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  • Define linear momentum.
  • Explain the relationship between momentum and force.
  • State Newton’s second law of motion in terms of momentum.
  • Calculate momentum given mass and velocity.

Linear momentum

The scientific definition of linear momentum is consistent with most people’s intuitive understanding of momentum: a large, fast-moving object has greater momentum than a smaller, slower object. Linear momentum is defined as the product of a system’s mass multiplied by its velocity. In symbols, linear momentum is expressed as

p = m v . size 12{p=mv} {}

Momentum is directly proportional to the object’s mass and also its velocity. Thus the greater an object’s mass or the greater its velocity, the greater its momentum. Momentum p size 12{p} {} is a vector having the same direction as the velocity v size 12{v} {} . The SI unit for momentum is kg · m/s size 12{"kg" cdot "m/s"} {} .

Linear momentum

Linear momentum is defined as the product of a system’s mass multiplied by its velocity:

p = m v . size 12{p=mv} {}

Calculating momentum: a football player and a football

(a) Calculate the momentum of a 110-kg football player running at 8.00 m/s. (b) Compare the player’s momentum with the momentum of a hard-thrown 0.410-kg football that has a speed of 25.0 m/s.

Strategy

No information is given regarding direction, and so we can calculate only the magnitude of the momentum, p size 12{p} {} . (As usual, a symbol that is in italics is a magnitude, whereas one that is italicized, boldfaced, and has an arrow is a vector.) In both parts of this example, the magnitude of momentum can be calculated directly from the definition of momentum given in the equation, which becomes

p = mv size 12{p= ital "mv"} {}

when only magnitudes are considered.

Solution for (a)

To determine the momentum of the player, substitute the known values for the player’s mass and speed into the equation.

p player = 110 kg 8 . 00 m/s = 880 kg · m/s size 12{p rSub { size 8{"player"} } = left ("110"" kg" right ) left (8 "." "00"" m/s" right )="880"" kg" cdot "m/s"} {}

Solution for (b)

To determine the momentum of the ball, substitute the known values for the ball’s mass and speed into the equation.

p ball = 0.410 kg 25.0 m/s = 10.3 kg · m/s size 12{p rSub { size 8{"ball"} } = left (0 "." "410"" kg" right ) left ("25" "." 0" m/s" right )="10" "." 3" kg" cdot "m/s"} {}

The ratio of the player’s momentum to that of the ball is

p player p ball = 880 10 . 3 = 85 . 9 . size 12{ { {p rSub { size 8{"player"} } } over {p rSub { size 8{"ball"} } } } = { {"880"} over {"10" "." 3} } ="85" "." 9} {}

Discussion

Although the ball has greater velocity, the player has a much greater mass. Thus the momentum of the player is much greater than the momentum of the football, as you might guess. As a result, the player’s motion is only slightly affected if he catches the ball. We shall quantify what happens in such collisions in terms of momentum in later sections.

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Momentum and newton’s second law

The importance of momentum, unlike the importance of energy, was recognized early in the development of classical physics. Momentum was deemed so important that it was called the “quantity of motion.” Newton actually stated his second law of motion    in terms of momentum: The net external force equals the change in momentum of a system divided by the time over which it changes. Using symbols, this law is

F net = Δ p Δ t , size 12{ F rSub { size 8{"net"} } = { {Δp} over {Δt} } ,} {}

where F net size 12{F rSub { size 8{"net"} } } {} is the net external force, Δ p size 12{Δp} {} is the change in momentum, and Δ t size 12{Δ`t} {} is the change in time.

Newton’s second law of motion in terms of momentum

The net external force equals the change in momentum of a system divided by the time over which it changes.

F net = Δ p Δ t

Questions & Answers

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lasisi
In Inelastic collision cunculate the vilocity
Anshu Reply
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Usman
explain how a body becomes electrically charged based on the presence of charged particles
Kym Reply
induction
babar
induction
DEMGUE
definitely by induction
Raymond
induction
Raymond
induction
Shah
induction
Korodhso
please why does a needle sinks in water
DEMGUE
induction
Korodhso
induction
Auwal
what are the calculations of Newton's third law of motiow
Murtala Reply
what is dark matter
apex Reply
(in some cosmological theories) non-luminous material which is postulated to exist in space and which could take either of two forms: weakly interacting particles ( cold dark matter ) or high-energy randomly moving particles created soon after the Big Bang ( hot dark matter ).
Usman
if the mass of a trolley is 0.1kg. calculate the weight of plasticine that is needed to compensate friction. (take g=10m/s and u=0.2)
Declan Reply
what is a galaxy
Maduka Reply
a galaxy is a type of phone e.g samsung galaxy there are diff types of samsung galaxy there is s5 s6 s7 s8 s9
lasisi
what isflow rate of volume
Abcd Reply
flow rate is the volume of fluid which passes per unit time;
Rev
flow rate or discharge represnts the flow passing in unit volume per unit time
bhat
When two charges q1 and q2 are 6 and 5 coulomb what is ratio of force
Mian Reply
incomplete question
lasisi
When reducing the mass of a racing bike, the greatest benefit is realized from reducing the mass of the tires and wheel rims. Why does this allow a racer to achieve greater accelerations than would an identical reduction in the mass of the bicycle’s frame?
bimo Reply
is that the answer
nehemiah
why is it proportional
nehemiah Reply
i don't know
Adah
y
nehemiah
what are the relationship between distance and displacement
Usman Reply
They are interchangeable.
Shii
Distance is scalar, displacement is vector because it must involve a direction as well as a magnitude. distance is the measurement of where you are and where you were displacement is a measurement of the change in position
Shii
Thanks a lot
Usman
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what is kinematics
praveen
kinematics is study of motion without considering the causes of the motion
Theo
The study of motion without considering the cause 0f it
Usman
why electrons close to the nucleus have less energy and why do electrons far from the nucleus have more energy
Theo
thank you frds
praveen
plz what is the third law of thermodynamics
Chidera Reply
third law of thermodynamics states that at 0k the particles will collalse its also known as death of universe it was framed at that time when it waa nt posible to reach 0k but it was proved wrong
bhat
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Rev Reply
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Jeff
I do think so, it will
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lasisi
If a magnet is in a pool of water, would it be able to have a magnetic field?.
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Practice Key Terms 2

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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