The resultant density of the sphere when its radius is halved is eight times the initial density of the sphere.
Let the radius of the sphere = r
The volume of the sphere = [tex]\frac{4}{3} \pi r^{3}[/tex]
Mass of the sphere = M
Now, The density of the sphere = D = Mass/Volume
So, The density will be,
[tex]D = \frac{M}{\frac{4}{3} \pi r^{3} } = \frac{3M}{4\pi r^{3} }[/tex]
It is given that the radius of the sphere is halved, then
[tex]D' = \frac{M}{\frac{4}{3} \pi (\frac{r}{2} )^{3} } = \frac{24M}{4\pi r^{3} } = \frac{6M}{\pi r^{3} }[/tex]
Now, Dividing both the densities, D and D', we get
[tex]\frac{D}{D'} = \frac{1}{8}\\ \\D' = 8D[/tex]
Hence, The resultant density of the sphere when its radius is halved is eight times the initial density of the sphere.
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the radius of a sphere decreases at a rate of 6 m/sec. find the rate at which the surface area decreases when the radius is 20 m. recall that the surface area of a sphere of radius r is given by s
The rate at which the surface area decreases is -960 π m²/sec.
The surface area of a solid object is a measure of the entire vicinity that the floor of the object occupies. the distance occupied by means of a -dimensional flat surface is known as the area. it is measured in square devices. The location occupied through a three-dimensional item by using its outer surface is referred to as the surface place. it is also measured in square units.
The surface area is the full area included via all the faces of a 3D object. as an example, if we want to find the amount of paint required to paint a cube, then the floor on which the paint might be carried out is its surface vicinity. it is continually measured in rectangular units.
calculation:-
Given,
The radius of the sphere decreases at the rate of 6 m/ sec
mean dx/dt = -6
The surface area of the sphere of radius r is = 4πr²
Differentiating with respect to t,
dS/dt = 4π(2r)dx/dt
= 8πr dx/dt
dS/dt = 8π(20)²(-6)
= -960 π m²/sec
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definition of sound waves
Answer:
Explanation:
a wave of compression and rarefaction, by which sound is propagated in an elastic medium such as air.
match the terms with their definitions. (4 points) b 1. average speed 2. acceleration 3. speed a 4. instantaneous speed a. speed at a particular instant of time b. total distance covered divided by the total time required c. rate of change of velocity with time d. rate of change of distance with time
The given question can be matched accordingly
Average speed= total distance covered divided by the total time required
Speed = rate of change of distance with time
Instantaneous speed = speed at a particular instant of time
Acceleration = rate of change of velocity with time
Explain the above terms.
Average speed is a scalar quantity. The formula for average speed is the ratio of the total distance traveled by the body to the time .Speed can be defined as distance per unit time . The SI unit of speed is m/s. It is the change in the position of an object with respect to time.
Instantaneous speed can be defined as the speed of a particle in the movement . It expresses the rate of change of displacement for any given instant of time. It is calculated as meter per second (m/s).
Acceleration is a vector quantity. It represents rate of velocity with time.
Si unit is m/s2
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O
I. An object of mass 8. 0 kg is falling vertically through the air. The drag force acting on the object is 60 N. What is the best estimate of the acceleration of
the object
A. Zero
B. 2.5 ms-2
C. 7.5 ms-2
D. 10 m s-2
The best estimate of the acceleration of the object 2.5 m/sec².
What is force?A force is an effect that can alter an object's motion according to physics. An object with mass can change its velocity, or accelerate, as a result of a force. An obvious way to describe force is as a push or a pull. A force is a vector quantity since it has both magnitude and direction.
Force due to gravity = mg
= 8*9.8 = 78.4 N
Net force on object = 78.4 - 60 = 18.4 N
Acceleration = 18.4/8 = 2.5 m/sec²
The best estimate of the acceleration of the object 2.5 m/sec².
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At the instant the traffic light turns green an automobile that has been waiting at an inter section starts a head with a constant acceleration of 2m/s square. At the same instant a truck. traveling with a constant velocity of 10m/s, overtakes and passes an automobile. How far beyond its starting point will the auto mobile overtake the truck?
Answer:
100 m
Explanation:
Distance truck will travel = 10 m/s * t sec
Distance car will travel = 1/2 at^2
find when these two are equal
10t = 1/2 (2) t^2
t^2 -10t = 0
shows t = 10 sec
In 10 sec the truck travels 10 m/s * 10 s = 100 m
what is the correct formula for cauculating speed
Answer: speed = distance ÷ time
During a baseball game, a batter hits a popup to a fielder 84 m away. The acceleration of gravity is 9.8 m/s 2 . If the ball remains in the air for 5 s, how high does it rise? Answer in units of m.
The ball rises up to 30.625 m high.
What is gravity?The force that pulls items toward the centre of a planet or other entity is called gravity. All of the planets are kept in orbit around the sun by gravity.
Given parameters:
Horizontal range of the ball; R = 84 m.
Time of flight of the ball: T = 5 s.
Acceleration due to gravity; g = 9.8 m/s².
We have to find, maximum height obtained by the ball; H = ?
In projectile motion, time of flight is; T = 2usinθ/g
Where, u = initial velocity of the ball and θ = angle of projection.
So, 2usinθ/g = 5
⇒ usinθ = 5g/2 = (5×9.8)/2m/s = 24.5 m/s.
Then maximum height obtained by the ball;
H = u²sin²θ/2g
= 24.5²/(2×9.8) = 30.625 m.
Hence, maximum height obtained by the ball is 30.625 m.
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If a collision results in a change of momentum of 45 kg m/s and exerts an impact force of
7.2 N, find the time that this collision took.
The time taken by the collision with a change in momentum of 45 kgm/s is 6 seconds.
What is time?Time can be defined as an ongoing and continuous sequence of events that occur in succession, from past through the present, and to the future.
To calculate the time ot takes the collision, that result to change in momentum, we use the formula below.
Formula:
t = ΔM/F............. Equation 1Where:
t = TimeΔM = Change in momentumF = ForceFrom the question,
Given:
ΔM = 45 kgm/sF = 7.2 NSubstitute these values into equation 1
t = 45/7.5t = 6 seconds.Hence, the time taken by the collision is 6 seconds.
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caleb is driving at a speed of 20.5 m/s when he sees a deer on the road ahead. he applies the brakes when he is a distance of 213 m from the deer. if the deer does not move and the car stops right before it hits the deer, what is the acceleration provided by the brakes?
The acceleration provide by the car is 1.26m/s².
What is acceleration?
The rate of change in both speed and direction of velocity over time is defined as acceleration. when anything moves faster or slower in a straight line, it is said to have been accelerated. Because the direction is always shifting, motion on a circle accelerates even when the speed is constant.
What is speed?
As opposed to speed, velocity describes the rate and direction of motion of an object moving along a path.
Given, u= 23m/s
v=0
s=210m
A=?
using the equation of motion from the context section we get
v²=u²-2as
0=u²-2as
u²=2as
a=u²/2s
a=23²/2*210
a= 1.26m/s²
The answer is deacceleration of the car is 1.
Therefore, the acceleration provide by the car is 1.26m/s².
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what is it called when heat cannot escape into space?
Brownlee Heat Exchange Anomaly -Greenhouse Effect. when heat cannot escape into space.
The greenhouse effect is a process that occurs when electricity from a planet's host star is going via its ecosystem and heats the planet's floor, however, greenhouse gases within the surroundings prevent some of the warmth from returning without delay to the area, ensuing in a hotter planet. Earth's natural greenhouse impact maintains the planet from having the under-freezing temperature that it would have if there have been no greenhouse gases. moreover, human-induced increases in greenhouse gases trap more amounts of warmth, inflicting the Earth to develop warmer over the years.
most gases inside the ecosystem are transparent to infrared, however, the small share of the surroundings that constitutes greenhouse gases absorbs some of the heat emitted through the floor rather than letting it get away into space. those greenhouse gas molecules then emit radiant heat in all instructions, passing warmness to the surrounding air and warming different greenhouse gas molecules.
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If a direct current of 5 Volts, goes through a primary coil, the voltage in the secondary coil will be double.
A) True
B) False
If a direct current of 5 Volts, goes through a primary coil, the voltage in the secondary coil will be double is the false statement.
The voltage across the secondary coil is greater than the voltage across the primary. There are fewer turns on the secondary coil than the primary.
The output power is greater than the input power. The current in the secondary coil is greater than the current in the primary coil.
The secondary voltage of a transformer may be either in phase or out of phase with the primary voltage. This depends on the direction in which the windings are wound and the arrangement of the connections to the external circuit.
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by simplifying and solving the continuity, momentum, and energy equations, determine the maximum temperature and where it occurs. the maximum temperature is
The maximum temperature is the temperature gradient profile.
Temperature is a measure of the average kinetic energy of the particles in the sample. There is no absolute maximum for temperature because there is no upper limit for kinetic energy. When the sun sets, the radiation from the sun and the radiation from the earth are balanced, the temperature stops rising, and we see the highest temperature of the diurnal cycle.
Use a special thermometer to measure maximum and minimum temperatures. It's called a maximum-minimum thermometer. Used in meteorology horticulture etc. to record temperature extremes in a location. The temperature difference is the difference between the maximum and minimum temperatures of a day. High and low temperatures are measured with thermometers attached to a slitted wooden box called a Stevenson sieve.
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Which sentence in the passage can be used to conclude that Eris is a dwarf planet and not a planet?
Eris takes about 557 Earth years to orbit the Sun. It has a mean surface temperature of about 40 Kelvin. It has a nearly spherical shape. It has several other objects in its orbit, though few are as massive as itself. Eris is too far away and small to be clearly visible from the Earth. Scientists used its moon, Dysnomia, to measure it. Eris is believed to be slightly more massive than Pluto. However, both of them are smaller than Earth’s Moon. Eris orbits the Sun directly; it is not a satellite of another planet or dwarf planet.
Answer:
It has several other objects in its orbit, though few are as massive as itself."
if the mass of the earth and all objects on it were suddenly doubled, but the size remained the same, the acceleration due to gravity at the surface would become if the mass of the earth and all objects on it were suddenly doubled, but the size remained the same, the acceleration due to gravity at the surface would become 4 times what it now is. 1/2 of what it now is. 1/4 of what it now is. 2 times what it now is. the same as it now is.
Answer:
Explanation:Physics is the branch of science that deals with the structure of matter and how the fundamental constituents of the universe interact. It studies objects ranging from the very small using quantum mechanics to the entire universe using general relativity.
If Mrs. Hankinson slides a 500 g book with 0.5 N of force, what is the acceleration of the book?
F = ma
A. 1000 m/s²
B. 500 m/s²
C. 250 m/s²
Answer: a = 1.0 m/s2
Explanation:
F = ma
a = F/m = 0.5 N / 0.5 kg = 1 m/s2
You have to convert g to kg
500g = 0.5 kg = 1.0 m/s2
The correct answer is not shown in A, B or C!
When two lamps are connected in parallel to a battery, the electrical resistance that the battery senses is?
Answer:
Explanation:
Parallel resistance:
R = R₁·R₁ / (R₁ + R₁)
An athlete is running at a constant velocity with a javelin held in his right hand. The force he is applying on the javelin to carry it is 5. 0 newtons. If he covers a distance of 10 meters, what work has he done on the javelin?.
If he covers a distance of 10 meters, the work he has done on the javelin is 0 joule.
In physics, it measure of energy transfer that occurs when an object is moved over a distance by an external force at least part of which is applied in the direction of the displacement. In its simplest form, for a constant force aligned with the direction of motion, it equals the product of the force strength and the distance traveled.
How to determine the work he has done on the javelin?
The actual formula of finding the work is
W = F × S cos a, a is the angle in which the athlete is carrying the javelin.
or, W = 5 × 10 cos90, angle is 90 with the vertical component of the force (because the force of 5N that the athlete is applying to the javelin can't possibly be in the direction that he and the javelin are moving, otherwise the javelin would be accelerating)
cos 90 = 0
therefore 5*10*0=0,
Hence work done in joules is 0 joules.
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the cable lifting an elevator is wrapped around a 1.0-m-diameter cylinder that is turned by the elevator's motor. the elevator is moving upward at a speed of 1.9 m/s . it then slows to a stop, while the cylinder turns one complete revolution.
The time taken by the elevator to stop if the cable lifting an elevator is wrapped around a 1.0-m-diameter cylinder and the elevator is moving upward at a speed of 1.9 m/s is 3.28 s
d = 1 m
r = d / 2
r = 1 / 2 = 0.5 m
Vertical distance travelled = Circumference of the cylinder
s = 2 π r
s = 2 * 3.14 * 0.5
s = 3.14 m
v² = u² + 2 a s
v = 0
u = 1.9 m / s
0 = 1.9² + ( 2 * a * 3.14 )
6.28 a = - 3.61
a = - 0.58 m / s²
v = u + at
0 = 1.9 + ( - 0.58 * t )
t = 1.9 / 0.58
t = 3.28 s
Therefore, the time taken by the elevator to stop is 3.28 s
The given question is incomplete. The complete question is:
The cable lifting an elevator is wrapped around a 1.0-m-diameter cylinder that is turned by the elevator's motor. The elevator is moving upward at a speed of 1.9 m/s. It then slows to a stop as the cylinder makes one complete turn at constant angular acceleration. How long does it take for the elevator to stop?
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weather balloon is designed to expand to a maximum radius of 20 m at its working altitude, where the air pressure is 0.030 atm and the temperature is 200 k. if the balloon is filled at atmospheric pressure and 300 k, what is its radius at liftoff?
The radius at liftoff is 6.83 m
What is an ideal gas?
A theoretical gas called an ideal gas is one that has lots of point particles flying around arbitrarily and not being affected by other particles.The ideal gas law, also known as the perfect gas law, is a relationship between a gas's pressure P, volume V, and temperature T in the range of low pressures and high temperatures where the gas's molecules move virtually independently of one another. In this situation, the ideal gas law, a state equation for all gases, holds true:PV = nRT
The universal gas constant, R = 8.31446261815324 joules per kelvin per mole, and the number of moles of the gas, n,
Given in the question the following informations:
P1 = Initial pressure = 0.03 atm
P2 = Final pressure = 1 atm
r1 = Inital radius = 20 m
V1 = Intial volume of gas = 4/3 x 3.14 x r1^3
V2 = Final volume of gas = 4/3 x 3.14 x r2^3
T1 = Initial temperature = 200 K
T2 = Final temperature = 300 K
Let the radius at the liftoff be r2
From ideal gas law we have
P1V1/T1 = P2V2/T2
P1V1T2 = P2V2T1
P1 x 4/3 x 3.14 x r1^3 x T2 = P2 x 4/3 x 3.14 x r2^3 x T1
P1 x r1^3 x T2 = P2 x r2^3 x T1
r2^3 = P1 x r1^3 x T2 / P2 x T2
= 0.03 x 20 x 20 x 20 x 300/ 1 x 200
= 360 m
r2 = 6.83 m
Hence, The radius at liftoff is 6.83 m
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how does energy cost per mile relate to body mass? group of answer choices it increases proportionately with body mass the two are unrelated it decreases proportionately with body mass energy cost per mile remains constant
It increases proportionately with body mass in this way energy cost per mile relate to body mass.
An individual's height and weight are used to calculate their body mass index. The body mass index (BMI) is calculated by dividing the body weight in kilograms by the square of the height in meters. It is expressed in kilograms per square meter (kg/m2) and is a function of both height and weight. Weight in kilograms divided by height in meters squared yields the Body Mass Index (BMI) of a person. High levels of body fat may be indicated by a high BMI. A person's body mass index (BMI) does not provide a diagnosis of their health or body fatness; rather, it is a screening tool for weight categories that may cause health issues. Based on your height, weight, and BMI, you can calculate your body fat percentage. BMI measurements are widely regarded by doctors as an easy way to assess a person's weight and determine whether they are overweight or underweight, or whether they are healthy.
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What should be the minimum power of a generator supplying 220V to simultaneously supply the following appliances: 1 fridge 1500W, 3 halogen lamps 500W, 1 electric coffee maker 1600W?
☐ 1,8 KVA
☐ 3,3 KVA
☐ 5 KVA
☐ 7,5 KVA
The minimum power of the generator to power 1 fridge, 3 halogen lamps, and 1 electric coffee maker simultaneously must be 5 KVA.
What is electric power?
Electric power can be defined as the measurement of electric energy flowing in the electric circuit per second.
The electric power consumed by the appliances is given as;
1 fridge = 1500 W3 halogen lamps = 500 W each1 electric coffee maker = 1600 WThe total electric power consumed by the appliances is calculated as follows;
total electrical power consumed = 1500 W + 3(500 W) + 1600 W
total electrical power consumed = 1500 W + 1500 W + 1600 W
total electrical power consumed = 4,600 W
total electrical power consumed = 4.6 kW = 4.6 kVA
electrical power consumed ≈ 5 kW = 5 KVA
Thus, the minimum electrical power to be generated to power all the given appliances simultaneously must be at least 5 KVA.
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The big surprise about the first planet discovered around another regular star was that it.
The primary surprise regarding the first planet found orbiting another regular star was the fact that its orbit took only 4 days to complete.
What method was employed by astronomers to make the first verified discovery of a planet orbiting a star similar to the Sun?Astronomy has long employed the method, also known as the radial velocity method. The same telescope that astronomers used to find this planet was also used to find the first planet ever discovered around a sun-like star using radial velocity.
Finding exoplanets can be done using the Doppler method. The motion and characteristics of the star and planet are examined using the Doppler effect. The planet and the star are revolving around the same mass.
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Cindy roller skates with a constant
speed of 18 km/h. How long will she
take to travel a distance of 54
kilometres?
Answer:
3 hours
Explanation:
[tex](54 km)\frac{1 h}{18 km} = 3 h[/tex]
Is the effect of adding bonded atoms and lone pairs to the central atom similar? explain why this could be the case.
The effect of adding bonded atoms and lone pairs to the central atom is similar in a way that both repel the other atoms away to create more space for themselves, taking all the available space.
While it's generally understood that the effect of adding bonded atoms and lone pairs to the central atom is similar, it is not all the same. The repulsions caused by bonding atoms are lesser than the repulsions caused by lone pairs because lone pairs are closer in position to the nucleus than the bonding atoms, resulting in a different shape of the molecule.
The difference above makes some people think the effect is more not similar than similar because of the result.
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Consider a level flight turn of a propeller-driven airplane in which the airplane makes a complete circular turn in 1.8 min. If the plane's speed is 160 m/s, what is the radius of the circle? What is the centripetal acceleration of the plane?
1. The radius of the circle is 2758.6 m
2. The centripetal acceleration of the plane is 9.28 m/s²
1. How do I determin the radius of the circle?
To obtain the radius, we'll begin by obtaining the angular velocity. This can be obtained a follow:
Period (T) = 1.8 mins = 1.8 × 60 = 108 sPi (π) = 3.14Angular velocity (ω) =?ω = 2π/ T
ω = (2 × 3.14) / 108
ω = 0.058 rad/s
Finally, we shall determine the radius. This is shown below:
Velocity (v) = 160 m/sAngular velocity (ω) = 0.058 rad/sRadius (r) =?r = v / ω
r = 160 / 0.058
r = 2758.6 m
Thus, the radius is 2758.6 m
2. How do I determine the centripetal acceleration?
The centripetal acceleration can be obtained as illustrated below:
Velocity (v) = 160 m/sRadius (r) = 2758.6 mCentripetal acceleration =?Centripetal acceleration = v² / r
Centripetal acceleration = (160)² / 2758.6
Centripetal acceleration = 9.28 m/s²
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if observations of supernovae in other galaxies show that such an explosion happens in a spiral galaxy like the milky way on average every 25 to 100 years, why have astronomers on earth not seen a supernova explosion in our galaxy since 1604?
Our galaxy's disk is heavily covered in dust, which tends to obstruct the light from supernova explosions in our galaxy's more distant regions.
It's a result of length, dust, and bad luck. Numerous astronomers from all over the world have remarked that the last supernova to be documented in any form of trustworthy source occurred in 1604.
It is noticed that a star with a mass similar to the Sun that is on the verge of dying is surrounded by a significant amount of dust and gas, which is stuff it has released during the last stages of its existence.
What is galaxy?
A galaxy is a vast assemblage of gas, dust, and countless stars and stars and planets. Gravity is what holds a galaxy around each other. A supermassive black hole also resides in the center of our galaxy, the Milky Way. You see additional stars in the Milky Way as you glance at the night sky for stars.
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Our galaxy's disk is heavily covered in dust, which tends to obstruct the light from supernova explosions in our galaxy's more distant regions.
What is galaxy?
A galaxy is a vast assemblage of gas, dust, and countless stars and stars and planets. Gravity is what holds a galaxy around each other. A supermassive black hole also resides in the center of our galaxy, the Milky Way. You see additional stars in the Milky Way as you glance at the night sky for stars.
It's a result of length, dust, and bad luck. Numerous astronomers from all over the world have remarked that the last supernova to be documented in any form of trustworthy source occurred in 1604. It is noticed that a star with a mass similar to the Sun that is on the verge of dying is surrounded by a significant amount of dust and gas, which is stuff it has released during the last stages of its existence.
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Your friend says that for a moving object to continue moving, a force must be continually applied to it. Do you agree with your friend? Explain your answer. Answer in complete sentences.
Answer:
I would disagree with my friend because that according to Newton's first law, an object in motion will continue to be in motion until stopped by another object/force. If the object is already moving, it will stay in motion until something else stops it. There is no need for a force to be continually applied to it while it's already moving.
Now our wavelength is getting longer because the waves are stretching out. This make the _________ lower as well as the pitch we hear.
Now our wavelength is getting longer because the waves are stretching out. This makes the 1. Frequency is lower as well as the pitch we hear.
Wavelength is the gap among equal factors (adjacent crests) in the adjacent cycles of a waveform sign propagated in the area or alongside a twine. In wi-fi systems, this duration is generally laid out in meters (m), centimeters (cm), or millimeters (mm).
Equation of the wavelength, we will tell that the wavelength of a wave is inversely proportional to its frequency, i.e., because the frequency of a wave increases, its wavelength decreases.
A better-frequency sound has a better pitch, and a decreased-frequency sound has a lower pitch. In discern 10.2 sound A has a better pitch than sound B. for example, the chirp of a bird would have an excessive pitch, but the roar of a lion could have a low pitch. The human ear can discover a huge variety of frequencies.
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Disclaimer:- your question is incomplete, please see below for the complete question.
Now our wavelength is getting longer because the waves are stretching out. This makes the _________ lower as well as the pitch we hear.
1. Frequency
2. Loudness
3. Amplitude
Select the correct answer. What happens to the potential energy of an object when it is falls from a height? a. It is lost. B. It is converted into another form, mainly thermal energy. C. It is converted into another form, mainly kinetic energy. D. It stays in the object.
When the potential energy of an object when falls from a height, It is converted into another form, mainly kinetic energy.
Potential energy is the energy held by an object since of its position relative to other objects, stresses inside itself, its electric charge, or other factors. Energy cannot be created or destroyed, meaning that the whole sum of energy within the universe has continuously been and will continuously be constant. In any case, this does not mean that energy is permanent; it can alter the form and indeed exchange between objects.
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you (mass 55 kg) are riding a frictionless skateboard (mass 5.0 kg) in a straight line at a speed of 4.5 m/s. a friend standing on a balcony above you drops a 2.5-kg sack of flour straight down into your arms. what is your new speed while you hold the sack?
The new speed while holding the sack is v₂ = 4.32 m/s as per the given mass and velocity.
What is meant by velocity?Velocity is the rate of change in position of a moving object as observed from a specific frame of reference and measured by a specific time standard.
Given,
The mass of first object m₁=55kg
The mass of second object m₂=5kg
The velocity of first object v₁=4.5m/s
The velocity of second object v₂=?
The mass of the object that is dropped m₃=2.5 kg
When two bodies contact, the momentum of the two bodies before the collision equals the momentum after the collision, according to the law of conservation of momentum.
Pa= Pb
Where Pa denotes the momentum before the impact and Pb denotes the momentum after the collision.
When we apply this law to the preceding situation, we get Momentum before collision= Momentum after collision.
Momentum before impact = ( m₁+m₂) x v₁ = (55+5)x 4.5 = 270 Kg m/s
Momentum after impact = ( m₁+m₂+m₃) x v₂ = (55+5+2.5) x v₂
We now understand that momentum before contact equals momentum after impact:
270 = 62.5 v₂
v₂ = 4.32 m/s
The new speed while holding the sack is v₂ = 4.32 m/s
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