# 8.3 Conservation of momentum  (Page 4/7)

 Page 4 / 7

## Section summary

• The conservation of momentum principle is written
${\mathbf{p}}_{\text{tot}}=\text{constant}$
or
${\mathbf{\text{p}}}_{\text{tot}}={\mathbf{\text{p}}\prime }_{\text{tot}}\phantom{\rule{0.25em}{0ex}}\phantom{\rule{0.25em}{0ex}}\left(\text{isolated system}\right),$
${\mathbf{p}}_{\text{tot}}$ is the initial total momentum and ${\mathbf{\text{p}}\prime }_{\text{tot}}$ is the total momentum some time later.
• An isolated system is defined to be one for which the net external force is zero $\left({\mathbf{\text{F}}}_{\text{net}}=0\right)\text{.}$
• During projectile motion and where air resistance is negligible, momentum is conserved in the horizontal direction because horizontal forces are zero.
• Conservation of momentum applies only when the net external force is zero.
• The conservation of momentum principle is valid when considering systems of particles.

## Conceptual questions

Professional Application

If you dive into water, you reach greater depths than if you do a belly flop. Explain this difference in depth using the concept of conservation of energy. Explain this difference in depth using what you have learned in this chapter.

Under what circumstances is momentum conserved?

Can momentum be conserved for a system if there are external forces acting on the system? If so, under what conditions? If not, why not?

Momentum for a system can be conserved in one direction while not being conserved in another. What is the angle between the directions? Give an example.

Professional Application

Explain in terms of momentum and Newton’s laws how a car’s air resistance is due in part to the fact that it pushes air in its direction of motion.

Can objects in a system have momentum while the momentum of the system is zero? Explain your answer.

Must the total energy of a system be conserved whenever its momentum is conserved? Explain why or why not.

## Problems&Exercises

Professional Application

Train cars are coupled together by being bumped into one another. Suppose two loaded train cars are moving toward one another, the first having a mass of 150,000 kg and a velocity of 0.300 m/s, and the second having a mass of 110,000 kg and a velocity of $-0\text{.}\text{120 m/s}$ . (The minus indicates direction of motion.) What is their final velocity?

0.122 m/s

Suppose a clay model of a koala bear has a mass of 0.200 kg and slides on ice at a speed of 0.750 m/s. It runs into another clay model, which is initially motionless and has a mass of 0.350 kg. Both being soft clay, they naturally stick together. What is their final velocity?

Professional Application

Consider the following question: A car moving at 10 m/s crashes into a tree and stops in 0.26 s. Calculate the force the seatbelt exerts on a passenger in the car to bring him to a halt. The mass of the passenger is 70 kg. Would the answer to this question be different if the car with the 70-kg passenger had collided with a car that has a mass equal to and is traveling in the opposite direction and at the same speed? Explain your answer.

In acollision withan identicalcar, momentumis conserved.Afterwards ${v}_{\text{f}}=0$ for bothcars. Thechange inmomentum willbe thesame asin thecrash withthe tree.However, theforce onthe bodyis notdetermined sincethe timeis notknown. Apadded stopwill reduceinjurious forceon body.

What is the velocity of a 900-kg car initially moving at 30.0 m/s, just after it hits a 150-kg deer initially running at 12.0 m/s in the same direction? Assume the deer remains on the car.

A 1.80-kg falcon catches a 0.650-kg dove from behind in midair. What is their velocity after impact if the falcon’s velocity is initially 28.0 m/s and the dove’s velocity is 7.00 m/s in the same direction?

22.4 m/s in the same direction as the original motion

what is thermodynamics
thermodynamic is a branch of physics that teaches on the relationship about heat and anyother form of energy
Emmanuel
if l cary box and stop is ther any work
no that because u have moved no distance. for work to be performed a force needs to be applied and a distance needs to be moved
Emmanuel
Different between fundamental unit and derived unit
fundamental unit are independent quantities that do not depend on any other unit while derived unit are quantities that depend on two or more units for it definition
Emmanuel
what is nuclear fission
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Shawty
are you there
Shawty
Shawty
what is a vector
vectors are quantities that have numerical value or magnitude and direction.
what is regelation
vector is any quantity that has magnitude and direction
Emmanuel
Physics is a physical science that deals with the study of matter in relation to energy
Hi
Jimoh
hello
Salaudeen
hello
Yes
Maxamuud
hi everyone
what is physics
physics is a physical science that deals with the study of matter in relation to energy
Osayuwa
a15kg powerexerted by the foresafter 3second
what is displacement
movement in a direction
Jason
hello
Hosea
Hey
Smart
haider
Explain why magnetic damping might not be effective on an object made of several thin conducting layers separated by insulation? can someone please explain this i need it for my final exam
Hi
saeid
hi
Yimam
Hi
Jimoh
An object made of several thin conducting layers separated by insulation may not be affected by magnetic damping because the eddy current produced in each layer due to induction will be very small and the opposing magnetic flux produced by the eddy currents will be very small
What is thê principle behind movement of thê taps control
while
Hosea
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this is the mass of an atom of an element in ratio with the mass of carbon-atom
Chukwuka
show me how to get the accuracies of the values of the resistors for the two circuits i.e for series and parallel sides
Explain why it is difficult to have an ideal machine in real life situations.
tell me
Promise
what's the s . i unit for couple?
Promise
its s.i unit is Nm
Covenant
Force×perpendicular distance N×m=Nm
Oluwakayode
İt iş diffucult to have idêal machine because of FRİCTİON definitely reduce thê efficiency
Oluwakayode
It is difficult to have an ideal machine in real life situation because in ideal machines all the input energy should be converted to output energy . But , some part of energy is always lost in overcoming friction and input energy is always greater than output energy . Hence , no machine is ideal.
if the classica theory of specific heat is valid,what would be the thermal energy of one kmol of copper at the debye temperature (for copper is 340k)