# 9.3 Conservation of linear momentum  (Page 7/10)

 Page 7 / 10

## 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.

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?

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 $\stackrel{\to }{F}=d\stackrel{\to }{p}\text{/}dt$ . 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.

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

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.

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

## 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 $1.50\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{5}\phantom{\rule{0.2em}{0ex}}\text{kg}$ and a velocity of $\left(0.30\phantom{\rule{0.2em}{0ex}}\text{m/s}\right)\stackrel{^}{i}$ , and the second having a mass of $1.10\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{5}\phantom{\rule{0.2em}{0ex}}\text{kg}$ and a velocity of $\text{−}\left(0.12\phantom{\rule{0.2em}{0ex}}\text{m/s}\right)\stackrel{^}{i}$ . What is their final velocity?

$\left(0.122\phantom{\rule{0.2em}{0ex}}\text{m/s}\right)\stackrel{^}{i}$

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 $30\text{°}$ with respect to its incoming direction. What is the velocity (magnitude and direction) of puck 1 after the collision?

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.

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. $70.6\phantom{\rule{0.2em}{0ex}}\text{N}·\text{s}$ , toward the bullet; c. $70.6\phantom{\rule{0.2em}{0ex}}\text{N}·\text{s}$ , toward the block; d. magnitude is $2.35\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{4}\phantom{\rule{0.2em}{0ex}}\text{N}$

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?

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

Explain why a cannon recoils when it fires a shell.

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

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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1 mile * 1609m
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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 .
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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.
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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
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Jacob
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kelvin
double
Devesh
The difference between vector and scaler quantity
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ron
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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
it is the tendency for a body to continue in motion if is or continue to be at rest if it is.
prince
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joining of two wire of different material forming two junctions. If one is hot and another is cold the it will produce emf...
joining of two metal of different materials to form a junction in one is hot & another is cold
Manash
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Hira
explain what Newtonian mechanics is.
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Arzoodan
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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
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concept of physics by HC verma, Fundamentals of Physics, university of physics
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SUNEELL
13.5*76 cm. because Mercury is 13.5 times dense than Mercury
LOVE
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LOVE
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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
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Manash
The definition of axial and polar vector .
Arpita
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prove Newton's first law of motion
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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