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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

how can I convert mile to meter per hour
Folorunsho Reply
1 mile * 1609m
Boon
hey can someone show me how to solve the - "Hanging from the ceiling over a baby bed ...." question
Shrushti Reply
i wanted to know the steps
Shrushti
sorry shrushti..
Rashid
which question please write it briefly
Asutosh
Olympus Mons on Mars is the largest volcano in the solar system, at a height of 25 km and with a radius of 312 km. If you are standing on the summit, with what initial velocity would you have to fire a projectile from a cannon horizontally to clear the volcano and land on the surface of Mars? Note that Mars has an acceleration of gravity of 3.7 m/s2 .
Eloisa Reply
what is summit
Asutosh
highest point on earth
Ngeh
पृथवी को इसके अक्ष पर कितने कोणीय चाल से घूमाऐ कि भूमधय पे आदमी का भार इसके वासतविक भार से 3/5अधिक हो
Vasudev Reply
best
Murari
At a post office, a parcel that is a 20.0-kg box slides down a ramp inclined at 30.0° 30.0° with the horizontal. The coefficient of kinetic friction between the box and plane is 0.0300. (a) Find the acceleration of the box. (b) Find the velocity of the box as it reaches the end of the plane, if the length of the plane is 2 m and the box starts at rest.
Kaitlin Reply
As an IT student must I take physics seriously?
Akaare Reply
yh
Bernice
hii
Raja
IT came from physics and maths so I don't see why you wouldn't
Brad
conditions for pure rolling
Md
the time period of jupiter is 11.6 yrs. how far is jupiter from the sun. distance of earth from rhe sun is 1.5*10 to the power 11 meter.
Abu Reply
lists 5 drawing instruments and their uses
Micahlolo Reply
that is a question you can find on Google, anyway of top of my head, compass, ruler, protractor, try square, triangles.
Rongfang
A force F is needed to break a copper wire having radius R. The force needed to break a copper wire of radius 2R will be
Lalit Reply
2F
Jacob
it will be doubled
kelvin
double
Devesh
The difference between vector and scaler quantity
Yakubu Reply
vector has both magnitude & direction but scalar has only magnitude
Manash
my marunong ba dto mag prove ng geometry
ron
how do I find resultant of four forces at a point
Inusah
use the socatoa rule
kingsley
draw force diagram, then work out the direction of force.
Rongfang
In a closed system of forces... Summation of forces in any direction or plane is zero... Resolve if there is a need to then add forces in a particular plane or direction.. Say the x direction... Equate it tk zero
Jacob
define moment of inertia
Manoj Reply
it is the tendency for a body to continue in motion if is or continue to be at rest if it is.
prince
what is Euler s theorem
Manoj Reply
what is thermocouple?
Manoj Reply
joining of two wire of different material forming two junctions. If one is hot and another is cold the it will produce emf...
Badri
joining of two metal of different materials to form a junction in one is hot & another is cold
Manash
define dimensional analysis
Dennis Reply
mathematical derivation?
Hira
explain what Newtonian mechanics is.
Elizabeth Reply
a system of mechanics based of Newton laws motion this is easy difenation of mean...
Arzoodan
what is the meaning of single term,mechanics?
jyotirmayee
mechanics is the science related to the behavior of physical bodies when some external force is applied to them
Lalita
SO ASK What is Newtonian mechanics in physics? Newtonian physics, also calledNewtonian or classical mechanics, is the description of mechanical events—those that involve forces acting on matter—using the laws of motion and gravitation formulated in the late seventeenth century by English physicist
Suleiman
can any one send me the best reference book for physics?
Prema
concept of physics by HC verma, Fundamentals of Physics, university of physics
Bhaskar
tq u.
Prema
these are the best physics books one can fond both theory and applications.
Bhaskar
can any one suggest best book for maths with lot of Tricks?
Vivek
what is the water height in barometer?
SUNEELL
13.5*76 cm. because Mercury is 13.5 times dense than Mercury
LOVE
water is 13.5 times dense than the Mercury
LOVE
plz tell me frnds the best reference book for physics along with the names of authors.
Prema
i recomended the reference book for physics from library University of Dublin or library Trinity college
Arzoodan
A little help here... . 1. Newton's laws of Motion, are they applicable to motions of all speeds? 2.state the speeds which are applicable to Newtons laws of Motion
Derek
mechanics which follows Newtons law
Manash
The definition of axial and polar vector .
Arpita
polar vector which have a starting point or pt. of applications is,force,displacement
jyotirmayee
axial vector represent rotational effect and act along the axis of rotation b
jyotirmayee
prove Newton's first law of motion
prince
Hello frnds what is physics in general?
Ngeh
A block of mass m is attached to a spring with spring constant k and free to slide along a horizontal frictionless surface. At t=0, the block spring system is stretched on amount x>0 from the equilibrium position and is released from rest Vx = 0 What is the period of oscillation of the block? What
Ella
What is the velocity of the block when it first comes back to the equilibrium position?
Ella
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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