The primary magnetic flux through a coil is increasing. The induced magnetic field is in the opposite direction as the primary field." is TRUE. Because, According to Faraday's law of electromagnetic induction, when the primary magnetic flux passing through a coil is increasing.
It induces an electromotive force (EMF) in the coil. This induced EMF creates an induced magnetic field that opposes the change in the primary magnetic field. This is known as Lenz's law. The induced magnetic field's direction is such that it tries to counteract the change causing it. Thus, the induced magnetic field is in the opposite direction to the primary magnetic field. This phenomenon is crucial in various applications, such as transformers and electric generators, where it helps regulate and control the flow of energy in electrical systems.
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A. -2 m/s 2
B. -1 m/s 2
C. 0 m/s 2
D. 2m/s 2
Answers
find w such that the maximum tensile bending stress is 3 ksi
Answers
To find the value of w that will result in a maximum tensile bending stress of 3 ksi, we first need to determine the moment of inertia of the cross-sectional shape of the material in question. Once we have this value, we can use the following formula to calculate the maximum tensile bending stress:
σ = M*c/I
Where σ is the maximum tensile bending stress, M is the bending moment, c is the distance from the neutral axis to the outermost fiber, and I is the moment of inertia.
Assuming that the bending moment is known, we can rearrange the formula to solve for the required value of w:
w = (M*c)/(I*σ)
This will give us the required width of the material to ensure that the maximum tensile bending stress does not exceed 3 ksi. Please note that this is a long answer that requires additional information about the material and the conditions under which it will be used.
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a speaker produces 1 w 1w of acoustical power. if the speaker projects sound uniformly in all directions, at what distance from the speaker will the loudness of the sound be 97.5 db?
Answers
The loudness of the sound from the speaker will be 97.5 dB at a distance of 2.9 mm from the speaker.
The loudness of a sound wave can be measured in decibels (dB) and is related to the power of the wave. The formula to calculate the sound intensity level (SIL) in decibels is SIL = 10 log(I/I₀), where I is the sound intensity and I₀ is the reference intensity, which is usually taken to be the threshold of human hearing, 1 × 10⁻¹² W/m².
To calculate the distance at which the loudness of the sound from the speaker will be 97.5 dB, we can use the formula for sound intensity, which is given by I = P/4πr², where P is the power of the wave and r is the distance from the source.
Since the speaker produces 1 W of power, we can substitute P = 1 W into the formula to get I = 1/4πr². Setting SIL = 97.5 dB, we have:
97.5 = 10 log(I/I₀)
9.75 = log(I/I₀)
I/I₀ = 10^9.75 = 7.94 × 10⁹
Substituting this value for I/I₀ into the formula for sound intensity and solving for r, we get: 7.94 × 10⁹ = 1/4πr²
r = sqrt(1/(4π × 7.94 × 10⁹)) = 0.0029 m or 2.9 mm.
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A car slows from 90mi/he to 55mi/hr when it sees the police what's the cars acceleration
Answers
A hammer drives a nail into a piece of wood. Identify an action-reaction pair.Group of answer choicesThe hammer exerts a force on the nail; the wood exerts a force on the nail.The hammer exerts a force on the nail; the hammer exerts a force on the wood.The nail exerts a force on the hammer; the hammer exerts a force on the wood.The hammer exerts a force on the nail; the nail exerts a force on the hammer.
Answers
Newton's third law states that if an object A exerts a force on object B, then object B must exert a force of equal magnitude and opposite direction back on object A.
Let:
A = Hammer
B = Nail
so:
\(F_{AB}=-F_{BA}\)Therefore:
The hammer exerts a force on the nail; the nail exerts a force on the hammer.
According to the realitivistic expression for momentum, if the speed of an object is doubled, the magnitude of its momentum.
Answers
Answer:
P = M0 V / (1 - (V / C)^2)^1/2
Let V / C = X unless V is a close to the speed of light (10% or so)
(1 - x^2)^1/2 is a small quantity and can be ignored at small speeds.
(1 - [1 - (V/C)^2]^-1/2 = (V/C)^2 using the first terms of the binomial expansion
P2 / P1 = V2 / V1 * (X2 / X1)^2
For V<<C the effect is small and the momentum is merely doubled
Explain how nuclear physics works?
Answers
Answer:
Nuclear physics are the study of protons, and neutrons at the center of an atom. This study shows the interactions between atoms, including what holds them together in a small space. Nuclear physics include fission, fusion, and decay.
Which ferromagnesian mineral is believed to constitute up to 50% of the mantle?
Answers
Answer:
Olivine, with the formula (Mg,Fe)₂SiO₄
Explanation:
Olivine is a mineral with the formula (Mg,Fe)₂SiO₄. It is a magnesium iron silicate (or ferromagnesian mineral) that constitutes the largest part of the earth's upper mantle. The mantle is the second layer of the earth found in between the core (below) and the crust (on top). It accounts for about 84% of the earth's volume (as regards the layers of the earth).
Every celestial object appears to go around the earth once a day. In addition to this motion, which celestial object has the fastest apparent motion in the sky?
Answers
While every celestial object appears to go around the Earth once a day due to the Earth's rotation, the celestial object with the fastest apparent motion in the sky is the Moon.
The apparent motion of celestial objects in the sky is a combination of their actual motion and the rotation of the Earth. As the Earth rotates on its axis, it creates the illusion that all celestial objects are moving across the sky from east to west once every 24 hours.
However, the Moon, being the closest celestial object to Earth, has a noticeable and relatively fast apparent motion compared to other celestial objects. Due to its orbital motion around the Earth, the Moon moves across the sky at an average rate of about 13.2 degrees per day. This rapid motion makes the Moon easily observable as it changes its position against the background stars and planets over relatively short periods.
In contrast, other celestial objects such as stars, planets, and distant galaxies have much slower apparent motion in the sky. Their movement is predominantly governed by their own motion through space and not primarily influenced by the Earth's rotation.
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A 9 cm tall object is placed 16 cm from a converging lens forming an image at 13 cm. What is the height of the image?
Answers
If the work required to speed a car up from 10km/h to 20km/h is 5.0 x 10^3 J, what would be the work required to increase the cars speed from 20km/h to 30km/h?
Answers
If the work required to speed a car up from 10km/h to 20km/h is 5.0 x 10^3 J, the work required to increase the cars speed from 20km/h to 30km/h is: 8.33 × 10³J.
How to find the work required?Using this formula to determine the work required to increase the cars speed from 20km/h to 30km/h
\(Wii = Wi (V^2_2- V^2_1) /v^2_2 - v^2_1\)
Let plug in the formula
Work required = (5 × 10³) (30² -20²) / (20² -10²)
Work required = (5 × 10³) ( 900 - 400) /(400 - 100)
Work required = (5 × 10³) ( 500) / 300
Work required = 8.33 × 10³J
Therefore the Work required is 8.33 × 10³J.
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What is the main function of b-cells?
B. They attack cells of the body that are infected.
None of these
A. They create antibodies.
They signal other lymphocytes to go after the pathogens.
Answers
Answer: They create antibodies.
A solution is prepared by dissolving 32.0 g of NiSO4 in water. What current would be needed to deposit all of the nickel in 5.0 hours?
Answers
A solution is prepared by dissolving 32.0 g of NiSO4 in water. 2.2A current would be needed to deposit all of the nickel in 5.0 hours.
NiSO4 in water
The inorganic compound NiSO4(H2O)6 is commonly referred to as nickel(II) sulphate or just nickel sulphate. This salt, which is extremely soluble and has the colour blue-green, is a typical source of the ion Ni2+ for electroplating.
In 2005, over 40,000 tonnes were generated. It is mostly utilised for nickel electroplating.
Nickel sulphate was the most common allergen in patch tests in 2005–2006 (19.0%).
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Name some appropriate units for measuring energy
Need ASAP
Answers
Answer:The SI unit of energy/work is the joule (J), named for English physicist James Prescott Joule (1818 - 1889). Joule discovered the relationship between heat and mechanical work, which led to the development of the laws of thermodynamics
Explanation:
For this object, what color will you observe?
Answers
Answer:
blue
Explanation:
blue is the only color being reflected, meaning it's the only one that will be visible
Select the correct answer from each drop-down menu. according to the giant impact theory, a giant mars-sized object collided with earth. this collision likely resulted in the , which creates on earth.
Answers
According to the giant impact theory, a giant Mars-sized object collided with Earth. This collision likely resulted in the spinning of the earth, which creates the length of the day on Earth.
The impact of the Mars-sized object caused a tremendous release of energy and angular momentum. This led to the spinning of the early Earth, which was initially in a molten state due to the extreme heat generated by the collision. As the debris from the impact settled and formed the Moon, the spinning of the Earth continued and eventually played a crucial role in the formation and stabilization of the Earth-Moon system.
The Earth's rotation rate changed as a result of the enormous impact's momentum transfer to it, as was previously mentioned. The impact accelerated Earth's spin, shortening days compared to those we currently experience. The Earth's rotation has slowed down over time as a result of tidal interactions with the Moon and Sun, which nevertheless have an impact on the length of a day. However, the original collision had a considerable impact on the early Earth's rotation rate, which in turn affected how long a day was at that time.
Hence, According to the giant impact theory, a giant Mars-sized object collided with Earth. This collision likely resulted in the spinning of the earth, which creates the length of the day on Earth.
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#Complete question is:
According to the giant impact theory, a giant Mars-sized object collided with Earth. This collision likely resulted in the ______ which creates _______ on Earth.
1st blank options:
craters on the moon
spinning of earth
formation of mars
tilting of earth's axis
2nd blank options:
tides
seasonal changes
length of a day
rotation
a thin-walled hollow circular glass tube, open at both ends, has a radius and a length . the axis of the tube lies along the z-axis and the tube is centered on the origin as shown in the figure. the outer sides are rubbed with wool and acquire a net negative charge distributed uniformly over the surface of the tube. use for coulomb's constant. to determine the electric field from the cylinder at location <> far from the tube, divide the tube into rings. an individual ring in the tube has thickness . how much charge is on this ring?
Answers
The charge on the individual ring is dq = σ * 2πr * dr.
A thin-walled hollow circular glass tube, open at both ends and centered on the origin along the z-axis, is negatively charged uniformly on its outer surface.
To determine the electric field it produces at a location a distance 'r' away from the tube, we can divide the tube into rings of thickness 'dr'. Each individual ring possesses charge 'dq'.
To find the charge on a single ring, we can consider an elemental ring with radius 'r' and thickness 'dr'. The charge on this ring can be calculated by multiplying the charge density (σ), which is the charge per unit area, by the area of the ring (dA).
The area of the ring is given by dA = 2πr * dr. Multiplying this by the charge density, we obtain dq = σ * dA = σ * 2πr * dr.
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I need a detailed answer
Answers
The mass of the beam, given that the beam is balanced is 400 g
How do I determine the mass of the beam?First, we shall re-conctruct the diagram given to better understand what we are looking for. Please see attached photo.
In the attached photo,
M is the mass of the beamNote: The mass of the beam act at the centre of the beam
Now, we shall determine the mass of the beam as follow:
Clock wise moment = M × 10Anti-clock wise moment = 200 × 20Mass of beam (M) =?Anti-clock wise moment = Clock wise moment
200 × 20 = M × 10
4000 = M × 10
Divide both sides by 10
M = 4000 / 10
M = 400 g
Thus, from the above calculation, we can conclude that the mass of the beam is 400 g
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Starting from rest, a 4-kg block slides 10m down a frictionless 30° incline.
Determine the work done on the block by the force of gravity, the normal force, the net force, and the KE of the block at the end of the 10m slide
Answers
Answer:
The work done on the block by the force of gravity is 392.4 J. The work done by the normal force is zero. The work done by the net force is equal to the change in kinetic energy of the block. At the end of the slide, the block has a kinetic energy of (1/2)mv^2, where v is the speed of the block.
Explanation:
How many force vectors would be shown on a free-body diagram of an elevator suspended by a cable descending at constant velocity.?
Answers
There would be a total of 2 force vectors on a free-body diagram of an elevator suspended by a cable descending at constant velocity.
What is a free-body diagram?FBDs are valuable tools for describing the relative magnitude and direction of all forces operating on an object in a given condition. The meticulous drafting of a free-body diagram is the initial step in evaluating and describing most physical processes. In a free-body diagram, the size of the arrow denotes the magnitude of the force while the direction of the arrow denotes the direction in which the force acts.
A free-body diagram often includes the following elements:
A streamlined form of the body (most commonly a box)A system of coordinatesForces are depicted as arrows indicating the direction in which they act on the body.Moments are depicted as curving arrows pointing in the direction in which they affect the body.The quantity of forces acting on a body is determined by the nature of the problem and the assumptions made. Air resistance and friction are frequently overlooked.
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A 8-kg load stretches an elastic belt 0.02 m. How much will a 12-kg load stretch the belt?
Answers
Answer:
0.06
Explanation:
a 6 load will be 0.03 so double it to get the answer which is 0.06