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Summary

  • The law of conservation of momentum says that the momentum of a closed system is constant in time (conserved).
  • A closed (or isolated) system is defined to be one for which the mass remains constant, and the net external force is zero.
  • The total momentum of a system is conserved only when the system is closed.

Conceptual questions

Under what circumstances is momentum conserved?

Momentum is conserved when the mass of the system of interest remains constant during the interaction in question and when no net external force acts on the system during the interaction.

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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?

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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.

To accelerate air molecules in the direction of motion of the car, the car must exert a force on these molecules by Newton’s second law F = d p / d t . By Newton’s third law, the air molecules exert a force of equal magnitude but in the opposite direction on the car. This force acts in the direction opposite the motion of the car and constitutes the force due to air resistance.

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

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A sprinter accelerates out of the starting blocks. Can you consider him as a closed system? Explain.

No, he is not a closed system because a net nonzero external force acts on him in the form of the starting blocks pushing on his feet.

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A rocket in deep space (zero gravity) accelerates by firing hot gas out of its thrusters. Does the rocket constitute a closed system? Explain.

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Problems

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 1.50 × 10 5 kg and a velocity of ( 0.30 m/s ) i ^ , and the second having a mass of 1.10 × 10 5 kg and a velocity of ( 0.12 m/s ) i ^ . What is their final velocity?

Two train cars are shown moving toward each other. The car on the left is moving with v sub i 1 equals 0.30 meters per second i hat to the right, and the car on the right is moving with v sub i 2 equals -0.12 meters per second i hat to the left.

( 0.122 m/s ) i ^

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Two identical pucks collide elastically on an air hockey table. Puck 1 was originally at rest; puck 2 has an incoming speed of 6.00 m/s and scatters at an angle of 30 ° with respect to its incoming direction. What is the velocity (magnitude and direction) of puck 1 after the collision?

Two sets of red and blue hockey pucks are shown. The first row has a blue hockey puck with an arrow pointing left toward a red hockey puck. The second row shows a similar blue puck with a shorter arrow pointing left toward a red hockey puck. The red hockey puck also has an arrow pointing to its left.
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The figure below shows a bullet of mass 200 g traveling horizontally towards the east with speed 400 m/s, which strikes a block of mass 1.5 kg that is initially at rest on a frictionless table.

A drawing of a block on a table, and a bullet headed toward it.

After striking the block, the bullet is embedded in the block and the block and the bullet move together as one unit.

  1. What is the magnitude and direction of the velocity of the block/bullet combination immediately after the impact?
  2. What is the magnitude and direction of the impulse by the block on the bullet?
  3. What is the magnitude and direction of the impulse from the bullet on the block?
  4. If it took 3 ms for the bullet to change the speed from 400 m/s to the final speed after impact, what is the average force between the block and the bullet during this time?

a. 47 m/s in the bullet to block direction; b. 70.6 N · s , toward the bullet; c. 70.6 N · s , toward the block; d. magnitude is 2.35 × 10 4 N

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A 20-kg child is coasting at 3.3 m/s over flat ground in a 4.0-kg wagon. The child drops a 1.0-kg ball out the back of the wagon. What is the final speed of the child and wagon?

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A 5000-kg paving truck coasts over a road at 2.5 m/s and quickly dumps 1000 kg of gravel on the road. What is the speed of the truck after dumping the gravel?

3.1 m/s

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Explain why a cannon recoils when it fires a shell.

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Two figure skaters are coasting in the same direction, with the leading skater moving at 5.5 m/s and the trailing skating moving at 6.2 m/s. When the trailing skater catches up with the leading skater, he picks her up without applying any horizontal forces on his skates. If the trailing skater is 50% heavier than the 50-kg leading skater, what is their speed after he picks her up?

5.9 m/s

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A 2000-kg railway freight car coasts at 4.4 m/s underneath a grain terminal, which dumps grain directly down into the freight car. If the speed of the loaded freight car must not go below 3.0 m/s, what is the maximum mass of grain that it can accept?

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Questions & Answers

What is Centripetal force
Taiwo Reply
y oxygen is shift to first place
Radhika Reply
What is coriolis firce
Shakeel Reply
Angular accelaration force,as the result of the rotatation of earth
Arzoodan
Due to the rotation of the earth the winds at the equator get deflected in opposite direction and therefore cause some currents in the Northern and Southern hemisphere which are opposite in there spin.
Varsha
Thats correct.
Arzoodan
if cos = x/y then sec = y/x if sin = y/x then cosec = x/y
Jan Reply
if cosβ=x/y then what is cosecβ
Abubakar Reply
. if cosβ=x/y what is cosecβ
Abubakar
if cosΦ=x/y what is cosecΦ
Abubakar
What are the unknown symbols?
Jan
β
Jan
Φ
Jan
It is defined that cosec = 1/sin and sec = 1/cos
Jan
Do you understand this?
Jan
of cours
Arzoodan
∇(f/g) = (g∇f − f∇g)/g^2 , at points x where g(x) 6= 0 please help me to solve the problem ....
11 Reply
sir please add answer sheet of spigel vector analysis ..
11 Reply
In a pulley system 2 boxes r hanging in both sides of pulley. An other box was joined to the left box through a rope & get accelerated downward. If all the boxes have same mass ,then what will be the acceleration of that system ?
bibek Reply
it may be mg
Amalesh
∇(f/g) = (g∇f − f∇g)/g2 , at points x where g(x) 6= 0 plus solve it
11
What is momentum
Rika Reply
is the product of mass to it's velocity (mv)
Ahmed
momentum
oladipupo
quatity of motion present in a body or product of mass and velocity
Shakeel
show that the kE of a uniform ring of mass m rolling along a smooth horizontal surface so that its centre of mass has a velocity v is mv×v
folder
what is hydration energy
osobase Reply
the energy................................................
Rika
what is momentum
Ogwu Reply
dont know want to know the answer
Rika
it's the product of mass multiplied by velocity
harsha
the quantity of motion possessed by a body is called its momentum.by virtue of which a body can exert a force in the agency which tend to stop it .it is a common experience that stronger force is required to stop more massive body.also faster the body moves harder it is to stop it .this is why
Manoj
momentum is product of mass and velocity and it is denoted by "P".
Manoj
show that the cross product of vector axb=-bxa
Teklu Reply
Nature of the physical low
Rashika Reply
1/2 mv2 =mgh prove that
Rashika
study work energy theorem properly
Rohan
v2=u2+2gh...u=0...so 1/2 mv2=1/2m(2gh)=mgh
Talha
how can I become confident in physics
arshdeep Reply
practice more and more question ,,,,if u get trouble in any one question infact do that again and again.
jyotirmayee
is theory important or numericals
arshdeep
both ,,,,because without understanding theory ,,,,u can't able to solve problemsss or numericals
jyotirmayee
which books I can follow for IIT jee prep for mcq and which for mcq
arshdeep
what can make me good in physics
lovet
how can I solve qsns in physics cuz I understand most of the theories but facing problem during solving the qsns.
Rohan
what can make me good in physics
Rika
Can someone please tell what really happened to planet Pluto
Ejiba Reply
Pluto was consider as a dwarf planet and not a planet a planet should satisfy the three criteria viz.it should have a orbit around the sun,it should be spherical in shap,and it should clear its orbit . since,Pluto satisfy the first two criteria so it was not considered as a planet .
Manoj
but it was seen that earth also not cleared its orbit but earth is a planet so another criteria was made that a planet should have grater gravitational force other than its orbit and earth follow this but Pluto wasn't satisfied this criteria .so Pluto wasn't consider as a planet.since it follow the
Manoj
first two criteria so it gets a another name called dwarf planet
Manoj
Practice Key Terms 3

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Source:  OpenStax, University physics volume 1. OpenStax CNX. Sep 19, 2016 Download for free at http://cnx.org/content/col12031/1.5
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