Answer:
24.1025641
Explanation:
Density = Mass ÷ Volume
We need to work out volume so the equation is going to be ⇒
Mass ÷ Density
Mass = 282 g
Density = 11.7
282 ÷ 11.7 = 24.1025641
Hi, I'm having a lot of trouble with this one. The answer I got to was 407.91 but I'm not confident in it.
Answer:
6.20×10⁴ V/m
Explanation:
The magnitude of electric field is:
E = √(Eₓ² + Eᵧ²)
where Eₓ = ∂φ/∂x and Eᵧ = ∂φ/∂y.
φ = 1.11 (x² + y²)^-½ − 429x
Eₓ = -0.555 (x² + y²)^-(³/₂) (2x) − 429
Eᵧ = -0.555 (x² + y²)^-(³/₂) (2y)
Evaluating at (0.003, 0.003):
Eₓ = -44034 V/m
Eᵧ = -43605 V/m
The magnitude is:
E = 61971 V/m
Rounded to three significant figures, the strength of the electric field is 6.20×10⁴ V/m.
Which substance has the highest specific heat? A. Soil B. Mud C. Sand D. Water
The substance with the highest specific heat is water. The correct option is D
Which substance has the highest specific heat?Water has a specific heat capacity of about 4.186 joules per gram per degree Celsius (J/g°C), which is significantly higher than most other substances. This means that it requires a large amount of heat energy to raise its temperature by a given amount compared to other materials like soil, mud, or sand.
Due to its high specific heat, water can absorb and store a substantial amount of heat during the day and release it slowly at night, moderating temperature changes in the surrounding environment. This property is essential for maintaining stable climates in various ecosystems and has a significant impact on Earth's weather patterns. In conclusion, water's high specific heat makes it a crucial factor in regulating the planet's temperature and climate.
Read more about specific heat here: https://brainly.com/question/27991746
#SPJ6
Affirmations and strokes relate to the power of adult
As the distance between two charged objects increases, the strength of the electrical force between the objects
varies
remains the same.
increases.
decreases.
) Intro
Done
OOOOOOOO
9 of 10
As the distance between two charged objects increases, the strength of the electrical force between the objects decreases.
Answer: Decreases
Explanation:
got it right on the assignment. Hope this helps peeps! :]
plz.. help me this out I am from nepal actually it is math
Answer:
tan (x eˣ) + C
Explanation:
∫ (eˣ + x eˣ) / (cos² (x eˣ)) dx
First, use u-substitution.
u = x eˣ
du = (eˣ + x eˣ) dx
∫ 1 / (cos² u) du
∫ sec² u du
tan u + C
Substitute back:
tan (x eˣ) + C
Cleaning tarnished silver is an example for which of the following.
chemical change
chemical property
physical change
physical property
I believe chemical change is the correct answer.
Silver is a chemical so it certainly will not deal with physical change or physical property.
It cannot be a property since it consists of only one element which is silver.
Cleaning tarnished silver is an example of chemical change, therefore the correct answer is option A.
What is a chemical reaction?A chemical reaction is a process in which one or more substances, also known as reactants are converted to one or more different substances, known as products.
A chemical bonding between a metal and a nonmetal molecule, often oxygen and sulfur dioxide, results in a tarnish.
The result of a chemical interaction between a metal and a non-metal substance like oxygen or sulfur oxides is a tarnish.
Since polishing tarnished silver is an example of a chemical change, option A is the appropriate response.
To learn more about chemical reactions, refer to the link given below;
brainly.com/question/22817140
#SPJ2
what is mechinical advantage
Explanation:
Mechanical is the ratio of the output and input forces.
For example, if a lever is balanced in the middle, then pushing on one end will yield the same amount of force on the other end. So the mechanical advantage is 1.
If instead that lever is balanced so that one side is twice as long as the other, then pushing on the long end will yield twice the force on the short end. The mechanical advantage would be 2.
the advantage gained by the use of a mechanism in transmitting force
specifically : the ratio of the force that performs the useful work of a machine to the force that is applied to the machine
A car increases its speed from 20 km/s to 50 km/ h in 10 seconds what its is acceleration ?
Answer:
0.8 m/s²
Explanation:
Convert km/h to m/s:
20 km/h × (1000 m / km) × (1 h / 3600 s) = 5.56 m/s
50 km/h × (1000 m / km) × (1 h / 3600 s) = 13.89 m/s
Acceleration is change in velocity over change in time:
a = Δv / Δt
a = (13.89 m/s − 5.56 m/s) / 10 s
a = 0.83 m/s²
Rounded to one significant figure, the car accelerates at 0.8 m/s².
What is the force that can cause two pieces of iron to attract each other?
A.
gravitational force
B.
magnetic force
C.
elastic force
D.
electrostatic force
Answer:
B. Magnetic Force
Explanation:
two pieces of irons cannot attract each other unless at least one of them is magnetize. That force is called magnetism.
How do you find the speed of an electromagnetic wave? Multiply the wavelength by the frequency. Dvide the frequency by the wavelength. Add the wavelength plus the frequency. Divide the wavelength by the frequency.
Answer:
Multiply the wavelength by the frequency.
Explanation:
The velocity of a wave is the frequency times the wavelength.
Physics is the study of what?
Answer: Physics is the study of Nature.
Explanation: The knowledge of Nature is the natural science that studies matter, its motion and behavior through space and time, and that studies the related entities of energy and force. Hope this helps. :D
A copper calorimeter of mass 120g contains 70g of water and 10g of ice at 0 °C. What mass of steam at 100°C must be passed into calorimeter to raise the temperature to 40°C.
Answer:
Approximately 73 grams if no heat is lost in this process.
Explanation:
Relevant data and their sources:
Specific heat capacity of copper: [tex]c(\text{Copper}) = \rm 0.385\;J\cdot g^{-1}[/tex] (cpanhd, IUN.edu);Specific heat capacity of water: [tex]c(\text{Water}) = \rm 4.179\;J\cdot g^{-1}[/tex] (ibid.);Latent heat of fusion of water: [tex]L_\mathrm{F}(\text{Water}) = \rm 334\;J\cdot g^{-1}[/tex] (Legates 2005);Latent heat of vaporization of water: [tex]L_\mathrm{V}(\text{Water}) = \rm 2.260\;J\cdot g^{-1}[/tex] (Datt 2001).How much heat is needed?The heat it takes to raise the calorimeter and its content from 0°C to 40°C includes three parts:
The heat it takes to melt that 10 grams of ice, The heat it takes to heat that [tex]70 + 10 = 80[/tex] grams of water from 0°C to 40°C, andThe heat it takes to heat the 120-gram calorimeter from 0°C to 40°C.Note that to avoid rounding errors, most calculations in this explanation do not follow significant figure rules.
How much heat will it take to melt that 10 grams of ice?The latent heat of fusion of water gives the amount of heat required to melt each unit mass of ice at 0°C to water without changing the temperature. (As a side note, that's also the amount heat released when unit mass of water turns into ice at 0°C.)[tex]L_\mathrm{F}(\text{Water}) = \rm 334\;J\cdot g^{-1}[/tex]. Melting each gram of ice requires approximately 334 joules of heat, so melting 10 grams of ice will require about 3,340 joules of heat.
How much heat will it take to heat that 80 grams of water from 0°C to 40°C?There's no state change involved after all that 10 grams of ice melted into water. There's now 80 grams of water at 0°C to melt. The specific heat of water gives the amount of energy required to raise one gram of water by one degree Celsius (which is the same as one degree Kelvin.) [tex]c(\text{Water}) = \rm 4.179\;J\cdot g^{-1}[/tex].
[tex]Q(\text{water}) = c(\text{water})\cdot m(\text{water}) \cdot \Delta T = \rm 4.179\times 80\times 40 = 13372.8\; J[/tex].
How much heat will it take to heat that 120-gram calorimeter from 0°C to 40°C?The melting point of copper is approximately 1,100°C, which is much higher than 100 °C. As a result, there will not be any state change in this process. [tex]c(\text{Copper}) = \rm 0.385\;J\cdot g^{-1}[/tex]. Similarly,
[tex]Q(\text{copper}) = c(\text{copper})\cdot m(\text{copper}) \cdot \Delta T = \rm 0.385\times 120\times 40 = 1848\; J[/tex].
How much heat is required in total?Combining all three parts:
[tex]\rm 3340 + 13372.8 + 1848 = 18560.8\; J[/tex].
How much steam at 100°C will be required?The steam added to the calorimeter will first condense to form water of 100°C before cooling down to 40°C. The energy released in that process will come in two parts:
The energy released while the steam condenses to water at 100°C, andThe energy released while the water formed cools from 100°C to 40°C.To simplify the calculations, let the mass of steam required be [tex]x[/tex] grams. [tex]x>0[/tex].
How much energy will be released when that [tex]x[/tex] grams of steam condenses to water?Similar to the latent heat of fusion of water, the latent heat of vaporization of water gives the amount of heat released for each unit mass of steam that condenses to water at 100°C without change in temperature. (As a side note, that's also the amount of energy required to turn unit mass of water into steam at 100°C.) [tex]L_\mathrm{V}(\text{Water}) = \rm 2.260\;J\cdot g^{-1}[/tex]. In other words, each gram of steam that condenses at 100°C will release approximately 2.260 joule. [tex]x[/tex] grams of steam that condenses at 100°C will release [tex]2.260x[/tex] joules of heat.
How much energy will be released when that [tex]x[/tex] grams of steam condenses to water?Similar to the heat required to heat 80 grams of water from 0°C to 40°C, the heat released when [tex]x[/tex] grams of steam condenses to water can also be found with the specific heat capacity of water. [tex]c(\text{Water}) = \rm 4.179\;J\cdot g^{-1}[/tex].
[tex]Q(\text{water}) = c(\text{water})\cdot m(\text{water}) \cdot \Delta T = \rm 4.178\cdot \mathnormal{x}\times (100 - 40)=250.68\mathnormal{x} \; J[/tex].
How much energy will be released in total when [tex]x[/tex] grams of steam condenses to water at 100°C and cools to 40°C?[tex]2.260x + 250.68x = \rm 252.94\mathnormal{x}\;J[/tex].
Again, how much steam at 100°C will be required?The amount of heat released shall equal to amount of heat absorbed. As a result,
[tex]252.94x = 18560.8[/tex].
[tex]\displaystyle x = \rm\frac{18560.8}{252.94}\approx 73\;g[/tex].
In other words, approximately 73 grams of steam at 100°C will be required to heat that calorimeter and its contents to 40°C.
Answer:
7.4 g
Explanation:
Heat absorbed by copper:
= mc Cc ΔTc
= (120 g) (0.39 J/g/°C) (40°C − 0°C)
= 1872 J
Heat absorbed by ice:
= mi Li + mi Cw ΔTi
= (10 g) (334 J/g) + (10 g) (4.18 J/g/°C) (40°C − 0°C)
= 5012 J
Heat absorbed by water:
= mw Cw ΔTw
= (70) (4.18 J/g/°C) (40°C − 0°C)
= 11704 J
Heat lost by steam:
= ms Ls + ms Cw ΔTs
= m (2264.7 J/g) + m (4.18 J/g/°C) (100°C − 40°C)
= 2515.5 J/g m
1872 J + 5012 J + 11704 J = 2515.5 J/g m
m = 7.39 g
Rounded to two significant figures, the mass of steam needed is 7.4 grams.
Driving to work one morning, you get a flat tire. When using the car jack, you apply 120 N of force to the jack and the jack in turn applies 2000 N of force to lift the car up. What is the mechanical advantage of the jack?
Explanation:
Mechanical advantage is the ratio of output force to input force.
MA = 2000 N / 120 N
MA = 16.67
Round as needed.
Answer:MA = 2000 N / 120 N
MA = 16.67
Explanation:
A box weighing 180 newtons is hanging by rope as shown in the figure. Find the tension T2.
A. 81 newtons
B.
171 newtons
C. 130 newtons
OD. 85 newtons
Answer:
B. 171 N
Explanation:
The equation of the forces along the horizontal and vertical directions are:
Horizontal:
[tex]T_2 cos 62^{\circ} = T_1 cos 20^{\circ}[/tex] (1)
Vertical:
[tex]T_1 sin 20^{\circ} + T_2 sin 62^{\circ} = W[/tex] (2)
Where W = 180 N is the weight of the box.
From (1),
[tex]T_2 \frac{cos 62^{\circ}}{cos 20^{\circ}} = T_1 [/tex]
Substituting into (2),
[tex](T_2 \frac{cos 62^{\circ}}{cos 20^{\circ}}) sin 20^{\circ} + T_2 sin 62^{\circ} = W\\T_2 (cos 62^{\circ} tan 20^{\circ}+sin 62^{\circ})=W\\T=\frac{W}{cos 62^{\circ} tan 20^{\circ}+sin 62^{\circ}}=171 N[/tex]
The tension T2 in the rope is equal to the weight of the box, which is 180 Newtons.
Explanation:To find the tension T2, we need to analyze the forces acting on the box. From the figure, we can see that there are two forces acting on the box: the weight of the box, which is 180 Newtons acting vertically downwards, and the tension T2 in the rope. Since the box is in equilibrium, the sum of the forces in the vertical direction must be zero. This means that the tension T2 must be equal to the weight of the box, which is 180 Newtons. Therefore, the correct answer is 180 Newtons.
Learn more about Tension in a rope here:https://brainly.com/question/30794023
#SPJ3
1.0. A body has a moss 5 kg, what does it mean? How
is mass of a body measured? Define one second
Answer:Kg is the unit of mass. So a 5kg object has a mass of 5kg. The weight you associate with it is only relevant on Earth (under its specific gravity) and in fact really the kilogram-force measurement which is measured in Newtons (5kg x 9.8m/s2 = 49.2N). ... Commonly, it means the object weighs 5kg
Explanation:
This is not my answer
Final answer:
A body with a mass of 5 kg contains an amount of matter equivalent to 5 kilograms. Mass is a measure of the amount of matter and inertia in an object, measured in kilograms using a balance. One second is the time duration of over 9 billion periods of the radiation of the cesium-133 atom.
Explanation:
Understanding Mass and Its Measurement
When a body has a mass of 5 kg, it means that the body contains matter equivalent to 5 kilograms. Mass is a property of an object that quantifies its amount of matter and its inertia. Inertia is the object's tendency to maintain its state of motion. The mass does not change regardless of the location because it is independent of external forces like gravity. In contrast, weight is the force on a body due to gravity and can vary with the change of gravity in different locations.
Mass is measured using a balance that compares the object to a standard mass, such as a known weight or the International Prototype Kilogram, which is a cylinder made of a platinum-iridium alloy kept at the International Bureau of Weights and Measures in France. The standard unit of mass in the International System of Units (SI) is the kilogram (kg).
Definition of One Second
One second is the duration of 9,192,631,770 periods of radiation corresponding to the transition between two hyperfine levels of the ground state of the cesium-133 atom at 0 kelvin. It is a unit of time in the International System of Units (SI).
According to the periodic table, which of the following is the correct symbol for
the element lead?
OA. Li
o B. Ag
o C. La
OD. Pb
Help
Answer:
D.
Explanation:
P
The symbol for lead is Pb: it comes from the latin name for it, which is plumbum.
Final Answer:
The correct symbol for the element lead is Pb.
Explanation:
This question demands basic understanding of periodic table and its elements along with symbols of all the elements in a proper sequence of their appearance.
The correct symbol for the element lead, according to the periodic table, is Pb. The element lead has an atomic number of 82, which means it has 82 protons. Mass of lead is 207.2. The symbol Pb represents the element lead in chemical equations and on the periodic table.
Some important properties of lead are that it is denser than many elements of periodic table and at the same time it is malleable and soft enough.
An electric charge in a magnetic field will experience no force if the charge is moving _______ to the field.
perpendicular
parallel
Answer:
Parallel
Explanation:
An electric charge in a magnetic field will experience no force if the charge is moving parallel to the field.
No force is exerted on electric charge when it moves parallel to magnetic field.
Answer: Parallel
Explanation:
When the electric charge moves parallel in a magnetic field, the component of velocity and field becomes zero which results in net force as zero.
This due to the sine component which makes zero angle and thus component as zero too. The force on the charge moving in magnetic field is perpendicular to velocity and field.
The centripetal force depends on the mass of body, angular velocity and radius of circular path. Find the expression for the centripetal force.
Centripetal force, directed towards the center of a circle, can be expressed using the formulas Fc = mv^2/r (using tangential speed) or Fc = mrw^2 (using angular velocity), where m is the mass, v is the speed, w is the angular velocity, and r is the radius of the circular path.
The centripetal force is the force that keeps an object moving in a circular path and is directed towards the center of the circle. The expression for centripetal force can be derived from the centripetal acceleration, which is given by ac = v2/r and ac = rw2.
When we apply Newton's second law (F = ma), we can express the centripetal force using the formula Fc = mv2/r; this version uses the tangential speed (v) of the object. Alternatively, using angular velocity (w), the formula is Fc = mrw2. The mass (m) of the object, the speed (v), angular velocity (w), and the radius (r) of the circular path all factor into the magnitude of the centripetal force.
The centripetal force is always perpendicular to the tangential velocity of the object and points towards the center of the circle. This ensures that the object continues moving in a curved path rather than in a straight line.
A turbine is an example of which of the following?
A.
motor
B.
generator
C.
transformer
D.
magnet
Answer:
B. Generator
Explanation:
A turbine (meaning "turbulence") is a rotary mechanical device that extracts energy from a fluid flow and converts it into useful work. The work produced by a turbine can be used for generating electrical power when combined with a generator So I prefer to go with option B. generator
Answer:
B. Generator (for Plato/Treca)
Explanation:
A turbine spins to create electricity, therefore, making it a generator.
The frequency of a wave determines which of the following?
loudness
reflection
energy
pitch
Answer:
loudness
Explanation:
Frequency is determined by speed / wavelength. The longer the wavelength, the lower the pitch. The 'height' of the wave is its amplitude. The amplitude determines how loud a sound will be
The wave frequency determines the pitch of the sound.
Answer: Option D
Explanation:
The wave frequency determines the pitch of the sound as the sound wave has the frequency which is sensibly understood by the human ear as the pitch. Pitch has two category, high pitch and low pitch.
A high pitch sound is one which has the rapid or more frequent oscillation and on the other hand, low pitch sound is the one which has slow or less frequent oscillation in the sound wave.
At 20 degrees Celsius, conducting wires made of different materials have the same length and the same diameter. Which wire has the least resistance? aluminum gold nichrome tungsten
The wire with the least resistance at 20 degrees Celsius, given the same length and diameter, would be gold due to its lower resistivity compared to aluminium, nichrome and tungsten.
Explanation:The resistance of a wire depends on its material's resistivity, length, and cross-sectional area. In this case, the wires are of the same length and diameter, so the wire with the least resistance would be the one with the lowest resistivity. Comparing the different materials listed, gold, aluminum, nichrome, and tungsten, we find that gold has the lowest resistivity, so it would have the least resistance at 20 degrees Celsius.
It's worth noting this concept with the base of Ohm's law. In general, materials with good conductivity, like gold, copper, and aluminum, are referred to as ohmic materials where the resistance remains essentially the same for a wide range of voltage and current. This is due to the abundant free electrons in these metals that allow for easy flow of electric current thereby reducing resistance.
Learn more about Electrical Resistance here:https://brainly.com/question/31668005
#SPJ12
When comparing aluminum, gold, nichrome, and tungsten wires of the same length and diameter at 20 degrees Celsius, the gold wire would have the least resistance due to gold's low resistivity.
Explanation:
The ability of a material to resist the flow of electrical current is measured as resistance. In this case, we are comparing the resistance of different types of conducting wires at the same temperature, length, and diameter. From the given options, which include aluminum, gold, nichrome, and tungsten, the wire that would have the least resistance, other factors being equal, would be gold.
The reason for this is that gold, amongst these options, has the lowest resistivity. Resistivity is the property of a material that determines the resistance of a wire made from that material. It basically measures how strongly the material opposes the flow of electric current.
In the case of gold, it is one of the most conductive materials known, meaning it has very low resistivity, and therefore a gold wire would have lower resistance than wires made from the other materials listed. While silver actually has the highest conductivity and lowest resistivity of any metal, it is not one of the options presented in this question.
Learn more about Electrical Resistance here:https://brainly.com/question/31668005
#SPJ12
Which type of process happens without gain or loss of heat
Answer: adiabatic
Explanation:
If a train is traveling eastward with a constant velocity of 15 m/s, what is the net external force action on it? There is not enough information, so it cannot be solved. There is no net force acting on the train. the force from the engines
Answer:
There is no net force acting on the train.
Explanation:
The net force equals mass times acceleration:
∑F = ma
The train moves at constant velocity, so its acceleration is 0. Therefore, the net force is 0.
QUESTION 6
The number of strawberries on a strawberry plant and the amount of water the plant recieves have a direct relationship. The the amount of water the plant receives increases, how will the number of strawberries on the plant change?
Decrease
Increase
No change
Increase and decrease in a regular pattern
Answer:
Increase. As the water increases, so will the strawberries if watered evenly throughout
What happens to energy “lost” during an energy transformation?
Energy loss. Figure 1. Energy losses in an incandescent light bulb are very large; most of the input energy is lost in the form of heat energy. When energy is transformed from one form to another, or moved from one place to another, or from one system to another there is some energy loss.
There is some energy loss when it is changed from one form to another, and relocated from one location to another.
What is energy?Energy is a quantifiable quality that may be transferred to a body or a physical system and is noticeable when labor is done as well as when heat and light are produced.
An incandescent light bulb has significant energy losses; the majority of the input energy is dissipated as heat energy. There is some energy loss when it is changed from one form to another, relocated from one location to another, or moved from one system to another.
There is some energy loss when it is changed from one form to another, relocated from one location to another, or moved from one system to another. This implies that some of the incoming energy is transformed into a highly disordered form of energy, such as heat, when energy is transformed into a new form.
To know more about energy follow
https://brainly.com/question/13881533
#SPJ6
If a person weighs 90 N on Earth, and the gravitational acceleration due to Jupiter's gravity is 25.98 m/s2, how much would the person weigh on Jupiter?
A. 3.46 N
B. 238.59 N
C. 882.00 N
D. 2338.20 N
Answer:
B. 238.59 N
Explanation:
First, use their weight on Earth to find their mass:
W = mg
90 N = m (9.8 m/s²)
m = 9.18 kg
Now use this mass to find the new weight on Jupiter.
W = mg
W = (9.18 kg) (25.98 m/s²)
W = 238.59 N
Select the correct answer. In a given chemical reaction, the energy of the products is less than the energy of the reactants. Which statement is true for this chemical reaction? A. Energy is absorbed in the reaction. B. Energy is released in the reaction. C. There is no transfer of energy in the reaction. D. Energy is lost in the reaction.
Answer:
D
Explanation:
If in a given reaction the energy of products is greater than the energy of reactants it means that reaction is endothermic and during the reaction, the energy is absorbed by reactants. In an endothermic reaction, the products have more stored chemical energy than the reactants. And in this reaction the reactants are more stable than products before the compounds with less energy are always more stable.
Answer:
B
Explanation:
In science, it is understood that energy cannot be created, nor destroyed, it can only change form. Hence, certain reactions require a lot of energy, since their products have a higher energy than their reactants, or they release energy because their products have less energy than their reactants.
A: Is incorrect, because a reaction will not absorb energy if the products have less energy than the reactants.
B: Is correct, because in a reaction where the products have less energy, there will be a release of energy into the environment (usually heat).
C: Is incorrect, because there is always a transfer of energy in a chemical reaction.
D: Is incorrect, because energy cannot be "lost". It may be released into the environment, but it cannot be lost.
Which compound is an unsaturated hydrocarbon?
cyclobutane
isopropane
ethyne
pentane
Answer:
i believe it is isopropane. sorry if this isnt helpful, but i believe thats correct
Explanation:
Answer:
Ethyne
Explanation:
gradpoint
what is 362 equal to 126 subtracted from r?
Answer:
488 = r
Explanation:
362 = -126 + r; 488 = r
I am joyous to assist you anytime.
31. A big 8 kg fish swimming at 3 m/s opens its mouth and swallows a small 2 kg fish swimming
away from it at 1 m/s. Presume water resistance is negligible. Show your calculations.
(A) What is the momentum of the two fish system after the smaller fish has been
swallowed?
(B) What is the speed of the two fish system after the smaller fish has been swallowed?
(Hint: first figure the mass of the two fish system.)
Explanation:
This problem is a good example of an inelastic collision, in which the elements that collide remain together after the collision, and althogh the kinetic energy is not conserved, the linear momentum [tex]p[/tex] does.
Thus: [tex]p=m.V[/tex] (1)
Where [tex]m[/tex] is the mass and [tex]V[/tex] the velocity.
[tex]p_{i}=p_{f}[/tex] (2)
Where [tex]p_{i}[/tex] is the initial momentum and [tex]p_{f}[/tex] the final momentum.
(A) Momentum of the two fish system after the smaller fish has been swallowed[tex]p_{i}=m_{i1}V_{i1}+m_{i2}V_{i2}[/tex] (3)
Where [tex]m_{i}=8kg[/tex] is the initial mass (mass of the big fish) and [tex]V_{i}=3m/s[/tex] is the initial velocity of the big fish, [tex]m_{i2}=2kg[/tex] is the initial mass of the small fish and [tex]V_{i2}=1m/s[/tex] is the initial velocity of the small fish.
[tex]p_{i}=(8kg)(3m/s)+(2kg)(1m/s)=26kg.m/s[/tex] (4)
By the conservation of linear momentum:
[tex]p_{i}=p_{f}=26kg.m/s[/tex] (5)
(B) Speed of the two fish system after the smaller fish has been swallowedIn this case we will focus on [tex]p_{f}[/tex] (after the "collision"):
[tex]p_{f}=(m_{i1}+m_{i2})V[/tex] (6)
Where [tex]V[/tex] is the velocity of the system of both fish.
Finding [tex]V[/tex]:
[tex]V=\frac{p_{f}}{m_{i1}+m_{i2}}[/tex] (7)
Solving (7) and remembering [tex]p_{i}=p_{f}[/tex]:
[tex]V=\frac{26kg.m/s}{8kg+2kg}[/tex] (8)
Finally:
[tex]V=2.6m/s[/tex]