An example of a collision without physical contact is a charged particle being deflected by another charged particle as they travel by one another.
Another illustration is a gravitational slingshot, in which a light object moves around a much heavier object to accelerate. A collision does not require the objects to actually touch; for instance, an asteroid passing by the earth is seen as one since its course is altered by the gravitational pull of the planet. The conservation of momentum and energy can still be used to assess the collision. Yes, even without direct touch, an accident may still occur.
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a group of ten friends, each of mass 50kg, want to test the strength of a trampoline. at their highest jump, each friend is 2m above the trampoline. they all land on the trampoline at the same time and decelerate at a constant rate to a point of zero velocity over a period of 0.5s. the trampoline has a threshold of 5000n, above which it breaks. do the friends succeed in breaking their trampoline? neglect air resistance and the distance the trampoline sags as a result of the friends landing.
Calculate the striking trampoline.
What is zero velocity?
The zero-velocity surface is a notion connected to the N-body gravity problem. It represents a surface that a body with the specified energy cannot traverse because it would have zero velocity there. George William Hill made the initial proclamation about it.
What is resistance?
A circuit's opposition to current flow is measured by its resistance. The Greek letter omega () stands for ohms, which are used to measure resistance. Georg Simon Ohm (1784–1854), a German physicist who examined the connection between voltage, current, and resistance, is the subject of the name "Ohm."
mass of each friends= 50kg
number of friends =10
total mass= 50×10=500kg
now initial velocity before, falling =0
let final velocity be V
v²-μ²= 2as
⇒v²+2as=2as(μ=0)
∴V=[tex]\sqrt{2as}[/tex]=[tex]\sqrt{2*9.8*2}[/tex] ( acceleration due to gravity =9.8m/s²) ( s=2m given)
=6.26ms⁻¹
∴The velocity of the friends, just before striking the trampoline= 6.26ms⁻¹
Now after striking the trampoline, the velocity of the people decelerate to 0, in a time interval 0.5s.
∴deceleration= 6.26/ 0.5= 12.52ms⁻²
∴Force required to decelerate=mass× deacceleration
=500×12.52
=6260.99
=6261N
but that trampoline has a threshold of 500N, which is less than force required to stop, the people.
hence the friends succeed in striking the trampoline.
Therefore, the friends succeed in striking the trampoline.
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10. A stone falls freely from the top of a tower 250.0 m above the ground. Calculate its
velocity half-way through the fall. [g=10.0 ms 2]
Answer:
50 m/s
Explanation:
Half of its Potential Energy (mgh) will have been converted to Kinetic Energy ( 1/2 mv^2)
1/2 mgh = 1/2 mv^2
gh = v^2
10(250) = v ^2 v = 50 m/s
The velocity of the stone halfway through the fall will be approximately 50.0 m/s.
To calculate the velocity of the stone halfway through its fall, we can use the kinematic equation for free fall
v² = u² + 2as
Where:
v is the final velocity,
u is the initial velocity,
a is the acceleration due to gravity (g),
and s is the distance fallen.
Given that the stone falls freely, the initial velocity u is 0 since it starts from rest.
The distance fallen halfway through the fall can be calculated by dividing the total distance fallen by 2.
s = 250.0 m / 2 = 125.0 m
Plugging these values into equation, now we solve for v:
v² = 0² + 2 × 10.0 m/s² × 125.0 m
v² = 0 + 2500 m²/s²
Taking the square root of both sides to find v:
v ≈ √2500 m²/s²
v ≈ 50.0 m/s
Therefore, the velocity of the stone halfway through the fall is approximately 50.0 m/s.
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a prescription for corrective lenses reads -5 d for each lens. these corrective lenses are group of answer choices diverging with focal length equal to 20 cm. diverging with focal length equal to 5 m. diverging with focal length equal to 5 cm. converging with focal length equal to 5 cm. converging with focal length equal to 5 m. converging with focal length equal to 20 m.
These corrective lenses have a 20 cm focal length and are diverging.
P=1/(f(m)) and "hence P= 1/(0.2)=10/2" and "therefore P=5 D" indicate that the lens has a 5 dioptre power.
What is a diverging lens?A lens that, after exiting the lens, produces parallel light beams to spread out and deviate from the optical axis.A lens that, as from a virtual image, produces a beam of parallel rays to diverge after refraction; a lens with a negative focal length.By extending the traces of the light rays traveling through the lens to a focal point behind the lens, negative lenses diverge parallel incident light beams to create an illusion of an image. These lenses typically feature at least one concave surface and are thinner in the middle than they are on the edges. When passing through a concave lens, light rays parallel to the principal axis appear to diverge from a point on the principal axis.To learn more about diverging lens refer to:
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If a ring particle survived for the age of the solar system, how many collisions would it undergo?.
Answer:
The answer is near 8 trillion
Explanation:
I hope this helps
Help!!! 23 points label these as Element, compound, mixture of elements, and mixture of compounds
The given images are labelled as either element, compound, mixture of elements or mixture of compounds accordingly.
The answers are marked according in order of the images as follows:
ElementsCompoundsMixture of elementsMixture of compoundsCompoundsCompoundsIf there are only single type of atoms present without being in contact with another atom, it is called as elements. If one atom is in contact with another atoms it is a compound. If there are more than one type of element, it is a mixture of elements. If there are more than one type of compound, it is a mixture of compounds.
Therefore, the given images are labelled as either element, compound, mixture of elements or mixture of compounds accordingly.
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If the gravity of the moon is 1/6 of Earth’s gravity, what is the mass of an object that has a weight of 115N on the moon? a)89 b)71.9 c)30.2 d)20
it's 115/6 which is 19.1667
Explanation:
The weight would be 115/6 because the moon has one sixth of the gravity on earth so the weight would be on sixth of that on earth.
if a cannonball were fired horizontally from a cannon atop a very high mountain what would its trajectory look like
The trajectory of the cannonball will be in parabolic motion.
A trajectory is an object that only gravity acts on. The downward force, gravity, accelerates the projectile downward. The vertical components of motion are independent of each other, so gravity does not change the object's horizontal velocity. A vertical force does not cause horizontal movement. A vertical force acting on a horizontally moving object causes the object to deviate from its linear trajectory.
When an object moving forward is affected by gravity, it falls in a parabolic arc. Since the projectile is an object affected only by gravity, the projectile's path forward from the initial thrust momentum is parabolic.
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a 110 g hockey puck sent sliding over ice is stopped in 15 m by the frictional force on it from the ice. (a) if its initial speed is 6.0 m/s, what is the magnitude of the frictional force? (b) what is the coefficient of friction between the puck and the ice?
The frictional force where k is the unitary force of kinetic friction acting on an object and k is the coefficient of kinetic friction. For the vast majority of surfaces, K is less than S.
Explain about the magnitude of the frictional force?The weight of the object and the roughness of the surface in contact determine how much frictional force is generated. The friction force will grow as the roughness increases.
The weight of the object bearing normal to the surface times the coefficient of friction for the contacting surfaces gives the amount of the friction force. The force's direction is perpendicular to the surface and is in opposition to any forces acting on the box.
The amount of kinetic friction is inversely proportional to the amount of normal force and the degree of roughness between the sliding surfaces. The amount of static friction is inversely proportional to the amount of normal force and the degree of roughness between the sliding surfaces.
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a 75.9 kg bobsled is pushed along a horizontal surface by two athletes. after the bobsled is pushed a distance of 7.9 m starting from rest, its speed is 7.5 m/s. find the magnitude of the net force on the bobsled. answer in units of n.
The magnitude of the net force on the bobsled is found to be 270 Newton.
The mass of the bobsled is 75.9 Kg, the bobsled is pushed by two athletes till a distance of 7.9 m with a speed of 7.5m/s.
The work energy theorem says,
The work done by a force is equal to the total change in kinetic energy of the body.
Let us say that the bobsled starts from rest, so, we can write,
Fs = 1/2MV²
F is the net force on the bobsled,
s is the distance to which it is moved,
M is the mass of the bobsled,
V is the speed of the bobsled.
Putting values,
F(7.9) = 0.5 x 75.9 x 7.5 x 7.5
F = 270 N.
The net force on the bobsled is 270 N.
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what does power mean in terms of electrical energy
Answer:
Electricity is the rate at which electrical energy is converted into motion, heat, or other forms such as electromagnetic fields.
Light passes straight through two vertical polarizers. The axes of the filters are aligned parallel to each other. How does the light that passes through the second filter compare to the light that passed through the first filter?.
Light passes straight through two vertical polarizers. The axes of the filters are aligned parallel to each other. The way the light that passes through the second filter compared to the light that passed through the first filter is that all of the light will pass through both polarizers.
What is a polarizer?A polarizer, also known as a polariser, is an optical filter that allows light waves of one polarization to pass while blocking light waves of other polarizations. It may convert an undefined or mixed polarization light beam into a polarized light beam by filtering it.
Calcite, a naturally occurring mineral, is used to make the majority of birefringent polarizers. Calcite is common in polycrystalline form, but optical-grade calcite is scarce, making birefringent polarizers more expensive than most other varieties.
Remember that polarising filters can lower the amount of light reaching your camera's sensor by up to two or three f-stops, so avoid using them in low-light settings. This includes photography during blue hour, at night, and when capturing the Aurora Borealis.
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is training for cross country in the fall she ran 5 miles east then she turned and ran 5 miles west. draw and label the vectors that show each segment of her tripand the resulant dispacement vector. find her resulant displacement
5j-5i is her resultant displacement.
velocity in east= 5i
velocity in west=5j
resultant magnitude=√5i+√5j
displacement =5j-5i
Displacement is the shortest distance, but distance is the length of everything covered. A vector quantity with a magnitude and a direction is displacement. The vector (or straight line) separation between an initial and final position is described by this term. Therefore, all that is needed to determine the resulting displacement is to know these two positions.
Calculate the inverse tangent of the ratio of the components of the displacement in the y- and x-directions to find the direction of the displacement vector.
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when there is no wind, an airplane is flying 70 m/s with its nose pointed due north. a wind begins blowing toward the west with a constant speed relative to the ground of 18 m/s. what is the direction and speed of the plane relative to the ground?
The relative velocity of the plane with respect to the ground will be 72.57 at an angle of tan⁻¹(0.25) from the north.
The speed of the airplane when there is no wind is 70 m/s in the north direction.
The speed of the wind is 18m/s related to the ground in the direction of West.
As we know, that both west and north are perpendicular to each other, the resultant speed by the observer on the ground will be observed in the direction of the resultant of both the speeds.
Let us say that we is the resultant of both the speeds,
Because the two speeds are perpendicular to each other the resultant is given by,
R = √((70)²+(18)²)
R = 72.27m/s.
The angle with north,
Tan A = 18/70
Tan A = 0.25
So, the speed of the airplane from the ground will be observed as 72.27 degrees and at an angle of tan ⁻¹(0.25) from the north.
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what is the de broglie wavelength (in meters) of a 148 g baseball thrown at a velocity of 35.1 meters per second?
The de-Broglie wavelength of the baseball is 1.27×10⁻²⁵nm
λ=h/m
h is the Planck Constant =6.63×10⁻³⁴Js
m = mass = 148×10⁻³
=0.148kg
v= velocity =35.1m/s
λ=6.63×10⁻³⁴/0.148×35.1
λ=1.27×10⁻³⁴m
λ=1.27×10⁻²⁵nm
When learning about quantum mechanics, the de Broglie wavelength is a crucial idea. De Broglie wavelength is the wavelength that is connected to an object in relation to its momentum and mass. Typically, a particle's force and de Broglie wavelength are inversely related.
Some people believe that matter has both a wave- and a particle-like nature. De Broglie wavelength, so named after the discoverer Louis de Broglie, are the characteristics of a physical object that fluctuate in time or space while acting like waves. Matter waves are another name for it. It is strikingly reminiscent of the experimentally demonstrated dual nature of light, which exhibits both particle and wave behavior.
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an obstruction is just ahead on the shoulder. your front wheel leaves the roadway at high speed. when do you countersteer?
An obstruction is just ahead on the shoulder. Your front wheel leaves the roadway at a high speed. You countersteer when the front tire touches the roadway.
Countersteer is usually done by the cyclists and motorcyclists to turn at higher speeds. It is advisable to be done only on the race tracks. This is because the two wheels do not follow the same path during turning and it may affect other vehicles on normal roads. The rider must be leaned in the direction of turn in order to complete the turn. As the front wheel leaves at a higher speed, countersteering is done when the front wheel touches the ground.
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two wheels, a and b, are both shaped like uniform disks and have the same overall mass, but wheel a has twice the radius of wheel b. how do we calculate the moments of inertia (around the axis of symmetry) for each wheel?
The ratio of I sub A to I sub B is 4.
How can you calculate the ratio of A to B?
A/B would be your formula if you were comparing one data point (A) to another data point (B). This indicates that you are multiplying information A by information B. For instance, your ratio will be 5/10 if A is 5 and B is 10. How do we determine each wheel's moments of inertia (around the axis of symmetry) I is equal to 1 over 2 times m times R squared is used to compute the moments of inertia for both masses and radii. We simply use a common factor to cancel. So 4:2=2:1 . The simplest representation of the ratio 4 to 2 is the ratio 2 to 1. Additionally, since each pair of numbers has the same relationship, the ratios are equivalent.
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the product of a force and the perpendicular distance from the force's line of action to the axis of rotation is known as
The product of a force and the perpendicular distance from the force's line of action to the axis of rotation is known as Torque.
Torque or moment of the force is the term used to describe a force's ability to turn.
The moment arm is the length that separates the line of action perpendicular to the axis of rotation. Torque is a mathematical combination of force F and moment arm L. Torque is equal to F times L. The moment arm affects torque. The torque will create more of an increase the longer the moment arm.
The line of action of a force is the path it travels when exerting its power.
The moment arm of the force is the length that separates the force's path of action from its axis of rotation perpendicularly.
The newton meter is the torque SI unit (Nm). A force of 1 N operating perpendicular to the moment arm's length of 1 m produces a torque of 1 N m.
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Waves that move the medium at right angles to the direction in which the waves travel.
Transverse waves are waves that move the medium at right angles to the direction in which the waves travel.
Types of Waves in PhysicsWaves are defined to be oscillations or vibrations about a fixed point, accompanied by the transfer of energy travelling from one medium to another. There are mainly two types of mechanical waves, namely longitudinal waves and transverse waves.
Longitudinal waves are waves in which the movement of the particles in the medium is in the same dimension as the wave’s movement direction. Examples of longitudinal waves include compression wave and sound waves. Transverse waves are waves in which the medium moves at an angle to the wave’s direction. Examples include stringed instruments and light waves.
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A 0. 0850-kg arrow is fired horizontally. If the bowstring exerts an average force of 89. 0 n on the arrow over a distance of 0. 782 m, with what speed does the arrow leave the bow?.
40.47 m/s is the speed of the arrow leaving the bow. When 0.0850 kg arrow fired horizontally, and If bowstring exerts average force of 89.0 N on the arrow over distance of 0. 782 m.
What is velocity?The primary indicator of object's position and speed is its velocity. It is distance that object travels in one unit of time. Displacement of item in one unit of time is definition of velocity.
By Newton's second law of motion,
F = ma
m is the mass of the arrow (kg) = 0.0850 kg
a is the acceleration of the arrow (m/s²)
F is the force applied (N) = 89.0 N
F= ma
a = F/m
a = 89.0/ 0.0850
∴ a= 1,047.059 m/s²
Now, object have acceleration, and the object will move in non-uniform motion. so the formula applied is:
[tex]v_{t}[/tex] = [tex]v_{0}[/tex] + at
[tex]v_{t}^{2}[/tex] = [tex]v_{0}^{2}[/tex] + 2×a×d
∴ d = [tex]v_{0}[/tex]×t +1/2× a ×t²
here,
[tex]v_{0}[/tex] = initial speed (m/s) = 0 m/s (arrow stationary in bowstring)
[tex]v_{t}[/tex] = final speed (m/s)
a = acceleration (m/s²) = 1,047.059 m/s²
t = interval (s)
d = distance (m) = 0.782 m
[tex]v_{t}^{2}[/tex] = [tex]v_{0}^{2}[/tex] + 2×a×d
[tex]v_{t}^{2}[/tex] = 0² + 2 × 1,047.059 × 0.782
[tex]v_{t}^{2}[/tex] = 1637.6
[tex]v_{t}[/tex] = [tex]\sqrt{1637.6}[/tex]
[tex]v_{t}[/tex] = 40.47 m/s
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please I'm so hurry
What is it answer this question ?
A disk rotates with rotational kinetic energy is 70J and the angular momentum is 30 kg.m2/s .what is the value moment of inertia the disk?
A) 6.4 kg.m2
C) 40 kg.m2
B) 2.3 kg.m2
D) 0.43 kg.m2
Answer:
The value moment of inertia the disk:
I = 6.4 kg·m²
Explanation:
Given:
Tk = 70 J
L = 30 kg·m² / s
_____________
I - ?
Rotational kinetic energy:
Tk = I·ω²/2
Angular velocity:
ω = √ (2·T / I)
Angular moment of a rotating body
L = I·ω = I·√ (2·T / I) = √ (2·T·I² / I ) = √ (2·T·I )
Raising to the second degree:
L² = 2·T·I
The value moment of inertia the disk:
I = L² / (2·T)
I = 30² / (2·70) ≈ 6.4 kg·m²
А) 6.4 кг·м²
In the period 6 inner transition element series, the 4f orbitals begin to be filled after the element _____.
In the period 6 inner transition element series, the 4f orbitals begin to be filled after the element Lanthanum(La) and Cerium(Ce).
The d and f Block elements in the groups of 3 to 11 are also called transition elements and inner transition elements respectively. 4f and 5f orbitals of f-block elements are steadily in the latter of two long periods.
Inner transition element:
Inner transition elements are those elements in which the last electron enters the f-orbital. The elements in which the 4f and the 5f orbitals are progressively filled are called f-block elements. These includes lanthanoids( Z = 58 - 71) and actinoids (Z = 90 - 103).
Therefore period 6 inner transition elements begin with Lanthanum and Cerium.
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A student travels on a motorcycle and moves at a constant speed of 80 k/h for 15 m, determine the distance traveled in that time
Uniform line movement
Data:
V = 80km/h
T = 15m = 0.25 h
d = ?
We perform a conversion from minutes to hours.
15 m * 1 h/60 m = 0.25 h
The formula for uniform motion is:
V = d/t
We clear for distance:
d = v * t
d = 80 km/h * 0.25 h
d = 20 km
The distance traveled in that time is 20 km.
How much gravitional potential energy would a 65.0kg rollerblader have at the top of a hill that is 45.0 meters high
Roller balder will have 28,665 J gravitational potential energy at the top of a hill that is 45.0 meters high
gravitation potential energy = m*g*h
mass = 65 kg
g = 9.8 [tex]m/s^{2}[/tex]
h = 45 m
gravitation potential energy = 65 * 9.8 * 45 = 28,665 J
Roller balder will have 28,665 J gravitational potential energy at the top of a hill that is 45.0 meters high
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A wheel with rotational inertia I is mounted on a fixed, frictionless axle. The angular speed ω of the wheel is increased from zero to ωf in a time interval T.
What is the average power input to the wheel during this time interval (hint: power = work / time)?
A:[tex]\frac{I^{2}\omega_{f} }{2T^{2} }[/tex]
B: [tex]\frac{I\omega^{2}_{f} }{2T^{2} }[/tex]
C: [tex]\frac{I\omega_{f}} {2T}[/tex]
D: [tex]\frac{I\omega^{2}_{f} }{2T}[/tex]
The average power input to the wheel during this time interval is (Iω²) / (2T).
option D is the correct answer
What is average power?The average power input to the wheel during this time interval is the rate at which work is done by the wheel or the rate at which energy is expended.
Mathematically, the formula for average power is given as;
P = energy / time
Based on work - energy theorem,
work done by the wheel = change in energy of the wheel
Energy of the wheel due to the rotational torque is given as;
E = ¹/₂Iω²
where;
I is the moment of inertia of the wheelω is the angular speed of the wheelPower = E/T
power = (Iω²) / (2T)
where;
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in a collision between two unequal masses, how does the impulse imparted to the smaller mass by the larger mass compare with the impulse imparted to the larger mass by the smaller one? 3) a) they are equal. b) it is larger. c) it is smaller. d) the answer depends on the ratio of the masses. e) the answer depends on how fast they are moving
In a collision between two unequal masses, the smaller mass by the larger mass compare with the impulse imparted to the larger mass by the smaller one they are equal.
Any incident where two or more bodies exert forces on each other quickly is referred to as a collision in physics. In physics, collision, which is also known as impact, is the abrupt, forceful coming together in close proximity of two bodies, such as, for instance, two pool balls, a golf club and a ball, a hammer and a nail head, two railroad cars when coupled, or a falling object and a floor. In physics, a collision occurs when particles, aggregates of particles, or solid bodies move in the same direction and get close enough to each other to interact and have an impact on one another. Distracted driving is the most frequent reason for an auto accident. Speeding, disobeying traffic signs, making improper turns, and driving while intoxicated or drugged-up are additional risk factors for car accidents.
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a flight attendant pulls her 2 kg flight bag a distance of 23 m along a level airport floor at a constant velocity. the force she exerts is 8 n at an angle of 30 degrees above the horizontal. find the work she does on the flight bag.
Work done on the flight bag will be 182.20 J.
Work done defined as the product of force and distance covered due to applied force.
The mass of flight bag m = 2 kg
Therefore the weight of the bag will be 2*g = 2*10 = 20 N
(g = acceleration due to gravity = 9.81 m/s2)
The distance covered by the bag is, d = 23 m.
The magnitude of force exerted on bag is, F = 8 N.
The angle of inclination with horizontal = [tex]\alpha[/tex] = 8°
The work done on the flight bag is given by the equation:
W = F * d *Cos [tex]\alpha[/tex]
W = 8 * 23 * Cos8
W = 182.20 J
Thus, the work done by the attendant on the flight bag is 182.20 J.
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According to the first law of thermodynamics, work done by a system will cause _________ in the internal energy, assuming that no heat is transferred to or from the system.
According to the first law of thermodynamics, work done by a system will cause decrease in the internal energy, assuming that no heat is transferred to or from the system.
First law of thermodynamics says that energy can neither be created nor it can be destroyed, it can only be transferred from one form to another form. This is also a law of conservation of energy.
It means if there is any work done by any system then that system has burned its energy to do the work. so when energy is used to do the work , there will be decrease in the internal energy of the system, and that will be equal to the workdone.
ΔU = ΔW
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a student slides her 80.0-kg desk across the level floor of her dormitory room a distance 5.00 m at constant speed. if the coefficient of kinetic friction between the desk and the floor is 0.400, how much work did she do? a student slides her 80.0-kg desk across the level floor of her dormitory room a distance 5.00 m at constant speed. if the coefficient of kinetic friction between the desk and the floor is 0.400, how much work did she do? 20.4 j 9.41 j 23.5 j 1.57 kj 15.7 j
Work she did 1.57kj.
Option d is correct
How do kinetic and static friction differ?Kinetic and Static Friction The friction that exists between two systems when they are in touch and immobile with respect to one another is known as static friction. Kinetic friction is the friction that occurs when two systems are in contact and moving in relation to one another.
F(net) = F(applied) - F(friction)
0 = F(applied) - F(friction)
F(applied) = F(friction) (1)
Work done = F(applied) *(desk travel distance)
From 1
Work done = F(friction)*(desk travel distance)
W = µNd
W = µmgd
W = (0.400)(80.0 kg)(9.81 m/s²)(2.00 m)
W =1568 J ← work done to move the desk.
W = 1.57kj
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a constriction in a pipe reduces its diameter from 6.5cm to 2.7cm. where the pipe is wider, the fluid velocity is 8m/s. find the fluid velocity where the pipe is narrow. answer in units of m/s
The velocity of the fluid where the pipe is narrow s 46.36m/s.
The diameter of the larger end of the constriction pipe is 6.5 cm and the diameter of the narrow end of the pipe is 2.7cm.
According to equation of continuity, the volume of the fluid incoming is equal to the volume of the fluid outgoing.
So, we can write,
A₁V₁ = A₂V₂
A₁ and V₁ are the area and speed at the larger end and A₂ and V₂ are area and speed at the narrow end.
Putting values,
π(6.5/2)².8 = π(2.7/2)².V
V = 46.36m/s
The velocity of the fluid where the pipe is narrow is 46.36m/s.
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determine what fraction of the kinetic energy of the ball before collision is lost during teh collsion. what happens to it?
1/2 m₁v₁²(m₁ / m₁+ m₂ ) is the fraction of Kinetic energy lost during an inelastic collision.
From the concept of law of conservation of energy, In an elastic collision when two objects collide with a particular velocity then the kinetic energy before the collision will be the same after the collision as well but that's not the case in an Inelastic collision where there's always loss of kinetic energy.
In case of inelastic collision,
pi = pf
here p = momentum
m₁v₁ = (m₁ + m₂)v₂
v₂= m₁v₁ / (m₁ + m₂) ------- equation 1
Ki = Kf
1/2m₁v₁² = 1/2 (m₁+m₂) v₂²
Put the value of v₂ from equation 1
1/2mv² = 1/2 (m₁ + m₂) [m₁v₁ / m₁+m₂]²
=> 1/2 (m₁v₁)² / ( m₁+m₂ )
∴ Fraction of Kinetic energy lost
= 1/2 m₁v₁² - 1/2 (m₁v₁)² / (m₁+m₂)
=> 1/2 m₁v₁²( m₁ / m₁ + m₂ )
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