The action - reaction pair as to do with the force of the water and the lifting of the man.
What is the Newton third law?We know that according to the Newton third law of motion, action and reaction are equal and opposite. This implies that when force is exerted on an object, the object would also be able to exert an equal but opposite force on the object.
Having said this, we know that when a force is exerted on the man by the water that is applied, the reaction is that the man would be lifted higher. This is thus the action and the reaction pair that is involved here.
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according to your observations and background reading, how would redesign the wind turbine to maximize its output? consider wind direction, blade attack angle, etc.
The wind turbine gives maximize its output when a turbine having longer blades.
Wind turbines :
A wind turbine is a device that uses the wind's kinetic energy to create electricity.
These early windmills were used to run mills powered by the wind, as their name suggests.Wind turbines can sweep more ground, catch more wind, and generate more electricity when their rotor diameters are larger.Wind turbines with blades and horizontal axis.Three things should be taken into account when determining value:
(1) Installation fees
(2) projected annual power output
(3) assurance regarding the projected yearly power production
The wind turbine gives maximize its output when a turbine having longer blades.
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a horizontal force is applied to a 4.0 kg box. the box starts from rest moves a horizontal distance of 8.0 meters and obtains a velocity of 6.0 m/s. the system is frictionless. the horizontal force is: a. 3.0 n. b. 5.0 n. c. 7.0 n. d. 9.0 n. e. 11 n.
According to Newton's first law, an object will accelerate at a constant rate if its net force is zero. The calculated value is 39.2 N
This indicates that the velocity is constant but does not necessarily imply that the item is at rest.
F = m a
= 4 kg x 2.5 m/s/s x 10 N, correct.
The formula for Fgrav is:
Fgrav = m • g
= 4 kg • 9.8 m/s/s
= 39.2 N since the mass is known.
The normal force is equivalent to the gravitational force since there is no vertical acceleration. A force in physics is any interaction that, if left unchecked, will alter an object's motion. An object with mass can change its velocity due to a force, which includes starting to move from a state,
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a car is traveling at 50 mi/h when the brakes are fully applied, producing a constant deceleration of 34 ft/s2. what is the distance covered before the car comes to a stop?
The calculated value is 84.03 ft. The deceleration will be calculated by multiplying the final velocity by the initial velocity, then dividing that result by the time it takes for the velocity to drop.
Given that you don't have enough time to complete this task, you can only apply the kinematic formula Vf 2 = Vi 2 + 2aD, which includes all the variables.
0 for Vf = Final Velocity (since you are trying to stop)
Initial Velocity = 50 MPH (Vi)
a= acceleration equals 32 ft/s2.
D is the distance covered (displacement)
We must ensure that all variables and constants are in the same units before we can use this formula. This means that all of your measurements should be in feet (ft) or miles (mi), and all of your time measurements must be in seconds (s) or meters (m).
Now calculate the distance by separating D by itself.
D= (-5377.7778/ -64)\s
= 84.03 ft
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if you throw a ball up into the air with an initial vertical velocity of 30 m/s how long will the ball be in the air before it comes all the way back down to your hand
Answer:
Below
Explanation:
Here is a way:
When the ball reaches its maximum height , it is 1/2 of the way back to your hand AND its velocity = 0 Find this time and double it to get to your hand.
Vf = vo - at
0 = 30 - 9.81(t) shows to to max height = 3.06 seconds
double it : = 6.12 seconds
Julius is using the setup below to find the velocity of a wave in the ripple tank. He found the average
wavelength by measuring the distances between the shadow lines. What else does he need to know
in order to calculate the velocity of the waves?
He need to know in order to calculate the velocity of the waves is time.
What is velocity?When an item is moving, its velocity is the rate at which its direction is changing as seen from a certain point of view and as measured by a specific unit of time.
Uniform motion an object is said to have uniform motion when object cover equal distance in equal interval of time within exact fixed direction. For a body in uniform motion, the magnitude of its velocity remains constant over time.
Given in the question,
Velocity =Distance /Time
He need to know in order to calculate the velocity of the waves is time.
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50pts!
If the water displaced by an object has a volume of 0.1 m3, what is the buoyant force exerted on that object?
980 Newtons
98 Newtons
9.8 Newtons
0.98 Newtons
Answer: 980 Newtons
Explanation:
Object A is positive
Object A repels object B
Object B I attracted to objects C and D
When C is touched to an electroscope, nothing happens.
When object D touches an electroscope, the leaves repel.
What are the charges of objects B,C and D? Explain your reasoning. (3 pts)
The charges on B, C , and D objects are negative, positive and positive respectively.
The electroscope instrument is used to find out whether there is charge present and how much of it there is.
The leaves at the bottom of the electroscope spread apart when a charged object is brought close to the top of the instrument (for example, a positive charge). The positive charge on the leaves has gotten stronger as they diverge more.
This occurs when the charged object imparts a positive charge on the leaves. When the object is positively charged, this is possible. They move farther apart the higher the charge.
The charges on B, C , and D objects are negative, positive and positive respectively.
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A weight lifter lifts a set of weights a vertical
distance of 3.66 m. If a constant net force of 370 N
is exerted on the weights, how much net work is done on the weights?
1.741.3
2. 1214.01
3.431.52
4. 381.92
5.874.68
6. 1179.02
7. 1354.2
8. 1154.56
9. 1509.12
10. 706.85
Answer in units of J.
Answer:
See below
Explanation:
Work = F * d
= 370 N * 3.66 m = 1354.2 J
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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at takeoff the aircraft travels at 55.0 m/s, so that the air speed relative to the bottom of the wing is 55.0 m/s. given the sea level density of air to be 1.29 kg/m3, how fast (in m/s) must it move over the upper surface to create the ideal lift?
The velocity of the aircraft to move over the upper surface to create the ideal lift is 67.64 m/s.
Describe Bernoulli's principle?
According to the Bernoulli's principle of fluid dynamics, a fluid's speed increases concurrently with a drop in static pressure or a drop in potential energy.The idea of energy conservation can be used to derive Bernoulli's principle. This implies that in a steady flow, the total amount of energy present in a fluid is constant at all points that are not affected by viscous forces. In order to achieve this, the total amount of kinetic energy, potential energy, and internal energy must remain constant.Because of Bernoulli's principle, which states that when air speeds up, pressure decreases, airplanes are able to fly. Thus, the reason a wing produces lift is because the air moves faster over the top, resulting in a region of low pressure and lift.
The ideal lift is determined by the fluid density and velocity relationship, so:
F_lift = 1/2 x p x A x (v_f^2 - v_i^2)
As a result, the fluid's density may be calculated.
p = 1.29 kg / m^3
The situation's environment indicates that the wings generate roughly 100N of lift per square meter of wings, therefore
A = 1 m^2
the beginning speed is
v_i = 55.0 m/s
Replacing
F_lift = 1/2 x 1.29 x 1 x (v_f^2 - 55 x 55)
1000 = 0.645 x (v_f^2 - 3025)
1550.387 = (v_f^2 - 3025)
v_f^2 = 4575.387
v_f = 67.64 m/s.
Hence, the velocity of the aircraft to move over the upper surface to create the ideal lift is 67.64 m/s.
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Given: Assume the near point (of the eye) is 25 cm . The distance between eyepiece and objective lens in a certain compound microscope is l = 17.6 cm . The focal length of the eyepiece is fe = 2.57 cm , and that of the objective lens is fo = 0.3 cm . What is the overall magnification of the microscope? Caution: a negative quantity this is. Use the approximation l − fe ≈ l and object distance do is approximately the focal length fo.
The overall magnification of the microscope is - 570.687.
A microscope is a laboratory tool used to have a look at items which can be too small to be seen with the aid of the bare eye. Microscopy is the technology of investigating small objects and structures through the use of a microscope. The microscopic approach is invisible to the attention unless aided by using a microscope.
The focal length of a microscope objective is generally between 2 mm and 40 mm. but, that parameter is regularly considered as less important, on account that magnification and numerical aperture are sufficient for quantifying the critical performance in a microscope.
Calculation:-
M = -(L/f) (near point/Fe)
M = - (0.176/0.003)(0.25/0.0257)
M = - 570.687
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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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one advantage of the hubble space telescope over ground based ones is that
Space telescopes have the advantage of being above the blurring effects of the Earth's atmosphere.
A surrounding is a layer of fuel or layers of gases that envelop a planet and is held in a region through the gravity of the planetary frame. A planet retains its surroundings whilst the gravity is exceptional and the temperature of the surroundings is low. A stellar ecosystem is the outer area of a celeb, which includes the layers above the opaque photosphere; stars of low temperature may have outer atmospheres containing compound molecules.
The atmosphere of Earth consists of nitrogen (78%), oxygen (21%), argon (0.9%), carbon dioxide (0.04%), and trace gases. most organisms use oxygen for breathing; lightning and bacteria perform nitrogen fixation to provide ammonia that is used to make nucleotides and amino acids; flora, algae, and cyanobacteria use carbon dioxide for photosynthesis.
The layered composition of the ecosystem minimizes the damaging results of daylight, ultraviolet radiation, solar wind, and cosmic rays to defend organisms from genetic harm. The modern composition of the atmosphere of the Earth is made from billions of years of biochemical modification of the paleo atmosphere by residing organisms.
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astronomers have detected storms in the atmospheres of the jovian planets, including giant storms that are larger than the entire planet earth. listed below are characteristics of storms. sort these characteristics according to whether they are associated with jovian storms only, terrestrial storms only, or both jovian and terrestrial storms.
The listed characteristics of storms are sorted according to whether they are associated with Jovian storms only, terrestrial storms only, or both Jovian and terrestrial storms.
Jovian storms are associated with oppositely-directed high-speed atmospheric flowsJovian storms are hosted by rapidly-rotating planetTerrestrial storms are powered by solar radiationTerrestrial storms are short-lived (hours to days)Both Jovian and terrestrial storms involve upwelling gassesBoth Jovian and terrestrial storms involve circulating windsThe terrestrial planets are the planets of inner solar system such as Mercury, Venus, Earth and Mars. Unlike terrestrial planets Jovian planets do not have a solid surface. They are primarily composed of hydrogen and helium in their atmosphere.
Therefore, the listed characteristics of storms are sorted according to whether they are associated with Jovian storms only, terrestrial storms only, or both Jovian and terrestrial storms.
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if the 140 g ball is moving horizontally at 23 m/s , and the catch is made when the ballplayer is at the highest point of his leap, what is his speed immediately after stopping the ball?
The speed immediately after stopping the ball is 0.049 m/s.
What is meant by velocity?Velocity is the directional speed of a moving object as an indication of its rate of change in location as perceived from a specific frame of reference and measured by a specific time standard.
Given,
The mass of ball m = 140 g = 0.140 kg.
The speed of ball u = 23 m/s.
We must determine the speed at which the ballplayer is at the peak of his leap. They will remain together. Allow them to move at the speed of V.
Allow a 65-kilogram baseball player to jump straight up to catch a hard-hit ball. Then, according to linear momentum conservation.
mu+ Mu'=(m+ M)V
In this case, u' represents the player's initial speed. Because the player was initially at rest, u' = 0.
(0.140×23)+(65×0)=(0.140+65)V
V=(0.140×23)/(0.140+65)
V=3.22/65.14
V=0.0494
Therefore, the speed immediately after stopping the ball is 0.049 m/s.
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question a toy doll and a toy robot are standing on a frictionless surface facing each other. the doll has a mass of 0.20 kg, and the robot has a mass of 0.30 kg. the robot pushes on the doll with a force of 0.30 n. the magnitude of the acceleration of the robot is
The magnitude of the acceleration of the robot is 1 m/s².
Acceleration is the rate of change of the velocity of an item with appreciation to time. Accelerations are vector portions. The orientation of an item's acceleration is given by the orientation of the net pressure appearing on that object.
Calculation:-
mass of doll = 0.20 kg
mass of robot = 0.30 kg
Force on dall by robot = 0.30 N
acceleration on doll = mass of doll / force of robot
= 0.20 / 0.30
= 0.67 m/s²
Same force applied to the robot by Newton's third law of motion = 0.30 N
acceleration of the robot = mass of robot/force
= 0.30 / 0.30
= 1 m/s²
Acceleration is the charge at which velocity modifications with time, in terms of each speed and route. A factor or an object moving in a straight line is accelerated if it quickens or slows down. movement on a circle is extended despite the fact that the rate is consistent because the course is continually changing.
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Select the correct answer from each drop-down menu. How can you summarize the ruler placement postulate? you can measure the between points a and b by using as zero.
The ruler placement hypothesis can be summed up as follows:
The set of points on the line and the set of real numbers are equivalent in every way, and the absolute value of the difference between the matching numbers is equal to the distance between two points.
According to this, a set of points on a line can be matched with a set of real numbers, and vice versa. In order to help you better understand the ruler placement postulate, a general overview is provided based on the fact that your question is incomplete.
A ruler is a tool or measuring device that is used to measure length and draw straight lines. A measure is used to determine the length in both measured and conventional units.
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The velocity components of an incompressible, two-dimensional velocity field are given by the equations u= y2 – x(1 + x) v = y(2x + 1) Show that the flow is irrotational and satisfies conservation of mass.
The velocity flow field is irrotational and the conservation of mass is preserved.
Irrotational flow for a two-dimensional velocity field happens when
[tex]\frac{dv}{dx} \:-\: \frac{du}{dy} \:=\: 0[/tex]
Conservation of mass for an incompressible happens when
[tex]\frac{du}{dx} \:+\: \frac{dv}{dy} \:=\: 0[/tex]
Perimeter
u = y² - x (1+x)Calculate the derivate in each function.
[tex]\frac{du}{dx} = 0 - 1 - 2x = - 2x - 1[/tex][tex]\frac{du}{dy} = 2y - 0 - 0 = 2y[/tex][tex]\frac{dv}{dx} = 2y + 0 = 2y[/tex][tex]\frac{du}{dy} = 2x + 1[/tex]Checking the irrotational flow
[tex]\frac{dv}{dx} \:-\: \frac{du}{dy} \:=\: 2y - 2y = 0[/tex]
Checking conservation of mass for an incompressible
[tex]\frac{du}{dx} \:+\: \frac{dv}{dy} \:=\: - 2x - 1 + 2x + 1 = 2x - 2x + 1 - 1 = 0[/tex]
So the velocity flow field is irrotational and the conservation of mass is preserved.
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Seetha is moving to a new house. Her old house is 5.8 km away from her new house. Find the distance between her new house and old house in meter.
Answer:
5.8km=5800m
Explanation:
You have to convert kilometres into metres
Answer:
It's 5,800 meters
Explanation:
In the question the distance has been already given, what's required is converting it from Kilometers to Meters. This means you will need to multiply 5.8 by 1000 to get your answer.
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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An object accelerates uniformly from rest. If the final velocity of the object after 4.7s is 15 m/s east, what is the magnitude displacement
The displacement of the object that accelerates uniformly from rest is 35.25 m due East.
What is displacement?Displacement can be defined as distance in a specified direction.
To calculate the displacement of the object, we use the formula below.
Formula:
s = (v+u)t/2............... Equation 1Where:
s = Displacement of the objectv = Final velocityu = Initial velocityt = Time.From the question,
Given:
v = 15 m/s eastu = 0 m/s (from rest)t = 4.7 sSubstitute these values into equation 1
s = (15+0)4.7/2s = 35.25 m due East.Hence, the displacement of the body is 35.25 m due East.
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a uniform slender rod ab rests on a frictionless horizontal surface, and a force p of magnitude 0.25 lb is applied at a in a direction perpendicular to the rod. assume that the rod weighs 2.15 lb.
The force implemented at the rod is P=zero.25lb P = zero.25 l b. the burden of the rod is w=1.75lb w = 1. seventy-five lb. The kinematic diagram of the rod.
Friction is any point in the consumer's journey with an organization wherein they hit a snag that slows them down or causes dissatisfaction. in the most primary concept, offering frictionless customer support way tracking the consumer adventure and improving the consumer revel in.
The overwhelming consensus is that ice has low friction because of a skinny film of liquid water coating its surface. for this reason, skaters balanced on skinny steel blades can float easily throughout the ice rink, but grind to a halt at the timber ground beyond.
Motion is certainly viable without friction even though an item is stationary in a single reference frame, in some other reference body shifting with admire the first, that identical object may be seen to be transferring. So movement actually does not need friction at all.
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What conditions can cause hurricanes to change direction?
need ASAP please
According to the research, the correct answer is that the conditions that affect hurricanes causing them to change direction are higher latitudes.
What are hurricanes?It is a tropical cyclone that generates strong winds whose storms circulate around a center of low pressure.
In this sense, this phenomenon usually has its beginning in the tropics around the area of low pressure whose direction is influenced by the Coriolis effect that diverts the trajectory of objects that move over the Earth's surface and the higher latitudes that reverse the steering winds.
Therefore, we can conclude that higher latitudes and the Coriolis effect are conditions that affect the path of hurricanes by changing their direction.
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An 9 kg object is accelerated with 450N of force. What will be the acceleration of the object? Show your work.
Answer:
Explanation:
Given:
m = 9 kg
F = 450 N
_________
a - ?
According to Newton's 2nd law:
a = F / m
a = 450 / 9 = 50 m/s²
Explain your understanding of water waves: 1. Use your own words and captured images from the simulation to show you can measure: a. Wavelength of longest wave possible b. Wavelength of shortest wave possible c. Height of tallest wave possible 2. Describe your experiments to make waves of different wavelengths and heights including which views and tools were needed and why. Support your explanation with images from the simulation.
A Water waves are formed by the interaction between the earth, moon and the sun and usually of short wavelength.
Gamma rays have incredibly short wavelengths that are only a small percentage of the size of atoms, but other wavelengths can extend as far as the cosmos, despite the fact that the relationship between wave frequency and wavelength is inverse. Although it is not often stated explicitly, electromagnetic radiation wavelengths are frequently represented in terms of the vacuum wavelength, regardless of the medium they pass through.
Electromagnetic radiation's behavior is influenced by its wavelength. Wavelength times frequency equals the speed of light. Energy is obtained by multiplying frequency by the Planck constant. The wave number in centimeters is 1/wavelength. A rough estimate of the wavelength size is shown along with the wavelengths of various regions of the electromagnetic spectrum.
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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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Lucy and her bike together have a mass of 120 kg. She slows down from 4. 5 m/s to 3. 5 m/s. How much kinetic energy does she lose?.
Answer:
The answer is - 480 kj
Explanation:
kinetic energy before: K1 = 1/2 *m*U1^2=} K1= 1/2*120*4.5^2=} K1= 60*4.5*4.5=} K1= 1,215 kj
kinetic energy after : K2=1/2 *m*U2^2=} K2= 1/2*120*3.5*3.5=} K2= 735 kj
if you want to find the kinetic energy that the mass has lost you need to do : K2-K1= 735-1.215= - 480 kj
2. consider two masses in a closed system. show that newton's third law results in conservation of momentum
Consider two masses in a closed system. The Newton 3rd law, F₁₂ = -F₂₁, will result in conservation of momentum m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂.
Suppose we have two masses, m₁ and m₂. According to the Newton's 3rd Law:
F₁₂ = -F₂₁
Where:
F₁₂ = force on m₁ due to m₂
F₂₁ = force on m₂ due to m₁
If there is collision between two masses, we can assume that the forces acted in the same time interval. Hence,
F₁₂ . t = -F₂₁ . t
Force is defined as the change of momentum (Δp) over time (t), or
F = Δp / t
Substitute F . t = Δp on both sides,
Δp₁ = –Δp₂
p₁_final - p₁_initial = –(p₂_final - p₂_initial)
p₁_initial + p₂_initial = p₁_final + p₂_final
This is the conservation law of momentum.
Let:
u = initial velocity
v = final velocity
Then,
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
This is another form of the conservation law of momentum. Hence, we have shown that the Newton 3rd Law will lead to the conservation of momentum.
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A sled and rider, gliding over horizontal, frictionless ice at 4.7 m/s , have a combined mass of 74 kg . The sled then slides over a rough spot in the ice, slowing down to 2.9 m/s . What impulse was delivered to the sled by the friction force from the rough spot? Express your answer to two significant figures and include the appropriate units.
The Impulse is - 74 Ns
Impulse (symbolized by J or Imp) is the integral of a force, F, over the time interval, t, for which it acts.
The SI unit of impulse is the newton second (N⋅s)
Examples of impluse in real life could include hitting a ball,tossing a coin, kick starting scooter etc.
The values known to us are -
J =?
Mass (m) = 74 kg
Initial velocity (Vi) = 4 m/s
Final velocity (Vf) = 3 m/s
To find Impulse-
J = ΔP = m ( Vi-Vf)
J = 74kg ( 3m/s- 4m/s)
J = - 74 Ns
The impulse is -74Ns, here the negative sign indicates the direction of impulse, in the opposite direction of motion.
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What will the density be if the radius of the sphere is halved, compressing the air within?.
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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